05_Clustering_Kmeans_DBSCAN_20171107.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Driven Modeling\n",
    "<hr style=\"height:3px;border:none;color:stillblue;background-color:black;\" />\n",
    "### PhD seminar series at Chair for Computer Aided Architectural Design (CAAD), ETH Zurich\n",
    "\n",
    "\n",
    "[Vahid Moosavi](https://vahidmoosavi.com/)\n",
    "<hr style=\"height:1px;border:none;color:stillblue;background-color:black;\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a></a>\n",
    "\n",
    "# Fifth Session \n",
    "<hr style=\"height:1px;border:none;color:stillblue;background-color:steelblue;\" />\n",
    "<span style=\"color:steelblue;font-size: 1em;\"> 07 November 2017</span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Topics to be discussed \n",
    "\n",
    "* **Data Clustering**\n",
    "* **K-Means**\n",
    "* **Limits and Extensions**\n",
    "* **Probabilistinc Clustering**\n",
    "* **Density based clustering** \n",
    "* **Fundamental limits to classical notion of clusters and community detection**\n",
    "* **Clustering as feature learning in comparison to PCA and sparse coding**\n",
    "* **Clustering as space indexing**\n",
    "* **Vector Quantization** \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "pd.__version__\n",
    "import sys\n",
    "from scipy import stats\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Clustering Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZGf1UdJFdugoHyneHWnRwfeQR95jsUFtfl9bWZks/SUevUwpVWidkfN9GAR1Z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\nEFwAgKD8fz8VOfiVSkRsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112af1610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A two dimensional example\n",
    "fig = plt.figure()\n",
    "\n",
    "N = 50\n",
    "d0 = 1.6*np.random.randn(N,2)\n",
    "d0[:,0]= d0[:,0] - 3\n",
    "plt.plot(d0[:,0],d0[:,1],'.b')\n",
    "\n",
    "d1 = 1.6*np.random.randn(N,2)+7.6\n",
    "plt.plot(d1[:,0],d1[:,1],'.b')\n",
    "\n",
    "d2 = 1.6*np.random.randn(N,2)\n",
    "d2[:,0]= d2[:,0] + 5\n",
    "d2[:,1]= d2[:,1] + 1\n",
    "plt.plot(d2[:,0],d2[:,1],'.b')\n",
    "\n",
    "d3 = 1.6*np.random.randn(N,2)\n",
    "d3[:,0]= d3[:,0] - 5\n",
    "d3[:,1]= d3[:,1] + 4\n",
    "plt.plot(d3[:,0],d3[:,1],'.b')\n",
    "\n",
    "\n",
    "d4 = 1.8*np.random.randn(N,2)\n",
    "d4[:,0]= d4[:,0] - 15\n",
    "d4[:,1]= d4[:,1] + 14\n",
    "plt.plot(d4[:,0],d4[:,1],'.b')\n",
    "\n",
    "\n",
    "d5 = 1.8*np.random.randn(N,2)\n",
    "d5[:,0]= d5[:,0] + 25\n",
    "d5[:,1]= d5[:,1] + 14\n",
    "plt.plot(d5[:,0],d5[:,1],'.b')\n",
    "Data1 = np.concatenate((d0,d1,d2,d3,d4,d5))\n",
    "fig.set_size_inches(7,7)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# An important question: \n",
    "# In real scenarios why and where we have these types of clustering problems?\n",
    "* **Custormer Segmentation**\n",
    "* **Product portfolio management**\n",
    "* **Sensor placement**\n",
    "* **Location allocation problems**\n",
    "* **Understanding the (multivariate) results of several experiments**\n",
    "* **What else?**\n",
    "\n",
    "# <a></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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++Xr+eze4mhI/8plFTJYH0LiouOCo0B7U4IoVssPDevhnP9Oi17cpGo8rGo1K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\n+WCSWGu9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ae4350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A two dimensional example\n",
    "fig = plt.figure()\n",
    "plt.plot(d0[:,0],d0[:,1],'.')\n",
    "plt.plot(d1[:,0],d1[:,1],'.')\n",
    "plt.plot(d2[:,0],d2[:,1],'.')\n",
    "plt.plot(d3[:,0],d3[:,1],'.')\n",
    "plt.plot(d4[:,0],d4[:,1],'.')\n",
    "plt.plot(d5[:,0],d5[:,1],'.')\n",
    "\n",
    "\n",
    "\n",
    "mu0= d0.mean(axis=0)[np.newaxis,:]\n",
    "mu1= d1.mean(axis=0)[np.newaxis,:]\n",
    "mu2= d2.mean(axis=0)[np.newaxis,:]\n",
    "mu3= d3.mean(axis=0)[np.newaxis,:]\n",
    "mu4= d4.mean(axis=0)[np.newaxis,:]\n",
    "mu5= d5.mean(axis=0)[np.newaxis,:]\n",
    "mus = np.concatenate((mu0,mu1,mu2,mu3,mu4,mu5),axis=0)\n",
    "\n",
    "plt.plot(mus[:,0],mus[:,1],'ok',markersize=10)\n",
    "\n",
    "fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Means clustering algorithm\n",
    "\n",
    "# Now thechnically the question in data clustering is how to get these center points?\n",
    "\n",
    "\n",
    "# <a></a>\n",
    "## Going back to the problem of regression as \"energy minimization\" (Least Square)\n",
    "##  $$S = \\sum_{i = 1}^n ||y_i - \\hat{y_i}||^2 $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QXACAqBBcAICoEFwAgKgQXACAqBBcAICoEFwAgKgQXACAqBBcAICoEFwAgKgQ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\nAABRIbgAAFH5f4m1vgXi76XqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112bc9890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 50\n",
    "x1= np.random.normal(loc=0,scale=1,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=5,size=N)[:,np.newaxis]\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.7, size=N)[:,np.newaxis]\n",
    "# y = 2*x1\n",
    "# y = x1*x1 + np.random.normal(loc=.0, scale=0.6, size=N)[:,np.newaxis]\n",
    "# y = 2*x1*x1\n",
    "\n",
    "fig = plt.figure(figsize=(7,7))\n",
    "ax1= plt.subplot(111)\n",
    "plt.plot(x1,y,'or',markersize=10,alpha=.4 );"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_regressor(a,b):\n",
    "    # y_ = ax+b\n",
    "    mn = np.min(x1)\n",
    "    mx = np.max(x1)\n",
    "    xrng =  np.linspace(mn,mx,num=500)\n",
    "    y_ = [a*x + b for x in xrng]\n",
    "    \n",
    "    \n",
    "    fig = plt.figure(figsize=(7,7))\n",
    "    ax1= plt.subplot(111)\n",
    "    plt.plot(x1,y,'or',markersize=10,alpha=.4 );\n",
    "    plt.xlabel('x1');\n",
    "    plt.ylabel('y');\n",
    "    plt.plot(xrng,y_,'-b',linewidth=1)\n",
    "#     plt.xlim(mn-1,mx+1)\n",
    "#     plt.ylim(np.min(y)+1,np.max(y)-1)\n",
    "    \n",
    "    yy = [a*x + b for x in x1]\n",
    "    \n",
    "    [plt.plot([x1[i],x1[i]],[yy[i],y[i]],'-r',linewidth=1) for i in range(len(x1))];\n",
    "#     print 'average squared error is {}'.format(np.mean((yy-y)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4f027fe0ca6b4cf298064ce3ace319dc",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description=u'a', max=6.0, min=-3.0, step=0.2), FloatSlider(value=1.0, description=u'b', max=5.0, min=-2.0, step=0.2), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "interact(linear_regressor,a=(-3,6,.2),b=(-2,5,.2));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now look at this objective function\n",
    "<img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/debd28209802c22a6e6a1d74d099f728e6bd17a4\" width =300, height=300/>\n",
    "\n",
    "### we have $K$ centers, $\\mu_i$ that create $k$ sets $S_i$ and each data point $x_i$ belongs only to one of these sets.\n",
    "\n",
    "## In plain word, this means we need to find K vectors (n dimensional points) where, these objective function is minimum.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.spatial.distance as DIST\n",
    "def Assign_Sets(mus,X):\n",
    "    Dists = DIST.cdist(X,mus)\n",
    "    ind_sets = np.argmin(Dists,axis=1)\n",
    "    min_dists = np.min(Dists,axis=1)\n",
    "    energy = np.sum(min_dists**2)\n",
    "    return ind_sets, energy\n",
    "\n",
    "\n",
    "def update_mus(ind_sets,X,K):\n",
    "    \n",
    "    n_mus = np.zeros((K,X.shape[1]))\n",
    "    for k in range(K):\n",
    "        ind = ind_sets==k\n",
    "        DD = X[ind]\n",
    "        if DD.shape[0]>0:\n",
    "            n_mus[k,:]=np.mean(DD,axis=0)\n",
    "        else: \n",
    "            continue\n",
    "            \n",
    "    \n",
    "    return n_mus\n",
    "\n",
    "def Visualize_assigned_sets(mu00=None,mu01=None,mu10=None,mu11=None,mu20=None,mu21=None):\n",
    "    mus0 = np.asarray([mu00,mu10,mu20])[:,np.newaxis]\n",
    "    mus1 = np.asarray([mu01,mu11,mu21])[:,np.newaxis]\n",
    "    mus = np.concatenate((mus0,mus1),axis=1)\n",
    "    ind_sets,energy = Assign_Sets(mus,X)\n",
    "    \n",
    "    fig = plt.figure(figsize=(7,7))\n",
    "    ax1= plt.subplot(111)\n",
    "    \n",
    "    for k,mu in enumerate(mus):\n",
    "        ind = ind_sets==k\n",
    "        DD = X[ind]\n",
    "        plt.plot(DD[:,0],DD[:,1],'.',markersize=10,alpha=.4 );\n",
    "        plt.plot(mu[0],mu[1],'ob',markersize=10,alpha=.4 );\n",
    "        \n",
    "        [plt.plot([DD[i,0],mu[0]],[DD[i,1],mu[1]],'-k',linewidth=.1) for i in range(len(DD))];\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "72d6d581dd8b4c7fa06c3cce570dfad2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=4.738554350299665, description=u'mu00', max=28.104375025138378, min=-18.261445649700335, step=1.0), FloatSlider(value=7.03023608551316, description=u'mu01', max=18.42571156027367, min=-3.9697639144868404, step=1.0), FloatSlider(value=4.738554350299665, description=u'mu10', max=28.104375025138378, min=-18.261445649700335, step=1.0), FloatSlider(value=7.03023608551316, description=u'mu11', max=18.42571156027367, min=-3.9697639144868404, step=1.0), FloatSlider(value=4.738554350299665, description=u'mu20', max=28.104375025138378, min=-18.261445649700335, step=1.0), FloatSlider(value=7.03023608551316, description=u'mu21', max=18.42571156027367, min=-3.9697639144868404, step=1.0), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = Data1.copy()\n",
    "mn = np.min(X,axis=0)\n",
    "mx = np.max(X,axis=0)\n",
    "R = mx-mn\n",
    "\n",
    "# Assume K = 3\n",
    "\n",
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "interact(Visualize_assigned_sets,mu00=(mn[0],mx[0],1),mu01=(mn[1],mx[1],1),\n",
    "                        mu10=(mn[0],mx[0],1),mu11=(mn[1],mx[1],1),\n",
    "                        mu20=(mn[0],mx[0],1),mu21=(mn[1],mx[1],1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Although it looks simple, this is a hard problem and there is no exact solution for it.\n",
    "## In order to solve this we need to use heuristic methods. For example the following steps:\n",
    "    * initiate K random centers and assign each data point to its closest center. \n",
    "    * Now we have K sets. Within each sets, update the location of the center to minimize the above objective function.\n",
    "    * Due to the structure of these objective function, the mean vector of each set gives the minimum value. \n",
    "    * Therefore, simply update the locations of center points to the mean vector of each set. \n",
    "    * repeat the above steps, until the difference between two sequential centers are less than a threshhold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h6sliPIftiUhiaeianfW5fzT0Wuq6Gx5jTBZeMvqktfbFys3fGWP2sdZ+Wzkkd2Pl9vVA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x112f5ccd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K =5\n",
    "mus_t = np.zeros((K,X.shape[1])) \n",
    "mus_0 = np.zeros((K,X.shape[1])) \n",
    "fig = plt.figure(figsize=(16,7));\n",
    "thresh = .01\n",
    "mus_0[:,0] = mn[0] + np.random.random(size=K)*R[0]\n",
    "mus_0[:,1] = mn[1] + np.random.random(size=K)*R[1]\n",
    "mus_t = mus_0.copy() \n",
    "diff = 1000\n",
    "plt.subplot(1,2,1);\n",
    "plt.plot(X[:,0],X[:,1],'.');\n",
    "[plt.plot(mus_t[i,0],mus_t[i,1],'or',markersize=15,linewidth=.1,label='initial') for i in range(K)];\n",
    "all_diffs =  []\n",
    "all_energies = []\n",
    "while diff> thresh:\n",
    "    ind_sets, energy = Assign_Sets(mus_t,X)\n",
    "    all_energies.append(energy)\n",
    "    mus_tp = update_mus(ind_sets,X,K)\n",
    "    diff = np.abs(mus_t- mus_tp).sum(axis=1).sum().copy()\n",
    "    [plt.plot([mus_t[i,0],mus_tp[i,0]],[mus_t[i,1],mus_tp[i,1]],'-og',markersize=5,linewidth=.8) for i in range(K)];\n",
    "\n",
    "    all_diffs.append(diff)\n",
    "#         print diff\n",
    "    mus_t= mus_tp.copy()\n",
    "[plt.plot(mus_tp[i,0],mus_tp[i,1],'ob',markersize=15,linewidth=.1,label='final') for i in range(K)];\n",
    "\n",
    "# # plt.legend(bbox_to_anchor=(1.1,1.));\n",
    "# plt.xlabel('x');\n",
    "# plt.ylabel('y');\n",
    "# plt.subplot(3,1,2);\n",
    "# plt.plot(all_diffs);\n",
    "# plt.ylabel('average abs difference between two results');\n",
    "# plt.xlabel('iterations');\n",
    "\n",
    "\n",
    "plt.subplot(1,2,2);\n",
    "plt.plot(all_energies,'-.r');\n",
    "plt.ylabel('energy level');\n",
    "plt.xlabel('iterations');\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def K_means(X,K):\n",
    "    mus_t = np.zeros((K,X.shape[1])) \n",
    "    mus_0 = np.zeros((K,X.shape[1])) \n",
    "    thresh = .01\n",
    "    mus_0[:,0] = mn[0] + np.random.random(size=K)*R[0]\n",
    "    mus_0[:,1] = mn[1] + np.random.random(size=K)*R[1]\n",
    "    mus_t = mus_0.copy() \n",
    "    diff = 1000\n",
    "    all_diffs =  []\n",
    "    all_energies = []\n",
    "    while diff> thresh:\n",
    "        ind_sets, energy = Assign_Sets(mus_t,X)\n",
    "        all_energies.append(energy)\n",
    "        mus_tp = update_mus(ind_sets,X,K)\n",
    "        diff = np.abs(mus_t- mus_tp).sum(axis=1).sum().copy()\n",
    "\n",
    "        all_diffs.append(diff)\n",
    "\n",
    "        mus_t= mus_tp.copy()\n",
    "    return mus_t,all_diffs,all_energies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The effect of the chosen K "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "K =5\n",
    "\n",
    "def visualize_Kmeans(K=5):\n",
    "    centers, diffs, energies = K_means(X,K) \n",
    "    ind_sets,energy = Assign_Sets(centers,X)\n",
    "    fig = plt.figure()\n",
    "    for k in range(K):\n",
    "#         print \n",
    "        ind = ind_sets==k\n",
    "        DD = X[ind]\n",
    "        plt.plot(DD[:,0],DD[:,1],'o',alpha=0.5, markersize=4,color=plt.cm.RdYlBu_r(float(k)/K));\n",
    "        plt.plot(centers[k,0],centers[k,1],marker='o',markersize=15,alpha=1.,color=plt.cm.RdYlBu_r(float(k)/K));\n",
    "    fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "76aae22f2f304e8384f18904829fe3a3",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=5, description=u'K', max=10, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data1\n",
    "interact(visualize_Kmeans,K=(1,10,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assumptions and Extensions to K-Means \n",
    "* **How to select K in advance (metaparameter issue)**\n",
    "    * **e.g. Elbow method** \n",
    "* **Similarity measures**\n",
    "* **Shape of the clusters**\n",
    "* **fuzzy k-means**\n",
    "* **Hierarchical Clustering**\n",
    "* ** Pribabilistic Clustering a.k.a Mixture Models**\n",
    "* **Sensitivity to outliers** \n",
    "* **Density based algorithms such as DBSCAN**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic Clustering\n",
    "## With different densities and shapes\n",
    "### Gaussian Mixture Models\n",
    "\n",
    "* **Gaussian Mixture Model**: To learn the distribution of the data as a weighted sum of several globally defined Gaussian Distributions:\n",
    "##  $$g(X) = \\sum_{i = 1}^k p_i. g(X,\\theta_i)$$\n",
    "### $ g(X,\\theta_i)$ is a parametric known distribution (e.g. Gaussian) and $p_i$ is the share of each  of them. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def GMM_cluster(K=5):\n",
    "    from matplotlib.colors import LogNorm\n",
    "    import sklearn.mixture as mixture\n",
    "    gmm = mixture.GaussianMixture(n_components=K, random_state=0,covariance_type='full')\n",
    "    gmm.fit(X)\n",
    "    Clusters = gmm.predict(X)\n",
    "    fig = plt.figure()\n",
    "    for k in range(K):\n",
    "        ind = Clusters==k\n",
    "        DD = X[ind]\n",
    "        plt.plot(DD[:,0],DD[:,1],'o',alpha=1., markersize=4,color=plt.cm.RdYlBu_r(float(k)/K));\n",
    "        plt.plot(gmm.means_[k,0],gmm.means_[k,1],marker='o',markersize=10,alpha=1.,color=plt.cm.RdYlBu_r(float(k)/K));\n",
    "#     plt.plot(centers[:,0],centers[:,1],'or',alpha=1., markersize=15);\n",
    "    fig.set_size_inches(7,7)\n",
    "    \n",
    "\n",
    "    x = np.linspace(X[:,0].min()-2,X[:,0].max()+2,num=200)\n",
    "    y = np.linspace(X[:,1].min()-2,X[:,1].max()+2,num=200)\n",
    "    X_, Y_ = np.meshgrid(x, y)\n",
    "    XX = np.array([X_.ravel(), Y_.ravel()]).T\n",
    "    Z = gmm.score_samples(XX)\n",
    "    Z = -1*Z.reshape(X_.shape)\n",
    "\n",
    "    # plt.imshow(Z[::-1], cmap=plt.cm.gist_earth_r,)\n",
    "    # plt.contour(Z[::-1])\n",
    "    CS = plt.contour(X_, Y_, Z, norm=LogNorm(vmin=1.0, vmax=1000.0),\n",
    "                     levels=np.logspace(0, 3, 10),cmap=plt.cm.RdYlBu_r);\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "183c27459d124a3abf71e4647e9b3048",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=5, description=u'K', max=10, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data1\n",
    "pttoptdist = DIST.cdist(X,X)\n",
    "interact(GMM_cluster,K=(1,10,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assumptions and Limits to K-Means \n",
    "\n",
    "### K-means is known to be sensitive to outliers\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Topology Based Clustering algorithms \n",
    "# DBSCAN\n",
    "#### Density-based spatial clustering of applications with noise \n",
    "\n",
    "![](https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/DBSCAN-Illustration.svg/800px-DBSCAN-Illustration.svg.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def DBSCAN_1(eps=.5, MinPts=10):\n",
    "    Clusters = np.zeros((X.shape[0],1))\n",
    "    C = 1\n",
    "    processed = np.zeros((X.shape[0],1))\n",
    "    for i in range(X.shape[0]):\n",
    "        if processed[i]==0:\n",
    "#             pttoptdist = DIST.cdist(X,X)\n",
    "            inds_neigh = pttoptdist[i]<=eps\n",
    "            pointers = inds_neigh*range(X.shape[0])\n",
    "            pointers = np.unique(pointers)[1:]\n",
    "            \n",
    "            if pointers.shape[0]>= MinPts:\n",
    "                processed[i]==1\n",
    "                Clusters[i]=C\n",
    "                #it is a core point and not processed/clustered yet\n",
    "                # A new cluster\n",
    "                #Find other members of this cluster\n",
    "                counter = 0\n",
    "                while (counter < pointers.shape[0]):\n",
    "                    ind = pointers[counter]\n",
    "#                     print i,pointers.shape\n",
    "                    if processed[ind]==0:\n",
    "                        processed[ind] = 1\n",
    "                        inds_neigh_C = pttoptdist[ind]<= eps\n",
    "                        pointers_ = inds_neigh_C*range(X.shape[0])\n",
    "                        pointers_ = np.unique(pointers_)[1:]\n",
    "                        if pointers_.shape[0]>= MinPts:\n",
    "                            pointers = np.concatenate((pointers,pointers_))\n",
    "                    if Clusters[ind] == 0:\n",
    "                        Clusters[ind] = C\n",
    "                    counter = counter +1\n",
    "                        \n",
    "                C = C + 1\n",
    "                \n",
    "            else:\n",
    "                # for now it is noise, but it might be connected later as non-core point\n",
    "                Clusters[i]=0\n",
    "                \n",
    "        else:\n",
    "            continue\n",
    "        \n",
    "        \n",
    "    fig = plt.figure(figsize=(7,7))\n",
    "    ax1= plt.subplot(111)\n",
    "    K =np.unique(Clusters).shape[0]-1\n",
    "    for i,k in enumerate(np.unique(Clusters)[:]):\n",
    "        ind = Clusters==k\n",
    "        DD = X[ind[:,0]]\n",
    "        \n",
    "        #cluster noise\n",
    "        if k==0:\n",
    "            plt.plot(DD[:,0],DD[:,1],'.k',markersize=5,alpha=1 );\n",
    "        else:\n",
    "            plt.plot(DD[:,0],DD[:,1],'o',markersize=10,alpha=.4,color=plt.cm.RdYlBu_r(float(i)/K) );\n",
    "     \n",
    "        \n",
    "#     return Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "dbec91d32bfa410c8473dc4bfc75353a",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description=u'eps', max=3.0, min=0.05), IntSlider(value=10, description=u'MinPts', max=20, min=4), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data1\n",
    "pttoptdist = DIST.cdist(X,X)\n",
    "interact(DBSCAN_1,eps=(.05,3,.1),MinPts=(4,20,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assumptions and Limits to K-Means \n",
    "### shape of the clusters : K-Means classically, find spherical clusters\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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L8PHHLevqyhWUs5IS1nZ1tcjp07gSh4f5v9xc3ImauFIDmrjSEPEjJnJyaNm0dSuduD/1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8AB4Gtfk2KMzWCtwvU9AN9TSp0HEAHw0mJhQmHt2A+fNBgvrLaW+0WU4qbl7GxuWDZFG4uJnoiZ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\n5eEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112d6b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dlen = 700\n",
    "tetha = np.random.uniform(low=0,high=2*np.pi,size=dlen)[:,np.newaxis]\n",
    "X1 = 3*np.cos(tetha)+ .22*np.random.rand(dlen,1)\n",
    "Y1 = 3*np.sin(tetha)+ .22*np.random.rand(dlen,1)\n",
    "D1 = np.concatenate((X1,Y1),axis=1)\n",
    "\n",
    "X2 = 1*np.cos(tetha)+ .22*np.random.rand(dlen,1)\n",
    "Y2 = 1*np.sin(tetha)+ .22*np.random.rand(dlen,1)\n",
    "D2 = np.concatenate((X2,Y2),axis=1)\n",
    "\n",
    "X3 = 5*np.cos(tetha)+ .22*np.random.rand(dlen,1)\n",
    "Y3 = 5*np.sin(tetha)+ .22*np.random.rand(dlen,1)\n",
    "D3 = np.concatenate((X3,Y3),axis=1)\n",
    "\n",
    "X4 = 8*np.cos(tetha)+ .22*np.random.rand(dlen,1)\n",
    "Y4 = 8*np.sin(tetha)+ .22*np.random.rand(dlen,1)\n",
    "D4 = np.concatenate((X4,Y4),axis=1)\n",
    "\n",
    "\n",
    "\n",
    "Data3 = np.concatenate((D1,D2,D3,D4),axis=0)\n",
    "\n",
    "fig = plt.figure()\n",
    "plt.plot(Data3[:,0],Data3[:,1],'ob',alpha=0.2, markersize=4)\n",
    "fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5a5b67a0977d4f5691dffe24fc0e44b5",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=5, description=u'K', max=10, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data3\n",
    "interact(visualize_Kmeans,K=(1,10,1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3c0c1d785ae2447ba8f5a235acab6ecd",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description=u'eps', max=2.0, min=0.1), IntSlider(value=10, description=u'MinPts', max=20, min=4), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data3\n",
    "pttoptdist = DIST.cdist(X,X)\n",
    "interact(DBSCAN_1,eps=(.1,2,.1),MinPts=(4,20,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# However, since DBSCAN has it own limit: It assumes a global ratio for density"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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X3aPt7qYmx5flivzJn5S2JHZnYV+5J6WA/fuBd74T+I3fkO21jtZ0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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ccae210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A two dimensional example\n",
    "fig = plt.figure()\n",
    "\n",
    "N = 200\n",
    "d0 = .5*np.random.randn(N,2) + [[3,2]]\n",
    "d0 = .5*np.random.multivariate_normal([3,2],[[.8,.6],[.71,.7]],N)\n",
    "plt.plot(d0[:,0],d0[:,1],'.b')\n",
    "\n",
    "\n",
    "d1 = .6*np.random.randn(1*N,2)\n",
    "plt.plot(d1[:,0],d1[:,1],'.b')\n",
    "\n",
    "d2 = .5*np.random.randn(2*N,2)+[[-3,2]]\n",
    "\n",
    "plt.plot(d2[:,0],d2[:,1],'.b')\n",
    "\n",
    "# d3 = 1.6*np.random.randn(N,2)\n",
    "# d3[:,0]= d3[:,0] - 5\n",
    "# d3[:,1]= d3[:,1] + 4\n",
    "# plt.plot(d3[:,0],d3[:,1],'.b')\n",
    "\n",
    "\n",
    "Data2 = np.concatenate((d0,d1,d2))\n",
    "fig.set_size_inches(7,7)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7930b1e638d64311a1bccc2438823c78",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description=u'eps', max=0.9, min=0.05, step=0.05), IntSlider(value=10, description=u'MinPts', max=20, min=4), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data2\n",
    "pttoptdist = DIST.cdist(X,X)\n",
    "interact(DBSCAN_1,eps=(.05,0.9,.05),MinPts=(4,20,1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e4c0774688784bd3a6c296f5124a15ba",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description=u'K', max=3, min=1), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data2\n",
    "interact(visualize_Kmeans,K=(1,3,1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# More than that, topological algorithms like DBSCAN have fundamental limits:\n",
    "## They are usually developed based on synthetic data sets, which usually never happens in reality\n",
    "## Further, they believe in some kind of underlying true groups!!! Or some kind of idealized set up such as having perfect communities!!!\n",
    "# <a></a>\n",
    "# More Important: They have NO data Abstraction and NO Generalization\n",
    "\n",
    "# Attention to these issues can be a turining point in the notion of clustering\n",
    "\n",
    "# <a></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# <a></a>\n",
    "# <a></a>\n",
    "\n",
    "# A different use of K-Means and its abstraction\n",
    "\n",
    "## Clustering as Feature Transformation and Dictionary Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# If we look at K-means ojective function\n",
    "![](https://wikimedia.org/api/rest_v1/media/math/render/svg/debd28209802c22a6e6a1d74d099f728e6bd17a4)\n",
    "\n",
    "## In comparison to Sparse Coding (SC) objective function\n",
    "![](http://ufldl.stanford.edu/wiki/images/math/f/1/1/f110901ddedcba59e339de5f16c547da.png)\n",
    "\n",
    "\n",
    "### Or to PCA\n",
    "\n",
    "## $$ x  = yP $$\n",
    "\n",
    "### Or to GMM\n",
    "##  $$g(X) = \\sum_{i = 1}^k p_i. g(X,\\theta_i)$$\n",
    "\n",
    "# We can think of cluster centers as new \"fictional\" dimensions.\n",
    "## Then, similar to PCA the identified cluster centers can be used as new latent space for the data points. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SweKfTxtDDSJTUSQse0YSwG9P24cBWu+7b3jcXAI0lv2SS38Abm0yOkb8LjwTGDWROl69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\n5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1198b06d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# A two dimensional example\n",
    "fig = plt.figure()\n",
    "\n",
    "N = 400\n",
    "d0 = .5*np.random.randn(N,2) + [[3,2]]\n",
    "d0 = .5*np.random.multivariate_normal([3,2],[[.8,.6],[.71,.7]],N)\n",
    "# plt.plot(d0[:,0],d0[:,1],'.b')\n",
    "\n",
    "\n",
    "# d1 = .6*np.random.randn(1*N,2)\n",
    "d1 = .5*np.random.multivariate_normal([3,2],[[1.3,.6],[.71,.7]],N)\n",
    "# plt.plot(d1[:,0],d1[:,1],'.b')\n",
    "\n",
    "# d2 = .5*np.random.randn(2*N,2)+[[-1,2]]\n",
    "d2 = .5*np.random.multivariate_normal([12,9],[[1.2,.6],[-.71,.7]],N)\n",
    "\n",
    "\n",
    "# d3 = 1.6*np.random.randn(N,2)\n",
    "# d3[:,0]= d3[:,0] - 5\n",
    "# d3[:,1]= d3[:,1] + 4\n",
    "# plt.plot(d3[:,0],d3[:,1],'.b')\n",
    "\n",
    "\n",
    "\n",
    "Data = np.concatenate((d1,d2))\n",
    "plt.plot(Data[:,0],Data[:,1],'.')\n",
    "fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112b420d0>]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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K7c39zAQ0tnZg9EVDUD1pFNbtPoq3DpzyFC0/uO0qfGHyGDz5xvtxtgUAdfOp\nNGEwOldOEQwIzK4sT/gzpjug1y2lyWm7PCIVwaJvGwwC995LBdzJapOSvQePUGEKlKSiSQhxO4AT\nUsomIUR1gu0Ka3YTk1HSaZVPtI/ba27DencfOQMB4K6ogPlN40G0HD6DP7x7Avd/7lPYfvDDhKJl\n+vhSfPrSEXj9neOQsEakSCkhhLClCXVumjTKVy1TMssEv6QrwJgsJBXBom8biQBPPgmsXElO3n15\nj0x5PzFMjuEn0vRZAF8WQtwGYAiAi4QQ/yml/H/0jfJ+dhOT8+gRqNKhxejs6sHsynJXTyRTSizb\n/AEWzZoSEy1qGzdbAN0aQQmd0qHFWPTKHvSGTQQCBiKmGeu4+8O7J/Ds1vZYgblOf6TSCs34Mq9J\nRbCobc+fpwI9Ken+d75Dr5eUuEeqkr0Hd9IxBUpS0SSlnA9gPgBEI03/4BRMDJMrKLGgREkwYOAr\n08sxu7IcMyeWwYhGhwDANCV2HzmDS0ZcgH3HzmLRK3s8O/x0QQJQOmzSmGE2kfajNS2x84iYEgte\n2h3X2af27Y9UWiEZX+Y1iQSLsw5JbVtXByxfTuaUpmm5end3u0eq/Igi7qRjChD2aWIKDtvcurCJ\nVVvbsbo5hGfun4lFs6ZQHZIpEQwIvNAUQjhiwogaW0rYhYxuCfDQTZfbokTBgIHqKy/GyGElOHL6\nXFzBeMSUqG8OJU0jciqNicNNsHjVIal/c+YACxcCr7/ubxQKiyLGD+l4fuUwKYkmKWUDgIZ+OROG\nGSCUKDnfS7kyXQg9dNPlmDRmGLa0duDI6XNYta0dpiTzS2VToISMWxrNKchUgXjQoP16NX8oCeCF\nphCmjBtuq1viVBqTFg0NFDkyTfcIUlUViaZNm+h1wwCeeKIgFjqmnyjALkqONDEFx/TxpVhw+2T8\n6KXdsbEoAYPcw1XNkooaPb/jEHoiFGGCEJgy7iLcfW0Fpo8vjZsLV98cggA5iPeqfaKETeAb15bj\nkhEX4O1Dp2OF4+EIddip2XfKSJNTaUxC3L7dl5WRYALotswlQsm1SEwmKcAuShZNTEHS2dUDGU1R\nCNDgXreapa/OuBTPbm2HBKXT3g6dwd5j5DKup9EChpXKCwYMfOHqUXGjVk6d7Y7VTr353kn0Rv2i\nwlHhFjYlfuRR58QwMby+3Xd0UPTINOm2w8MkltNujBepptoKsIsyFUdwhslZnG7YunN2SZGBkcNK\nXF3JJ48bjoDDPrwnbGJ1tBbpmftn4uvXVeCqsRchHKH9IxETn750BL7ucA1//Z3j+OayLQCAZ+6f\nie9/cRIWzZpiO37ElFjdHOoj4HxOAAAgAElEQVTPXwWT63g5eldXUzdcIEC3BbCAMRlEifEf/Yhu\n/Ti9q8jlj39cEKk5gCNNTAHg1cLv7Hhb3RyyFV83tXVi0St7EDElhLBqZwG7m3d9c8g2A08v3tZf\nc9ZOqWjSxn0nbHPv2K+DSYjXt3tOvTF9Id1UW4FFLlk0MXmPVwu/s27IWXytapbUfDtD0Iy6Is3N\n2zn8d+olw3H3tRWx4zxz/0ysbg7h+R2HEDGlazfc39x4Gd7YdwK9EWk7NsO4kkgc9XUBy3QnVIF1\nVuU0BZhqSwcWTUze46w9OnL6HJraOuPqhnQRpQb7Bg0REztu7twzJ5YhaAj0ROexvHP0Iyx8eTd6\nI1Zh9//5q6m4q7Lcsxtu+vhSrKqp4m45xj9+xFGqgiXTnVAF2FmV03Ck0hcsmpi8R6Xi6ptDeKEp\nhFXb2lEf9WVyEyhOr6W7r7vU5hzuPLZeLB7WuubCDgPLRGKIu+XynIGOuOiCJRAA5s4ln6ZE753p\nTqgC7KzKeQos1ZYOXAjOFATTx5fikhEXxIq19WJvJ3o6LxwxcejDLgAkpv7xxRb88MWWWEE5QHPr\nSoqoqLwoWlyuMKX0fB+mQEinwDbV4y9ebD+uU7A8+WTy91bpmUDAOz3j9l59OR7D5BgcaWIKBr9O\n22o7JZw2v3cKW1s7qJA7moZ7YcchrKqpcjWj3HfsLLmKS4lidvRm+jPi4pUCc5s5l+y9k6VnUk23\ncbqHyUNYNDEFg1+nbbXdkvX7sfm9UzGxpHe19USkbSacnl6bPr405ipeOrQ4Fmni9FuB0p8Ftl6C\nTJ85t2IFzZzz896J0jPpiD/1urJFcBNiLKqYHIJFE1NQ+K0dmj6+FPNuuRLbD34YKyCPSGkzqywd\nWhy7r8+g09/DzerAiXNfJs/oz4hLIkGmz5zLxHunI/4SRae4UJzJQVg0MYwHzsjU6uYQntnaDoDs\nBzq7egB4+0B5WR3oNLV14p6ntsRShqsemBk3CJiFVB6QboFtskhMIkGm7zt/fjpn7f+9vEgUneJC\ncSYHYdHEFCRKlJQOLY6zEdBxRqbqHQaYgLcPlJ8aqtXNIfSEKXylnMYBfxEqJs/xG4lxE2T9FcVJ\nVfyp6JQaEKzPw2NfICYHYdHEFBx6ZMiUNHuupCi5OPGqifISR35qqJzu3xLeIowpMPoSiUm270DV\nElVVAUuWAA89ROcybx4wdaq97oprmpgcgkUTU3DoogQgodLT60+cuNVEJRJH6r5XMfjsynK8sONQ\nnBu4ny4/Js/pSyQm0b4DXUvU0UHde6YZL+DYF4jJMVg0MQWHigypmXAAYMJe2J0qXgXmXvVO+n5u\nbuB+uvyYPMdvvVKqtU4DXUvEabj8pEA7H1k0MQWHm6WAXtidSfyk2ryiVyyWGN/1SoC1gKn7ZR4R\nynRFTLqLJKfh8o/aWkq5miZQUlJQnY8smpiCxGkp0F9pML+GmgzjG2ekqK4OWLmS7geDlAoLh2lB\nMwz7oqaEzyOPALt2AbNnD8xcOk7D9R+DMaLn4YfpGgOoyL+AOh9ZNDEFi1+zSzf8WgL05T2YAiCd\nobrt7ZY4EgI4dswSUWbUSExGE896HRFAwqe72xJUmzZZhdmJYHuA7GQwvK4aGug6UBhGainXHE/r\nsWhiCpp00mDJ6pQy8R5MAZDqgqdvLwT9M01g3Tqa7wa4R5oCARJadXW0rxJWpkljVurqki9eunWA\nEN6pP2ZgGQwxW11N0cvubrq2nnjC/3vmgaEpD+xlmBRxq1NiBgchxF8KIfYJIQ4IIX7g8vq3hRAn\nhRC7ov/uH4zzjKOxEVi4kBYefcFLhL5AqqiSaZJAmjsX+PGPgY0babuf/ISG9NbUkMh56ikapxII\nkJBSSEnPJxvAq6wDAgF6z3nz3PdJZaAv03cGYyiyqlH7yU+AN96ga8wvbiIvx+BIE8OkCNcpZQdC\niACApQC+ACAEYLsQ4mUp5TuOTZ+TUj484Cfohfq2rafJ/Cx4egF3IEBiSM2UmzPH/o1d3V+8mLZR\n6ZQHHgAqKoBt24CXXrKiUn58nDo6LKHm5f2U41GEnGOwiuzTrVHLg05KFk0MkyLp1CnxWJR+4ToA\nB6SUrQAghPgvALMAOEVTdqG+bSvBdMstFHXyM/xWXyDVsdT9xYvjF07nIqXEVW0t8LvfkZjy6+OU\nbMHjuqfBIZeK7L1EXg7VObFoYpg0SKVOKdUaKMY3lwA4pD0OAbjeZbvZQogbAOwH8HdSykMu2wwc\nTvHhRzAp9LltaqacLnICAUrVKXHktkg1NlJ6LRIh0bZkiT8fp2RRjTyIImScHBIDA4ZT5OVYhJJF\nE8P0MzwWZVBZC2CVlLJbCPEggJUA/sK5kRCiBkANAFRUVPTvGfUlpeK2wDhrnX79a2D5crvY0d+j\nro4KwFX3XYejJi+R+EkU1WA/JjvZIgayXbjlWISSRRPD9DNcA9VvHAZwqfa4PPpcDCmlrgiWAfiZ\n24GklLUAagFgxowZzpGAmSfdlIrbAqNEzrlz1nbKv8nNGHP5csuSIBi0RJG+uKYrfnIpVdTfZIMY\ncAq3JUtIJKcjoPpLfOVYhJJFE8P0M+zV1G9sB3CFEOJTILH0dQDf0DcQQoyVUh6NPvwygL0De4oZ\nxq31X0V47rsP2Kv9eMeOxe/v9NiZOJHEVUsLpez0qMj8+f390+Q32SAGdOHW3U0u3lKmHvnqz6hZ\njkUoWTQxzADAXk2ZR0oZFkI8DOD3AAIAlksp9wghFgHYIaV8GcD3hBBfBhAG8CGAbw/aCXuRyjd4\n1fr/8MO0EM6bZ5lT3nijXTSNGRN/fF10mSZtv3cv1UJ5DdVl0iMbxIAu3AzDsqpI9TPu76hZDkUo\nWTQxDJOzSClfBfCq47kF2v35ALI3ZJLON/iODmvx00dYzJlDnkt6p5xbkfgjjwCrVwMHDljHNE3L\nxkCPiqTjWJ4jEYMBIRvEwLe+RbfTptmjianMHGxvtwxVA4GsT6H1JyyaGIZhBot0vsGXldldvZU7\nd1WVZW6pFjVloGmaVpE4QIufTnEx8KtfWfUuAPCd75AIU15QqTiW50AXVN7j/DzmzEk98uX0FFPC\nqYBJKpqEEEMAvAmgJLr9C1LKf+7vE2MYhsl70ql76eigVIvyeaqvt1J0aiGsqyPB09trCSwdKWnf\nGTOAceMolaeOoRZK1WEH+BN02VD4zFh4NQ2kcwx9pqGbGWoB4SfS1A3gL6SUHwshigBsFkKsk1Ju\n6edzYxiGyW/SqXvRZ3+ZJrB+PQ3e3bCBXncKHh0hLMFUUkLF49/7Hi2MK1ZYkaqeHmt/Z8ou0XkN\nduEzY+H8PMrK/HfSqTRrWZm9Bs6ve30ek1Q0SSklgI+jD4ui//q/JZdhsgB28mb6nVTrXpTQWriQ\nBJNe2AvYBY+Och+fPdtaLOvqaEEE6LaujmpfhKDtDQOorCRx5bdIvb4euOYa63wKNCIx6DgFud9O\nOi+bgrIyd5HlVseWx7VtvmqaojOemgBcDmCplHKryzYDZw7HMAMAO3kzWUtVFYmmTZusIu/2duCi\niyzBEwwCt90GrFtn1SU53cfr6uzHPXaMioX1+pWmJrIkUOk7L5TTeHc38NprVjSLa5sGD6cgd+uk\nO3+ePrclS2gbvQ6up4eEkpf9hFsdG5DXtW1G8k0AKWVESnkNyDzuOiHEFJdtaqWUM6SUMy6++OJM\nnyfD2Ghq68TSjQfQ1NbZb+/h5uTNMFmDiiQ88ACJm9pa4Gc/o8VQCBJMjz1GKbcf/9h98ZozhxY2\nlYIbM8aqYTFNa9ivn4n0zvoXZwSMGVz06+VLXyLhBFC0ads2sqyorrail35ScW51U27P5REpdc9J\nKU8LITYC+EsAu/vnlBgmMQMVAWInb2bASTWtUVVF0SI9JSclLVgvvQT8/vdWBMFrf7XQqcVx5Uo6\nXjBoCSfdOdwLpwcU179kJ+rzddLba388YwalZhPhVccWCFg2Fnn2+fvpnrsYQG9UMF0A4AsAftrv\nZ8YwHgzULDd28mYGlHRa9p1jUQCr2FtKq3ZFLWBPPAHU1NiP4UzhqDqYsjLydALca6Sc6DU0XvUv\nzOCizx00DLomlEO8fh+gtGxTE4kslXZzCnqvgdDKliAP7Qn8RJrGAlgZrWsyAPxWSvlK/54Ww3gz\nkBEgdvJmBgy/Lft6NEofiyIEMGsWpdiWL6fnDYMiRcrt+6GHqDYJsOqZ5syxv48SUYsX0zFU5MpP\nm3k2mDky8TQ20ue9bJklgIuKyJtr3TrgyBHg7Fm7o7y6rtQcQxWhcgp652fe0GBdc172BDlcKO6n\ne+6PAKYNwLkwjC84AsTkJW6pDufi0thI93t7adF7/HH7Po89ZrmDq4jPww9bqRfTpAVw+XIrRaOs\nBpyLVyILAf28gJxdAAsCN98tIYB77yUBrYr3nRQV0fVSXEyP/XpwVVdbqV23tG6Om6CyIziTk3AE\niMk7nKkOIH5xUfVLAN3u3Gk9r3D7Fv/d71qLGGCvX+nutrqnnBEnZSEwe7Z7S3owaEWicnABLAjc\nfLeGDCFriYUL7WJKGZ7edx8JKrdaN7c6Nf2aa2mhCBPgntbNcRNUFk0MwzDZgp7qWLzYfxeSWtCW\nL6dFUVkMLFlCwko5iAtBi2VRkb0YeNs2K92niyM1q2zTJstyQF/0dKfoHFwACwI9YhgMUoRJzaHr\n7o4XNnfeadW9udW6ufk06SJadVwC7um5HDdBZdHEMAyTjbgtLi0t9m2mTfMWMefP0/w4VRQOUIRp\n504a3LtuHdDWZh2rp4ciDwsX0mOnX49a/JyLsB5pyrEFMCdJpR5Ibet0/1aCXPfjUsXhZWXux6iu\ndvdr0ovLnSN73LrnUnHBr621Ip3OBoZBgkUTk9ewozeTM+ijK9QC51xcGhrsc+fUdkrEBAK0AKqZ\nc84ogmnai4GdvPYa1TcZhnUMp3WAWxqRa5oGBn2Arlc3pHNb3dlbRSudgvyRR4Bf/ILE7/e+Fz+H\nUF1bt91GjQaqecDZvRkMWpFOw6Dzc7sm1HOJXONra4EHH6T7r71Gt1kgnFg0MXkLO3ozOUNtLXW2\nqW413U1bfbtvbCTX72DQHtmpqqJFb/Vq4K67KL2ycCHw+uvu4kjVm6iWcz06BZBY0iMPt9wS7yTu\n7JhisTQwNDRY0T+9G9Lt969HIM+fp7o2wKo904VvXZ2VUlPjdAB7tDESAdasoef1OYV69+Z991lN\nCIlEtJ9i8Pr6+MdZIJp8OYIzTC7Cjt5MTtDYSB1uqk0biHfTVotMbS0tUnfcYS00ygn8wAG6bWmh\ndIb61u/llWOawGc/S9/mZ82yv6YEVUlJvGBiBo/qavpcFKbpXeumb6tSqGrunErBzp/v/tkeO0bX\nm3IHd15D6tpUEatAgIrLVQRKHbexkVKBjY32/f24hs+enfjxIMGiiclblJ9TQIAdvZnsRf+2rnCm\nxPQIQyQCrF1L0YDGxvhv5E8/TUW+kQgtZo8+SoXfbmzaREXkt95qH6fy7//uPXrFDa/FkcksVVWU\n8goGrWikVx1ZVRXVrumCRwi6htavJ1GkPi81Tkdtc/AgRaeUYLrkErtY06OcGza4Xyu1tTSa5Z/+\nyf5egF1sedXC1dQATz4JfPGLdJsFUSaA03NMHsN+TkxOUF1Ni5+qU/m7vwNGjLCnN6qr7YtfJEIL\nycqVlJpTNR8AMG4csH27VQA+YgTwxhskso4dI8GlRJrqeuvosI9TSSWylOO+OzlHTY3dDiBRCgyg\nz0TVGI0aRUaWzuL+qirgq18FnnmGroldu6zjSAkcPkxC7Y477DVNgLuhaWMjpQ5VKri7295F57cY\nvKYmPbHUj+aZLJqYvIb9nJisxPlH3c8C4kyRKMEzYgQJKNVl9P779jl0p09bC1ttrVWXoo6pRw3S\nWWBy3HcnJ9E/KzeB4CzgvuMO4NVXgaNHrVo1PcLT2AisWuX9flLavb1UzZPX59zQYO+kc+uia2mx\nGh8y6RjezyKeRRPDMMxA4vVHPdEf9oYGuzmhmlAfCFBxeHW1FX1Yu9a+rx41cKbyLruMFkCn704q\nC1aO++7kNF7Xkm4DAABdXZYlhVtxv3596ahOTcXLL1uPly/3FshlZbSvlFaXnzN15+yMU9dvWZnl\nD5aO6OlnEc+iiWEYZiBJ5496WZkllkpKLNPKFSuAp56iW1Xo61z8rrnGuj97tj2V9+ij3kaFfhes\nVHx3mOS4jc5xiyQ1NJBgdiuoXrHCug4CAfrcN22ibQyDoo8tLfb075AhwLlz1nkIAXz5yxSh6u2N\nF1C9vfFmqLroiUToGN//fnyKza0Or6XFOj8l8NIRPf0s4lk0MQzDDCSp/lFXztymSQvgkiW0CC1e\nbLkvu3kyKT76yLqvFq/6ehJTHR10fLU4Ow0t6+r8iSEe1JsZ3LyVnFEXwPJq0qOO6lpqaLBqiYQg\nb6WODjrWunWUnt22jf4BdE0o4avmEipLi8ceo3+qHu53v7PSdLoRpu4fBdhtLH7xC7oG9Toop3gf\nMsSKjKn0oZ46ToV+FvEsmnIcNm9kmBwj1T/qeuccYAkd5dmkcHbg6ejRiqlTKUq1ZIm1OKrFWb2P\nshxYscIaycIF3v2PMwpZX+8eSdKvB9Mky4jHHqPH7e1Wp1sgQEJp7Vr6DKdOtb+f7n2khK8+7FmJ\npVdftboxb7gBeOstEjfz5llpNf2cdPSmBXUNOcX7L39pN8h8/HG7g3mq9KOIZ9GUw7B5I8PkKKn8\nUS8rsy+Qp0/bi3wfeIDGqXzve9ZzKvJUXAxcdBHw+c9bA3uFsM+d0xdnveZl4kRK/XGB98DhjELq\naTU96qKnyqQEXnmFbCNUVCoYpOsCsH+G48bZ309P3SrUZ3zTTVbkSGfIELrV02fO7k4nbrMJp04l\nYdTebo+MzZ1LokoJff2csgAWTTmMm3kjiyaGyTM6OuyjU3btip81N3UqDWIFKFIAWNGC737XikLp\nHVAKZ81LcbFlfrhihSW2uMC7/3GLQur2AgDd//73gZ//3Pr8w2GKFurF3xUVtI8a5qzSbVdeSftK\nSRGdO++Mr2tbuNAurAErXXbNNeQGrkS5monoFmVSuHXr6UN+VWSsuJiu3yy2sWDRlMMo88besMnm\njQyTrygfJz36sHGjVfS9bJk9jaZqR9RgVudipkakqPvqm71zcf7ZzyyR5VUvxfjHb1ei24ga5xy4\n4mLgH/7BmhcHAHv3WvsYhvU5futbdKuui4YGy+Ty/Hn6nK+7ztpe1Sbpn3lREY1ImTbNKvI2DBJq\nAHkyJbpGZsygbfVuPSX8AYqKKZGnDxTOwigni6Ychs0bGaYAcEYfWlqsdAZg75pzLjDV1bTgqahB\nURGZZ/7iF7RoKpGl3kctzjfeaI9KOTulmNRIJXLiJa6c9U4jRpDYePJJ98HMLS32IvJp06zoYyBg\nXTNr1pCVQEkJCSw9TTtjBlBZaQkuJWaUU/jOnZTa1a9HNyor7T+LMw2pF4m7vZ5FUU4WTTkOmzcy\nTB6QLAqhC5qHH7YvklKSGFIiSF9gVGRBFfSOGUPeTHrdk/M85s2LT+NJSYttPzot5zV+bSYSiSsl\nJFTXXFkZPff00/Gfl2kC//IvVnF2d7cVDSouBmbOBN580769Eta6WLnvPkoPK9Q8OyWaVqxwT/nq\nlJRYwlyRrBkii20sWDQxDMMMJk735rlz4795Kxoa4rvk1HR5Pb3hxrp1FBFQqRk1xFUV2/7sZ3bz\nQh3DoKhCX0wHCxm3yImbANVNKZ3iqqqKUlwPP0yf2/e+R8Xfbl2TUlrO8KoTUvc+am+P38cwKBql\nd8/pn7fyBtPd5nt7va8XKale6Ve/SvxFwIsstbFg0cQwDDOY6AulW3u2jqpvUtsLYZ8u70QJMr1A\nWC2iqrC3rMy7U0ptX1QENDfbIxcLF9pdpRlvnJETID6iBMSbUjrTUh0d9PtXn4E+EseJEky33EJ1\ncEoAGQYN5FUIQf96e0mQ3XefJZxUdKy7m14Lh+2iya1jTtXMSUnnqUeq8gBjsE+AYRimYGlsJDNB\nZ7pN9+TRUdEGJXqU2aWXYJo3j1ye9cLvkhIaa6Em03d0xHdKAVQcrKbLSwns2GGlZUwTWL8+fno9\n401VFTB/vpUydabrnKaUc+fS/cWLrd+xilglau/XKSqibrf6ehrs/MADwOjR9m2GD7eiRb29wK9/\nTV5M//mflsBWLt36dVpSQjPt9HNR16Rh0L9gkKJaeXSNsGhiGCZnEUL8pRBinxDigBDiBy6vlwgh\nnou+vlUIMWHgzzIBznSbn8Wmo8P6Ji+l+zf5xkaKHinXZ4AWswcfJKFUU2O5R5eV0UKsozuPV1TY\n55ZddpllgeAl7pjEKPETCFjpOv25IUMoVXbzzcCPfmSJUxWxevBB+/533mk5g+v09lLa9bXX6Pbp\np4HDh+3b6I7xinAYeOcd2v+OO4ClS+1Gqur6uPVWu5D6/OfpNRWFMk3yicojcc3pOYZhchIhRADA\nUgBfABACsF0I8bKU8h1ts/sAdEopLxdCfB3ATwHcPfBn64Fe3KvqjNS3+qeestJ0gJXa8dNZpCIZ\nTlQaz1lw/KtfUc3Tyy9btSjOc1TbPvqovdYlizqbcgavQmf1XFkZRYf0kTaqvsnp3K3E78svx7+P\ns95IH4EycSIwZYr7fjpdXSSed+60d+opsa57iJ0/T+eqiya3+qwchkUTwzC5ynUADkgpWwFACPFf\nAGYB0EXTLAALo/dfAPCEEEJImSXGQ2rxXLiQ0l2qXgWwFpu6OrtB4YYN9C2/vp5qVZwDU3Vhpdcp\nSWnNknMOeu3ooHTc2rX0/uGwfZFWc8kA8nPK0s6mnMKt0Fk9Vl5JSoy4iVPn/kVF3nVp+jaqy/LR\nR0koq5qmQAD4zGfsXXUACaHaWrpfXGz5ganzUR5igQDQ1GQfh2IY8dvnOCyaGIbJVS4BcEh7HAJw\nvdc2UsqwEOIMgDIApwbkDP1QVUWiSTlyB4NWUbhKm+kCRxdRmzZZ88SchcUbN1JKZu1aK3r09NO0\niDldmNWCliiCtXw5RSqWLyfBNH9+//9uChEVJdRH2vgpuFfRHSV+Nm+2R5ruvNM+fPfhh63IUyBA\nKbj3348XTW++Sf+EINH1wAP2xgMloLdtsxemf+lL9H55Jq5ZNDEMU/AIIWoA1ABARUXFwJ+AW3eV\nfl+PNAH2rqaFCynV4iwsnj8fePFFikDV1dHC9040CNfbS4uocoJ2LoDORa6uzkr3KeGWJ4tgVqEG\nMeuCVgmmRB5ZqjZOdawdOWKvNQoGrYG+K1fauykBq8tt1y7vc5OSBLf6/7F4sXUuVVVkiKpz5Ajd\nzp9P565vn8OwaMozmto62SGcKRQOA7hUe1wefc5tm5AQIghgOIC4ymkpZS2AWgCYMWPG4KTu3MZn\nKJyCSi18pgm8/rrVUaXavbdtswqH9e11xoyxFrTvfIeemzOHI0iDhXMemx7RcdagKc8kgLZR6Vh1\nTRw4QK8JQcf6u7+zp2Wd2emiIjrG6dNUNO6FMtV0RjVbWuIjVDt20HZLlqTn75WlRqosmvKIprZO\nfHPZFvSETRQHDTxz/0wWTkw+sx3AFUKIT4HE0dcBfMOxzcsAvgWgEcBXAPwha+qZUqGqihamhQup\nhfzaa61FSpkMqvtqNMbvfkeeO0D8QqkPRtU9mlTqzblIzZlDHkL62AsmszjnsVVUuM9q6+62D2Fe\nsYIK+f/X/7IK+RVCkGB6/HHLSVx12RkGcMUVNMBXRaESRZrUPjt3xkc13fyiVAF7fX3qc+R4YC8z\nEGxp7UBP2IQpgd6wiS2tHSyamLwlWqP0MIDfAwgAWC6l3COEWARgh5TyZQBPA/j/hBAHAHwIEla5\nR20ttZkD3pEAt06pJ5+kKILqhgsGgXvvjZ8lpu+zcCEVmHd02NMvGzfao115km7JGhJ1RZZpw9hV\nV5qip4dGpDh9lBS7dllF5QBt82d/BuzfD+zbB3zwAVkHzJtniWdlfeGcKaeOoZ9nWRkZn+qoujw1\nYFrV6/ktCPc7dmYQSCqahBCXAqgDMBqABFArpfxlf58YkzozJ5ahOGigN2yiKGhg5sSy5DsxTA4j\npXwVwKuO5xZo988D+OpAn1fKJEtF1NcnP0ZRkfvMuEgkfoq8wtllJyWl+157zTI2nDaNIlY1Ne6p\noiyKAuQ0XjYEjY00MkX38woG7fYBbnMEDYM622bPps5MhWlatW2APRrkLD5vaaHmgeZmSwTNmRNv\nd+AU7FdeCYwcCVx9dXrdljk+sDcM4O+llM1CiGEAmoQQrzu8UJgsYPr4Ujxz/0yuaWKYXMKPCJk9\nO3GtiWkCn/scfaN3pmfcpsgrVASpro4Wxu3brf2V/cG2bZZJZk1NVkcBch43GwKn55ZpkggGqAsO\nAF59laJCyrE9GLTGoaxZ4z4fTj/eiROWKaVhABdfbEUct251F/X6eSrhplCibNMmy2vMT62c/j5Z\namuRVDRJKY8COBq9f1YIsRfUxsuiKYvQC8AfuunywT4dhmH84keE1NTQbX091TR99JG9Gw6gImBV\nCA7QIuhsD3eiFqk5cyiipDuIO6mvt5zEszQKkJc4o4FFRfR5tbRQWs406blJk4B337W63BQ//3ni\n40tJKTw1ZDccBp55hl577TWyIfjpT+3XkLpuysoojXv33cCqVfHizM3Y0iuqWltr/TwlJf6F1gCT\nUk1TdATBNABb++NkmPTgAnCGyWF0EaKPT9EXGWUsqfv1qCJuJV7uu48WUiWe/v7vabHzQi1SkQi9\n75e+ZBddTmbPpluvNBLTP+jRQMAqwlcDdAG6Bvbvtw/TXbHCuu8Hr2jUz39O9hT6daebb6prRhWZ\n68dRkU4lrL2iqo2N9p+nuztrI5i+RZMQ4hMA6gHMk1LGDasZdJ+TLKa/bQC4AJxhchjdcXv58vjx\nKXp327JlwP33W9GjXxJbqegAACAASURBVP3KcgZX0ajvfpcWrn/7N4pIuUWaamvJZkAf1Lp2rb1W\nJhAAvv514ORJ+/HVOTuPmaUt4lmPn9+b8/e9eLG9xslN7CoBMmRIvC9TKkhJ19wnPkHCXA141gvL\n1a1hkMA6coTe9+qr7defV1RV+UwpDCNrI5i+RJMQoggkmJ6RUq522yYrfE6ykExFgRIJr3QKwNnP\niWGyCH3h0BcUwF7PEg5TR9zKlXb/G+UMvnOntfioifXLlpHbc02NFbV66qn4yIKqlTl2zHIRX73a\nX6E3F4enR7q/t+pqSmF1d5O41W0F9M912jT69y//Qmk2JXASRRR11HYqDbxtG/DNb9o9wfRjBYNW\nJ15PD9XI6fYUXqld58/zxBNZe/346Z4ToLbdvVLKf+3/U8ovMhEFSia8vArAvYQRp/MYJgvxWlDc\nZsh5+d+4EQ5T9Amgxcwr6iAlLbAdHdYMOrcaK2c9i+qg4uLw5DijSqn+3hIVSt95pyWIlfj+znfs\n3XWGQcLmmmsS168BtO2MGfHbrVplvT51KvDHP1rXUzhM3XZug4YB79RuDqV8/USaPgvgrwG0CCGU\n89UPo62+TBIyYQOgC6/uXhN//9tdqLnhMnzjeisNOn18qW9hxOk8hslCvBYOVc9y7BgNWFUDUJ3+\nN2VlVA9VVETb6MIoEqHFTDe51KMFakFVIsir0NtZz6La2pcs4eLwZLhFlfwU1avo4DvvAG+9RZ+V\nW6G0EmF6pEkfAG0YNG7n0UfpcTLRJCVQWUnRS93KQj++0wwzErE6MJ2DhnXB51bg7ZbyzUL8dM9t\nBiAG4FzykkzYACjh1d1rQgI42NGFH77YAgA24aSTSBixnxPDZCluC4f+nDNSMXWqFfVR5oRCALNm\nAR9+aB9t8fHH1kwzIWhBrK4GfvlLWrTVKA23OXjKyFIfJgtY0YSOjpyJFAwablGl+fMT/94aG+l5\nPUUL0OdcV2cvDq+qouvALYqoDDFbW+k6+da3kp+vYdBxL7qIBj/7RQmmW24hYd/QQA0K6YxSyULY\nEXwAcEaB/OBMrT1z/0z8/W934WBHV2ybdbuPeoqmZMJodmU5ZPSWo0wMk2X4LapWgmrxYns9y+9+\nR3UhW7da0aV33yVhdMcdFLFqagLeftuqgdIXW3Vct5lnKl2oIk0qmpAjkYJBwyuqlOj31tAQb1gK\nkAhatswq9n76aWtkjrODraQE+PSnaRacErmAuxmqTiRCtXC//a39ecMgT7C33rIXb+vnpkw1lVBS\nos0r5ZtDsGjKEnSRBMA1tVZzw2WxCBMADCkKoKmt07OGyavOST/27MpyLgpnmP4g3W6yRG3Z1dW0\n0BUV2Ree6mr7YhmJUPRn40ayKVi/nl4Lh4GuLrqNROwdUJGIdUx17mrAq4qO6BElvaYpRxfAASWd\nup3qavqs9UhTIEDC96WXrOfUyJziYsukUje4BOzX1LRpJGScjBhBQ3sVyq9JRwgS41JakUslnoqK\nrPfUI2vKXd7NguBnP6NuO+U6n+WwaBpkmto6Ud8cwgtNIYQjlpBxS6194/oKtHf8CWt2HcbJj7ux\nYe9xbHrvJJ65fyYAd6HlFEHOtN3q5hDqm0NcFM4wmcRPV5SXqPIqDq6rsxbPnh56XFVF9gH19WQw\n+Nvf0n4lJSRqGhria5+uuYbElJS0yCnBpBYz/dwDAUuMBYMcUeorqfzu1PXx+OMUGdy/3z5c95VX\n7CaWqkFAf6y/ry526+vj58oBwJkzyc9LRYtU59ysWcCYMfSa095Cj6wtWUL1UfrPd+ONVrRLd53P\nYlg0DSIq6qNqlQASMhKwpdZKhxZj6cYDKB1ajN80HozbfktrBwD4Ku52pu2kz/0YhkmBZF1RiUSV\nVxpHjcxQHDsG/NVf2SfMP/aYFS3Q3ZWXLKGokKp9Ut/+//ZvycsJiB/iqwbAqohEshZ19mnKHE7h\nKgSJnA8+oM+4qoq8k379a/t++mek21Po15cyRHXaBTj311HGlYAVyertpdu1a4F//3dL7OhmrOq6\nU9ewStetXEl1Vc70oHKdz2JYNA0iKuqjX6aGQX+gFtw+GZ1dPSgdWoxFr+xBT9iEIQQipoxtLwBb\nvZKf4m5n2g4AVjeHuCicYTJJsq4oN1GlnndrJ29spPliimCQHjsLhHftonTcjTfa3ZV37qSBvTt3\n2gu5/+3f6L6aT+c8d8OwxJOevnPCPk2ZRb8+9BSqLsDnzCHXb2VH4ea95Nynrs5uX3HttcC4cZTq\nc+571VXk7RQO03Xw/e+TIK+upuM8+aR1XTz8MDUlAHYz1uJi6711Me5VV6Vc57MYFk0ZJNXaIBX1\nUZEeAOiNSPzXtvZYqkxPpwESAUNASrr96oxLcZdWyO23S8+ZtuMhvwyTYZLVrzhFVVlZvOjQ27J1\nx2TV+dbUFP++qlvJ6Ra9YoW1+AF0qwSRszjXmcrRu568rATYpymz6NeHiuyEw1aKFIgfrzJtmuXD\nBVj7qetr8WJgyxb7+1RWkvj6/e/j/bsqK2menfLsevxxuxjWC9GVoAbsQr6317oWnNf8nDn0j2ua\nChO9wDoYMPCV6eVJO9NU1GfR2j14O2Tlkk0J9PSaMSGjR5BUBMpN4CTq0ksk6NLp7mMYJgmJ6lec\noiqZ6KiupkVQDWdVc+bUN/qKCqpVUt/2dXflL32JFj5leCgELb7KRdpNEOnnrmwNEqXdeIhv33Gm\nN3Xh+sgjtI0zGuR2jal5glJSwbhy6HaKokDASslu2AB87WtAKGS9vmqV5eEFxAvrpUspwqRq6NzM\nWAMBu8hz+yLx4ovp/84GARZNDtLtJNMjQj1hE6u2tmN1cyhhYXVTWydWN4ew52jcKD+YAEqHFgMg\nW4ATZ7sxalgJJo0ZlrIwYgdwhslCnAteMtGhaouEICGzZIk15PTgQep0+/3vaWFy+izpkQQpSXyN\nGOGvmyuRT5S+Dfs0pY9XelOltfykSAGqH1Lu35EIWU+MGWM3NVWMHUvCWwkzZ82cLphUTVOZVr5R\nU2MX1ADd/9u/BX7xC3p/1V2nyIMmAhZNGn0RF04DSonEhdXqvc73uk+WNgSw+8gZLHplT+yYhgDq\nPYQYO4AzTA6TTHQ0NFgu3+GwlQpRiylgT7M5o0b6QGC9Uy4VktUt5cGCmFFSKYx3Rhrr6qx9/Ubx\nGhtJOOtWAipNGwzGeyqFQsCDD1p2ALq304QJlDJTDQOmSffnzSOhpI8/cfp5KU8mwJ6eyxNYNGn0\nRVyoVNvq5hCe33EIEVMmLKxW7+VFMGBAALZCced56ZEldgBnmCwh3S6yRKLDbeFsabEvdMpo0q0+\nSh1b+efog1LdfJ/c4Lol/6RaGK9/vsGgXdw6I4fJCvFV3Zoat6IK/FXhthN9zIp6rMbxPPAAPacG\nPHt97vq1oRekm6Y9OpUHsGjSSEdcOFNi08eX4q7K8qQpvpkTyyA8Jk0LAF+ZXo7J44bHCsTV84GA\ngcOnz+HZre2xrrpgwMCNV16MYMBAJBJ/7pkY5cIwjA8y3UWWaEBrQ4N9gZoxg1J2icSNuq2rA954\nw933yQuuW/JPqgJTjzS2t1tDd/VxK15iSe2j3g8gsVNRYf+MioqslJkQJJad8wPr64HXX6fn9a42\nlWbz+tz1a0MIKwKq5hnmESyaNFIVF27F31PGDY8VagPA0o0H4hy5t7R2oHRoMcYMH4LDnedixzNE\nVBgZAgKUnhOgVJ8AcNnFF+KDU3/Cqq3tCBgCppSxGqr17xxHUUDg69dV4K7K8rj35mJvhhkAMhWN\nUV43KuIQCABz59rNA51zxpRxYFkZLVaqc0pf5Bob7S3hyc5BF2lct+Qft+5INb8vWe1YYyP5GPlJ\nx+leTsHocq4605xps2CQxJSKPKlaJqer+2uv0a1pUoecaZIQuuMOyyPK7dxT7bjMUVg0OUhFXLgV\nfyuBUxSgCeLhiBUJEgAa9p+MGVg6CRgC1ZNGYeO+E3h2azsCAYGigEA4Qlu/f/JPsf3CpkQwaj+g\naqgipsS4ERcAQMw0M2AILJo1xXNGHcMwGSQT0Ri10OndTpFIvFGh8xt8OExCa+VKqxZlyRL3sShO\n9DSOfg5uKT4WS8lJJCKSRR8TiVNdyOoCHbBHl9Q+zm0qKuxRR3U8he7YDdhdw3/3O8uN3Ou81Xvq\nppZ5dr2waOoDbsXfiN72RKxnesImXn/neNLjmabEiY/Ox0RSOCJx1Zhh2H/8LCIuKuv2Px+LC0uC\ncTVUW1o7YucUNiUWvLQ7YdcdwzAZIhPRGLXQuRkVnj9vpdGctSKGATQ32wf31tfT7SOPULpFRSRU\n6iUQAKZPJwsDP6NcGP/o3W+p/i7dxKkzsnTbbfa02UUXWSLN6S7f3U3RInXNqEim8u8qLiah89//\n7X1OuheT8/rWI6PKD2zp0ry8Zlg09ZG7Ksuxq70T7xw92+djCSFQEjRsz717/Kyns/0rfzyK5x6s\ncq2hMgRiQsuUkjvmGGag6Gs0Ri10Tl8dgB4/9RQZGXZ0xE+0V5Ps1fOvv07/1HHCYeDqq2mGGUAz\nzZqaqKhcdUWpLqxg0Bq1kWfFvANKpmrBdCEbiZCLd3ExRZguuohMIgErvVZTQ5/nI48AP/+51f0G\nxPs2dXcD3/1ufIedQtU9uTUZAPGRUdO0XMLzTDixaEoTt7lxihFDi3CmqzeWqhMCsYLugAGMvWgI\nQqfPxx0zbEo0t3fanpMSCGgCSMc0SQw9dNPlsW46NaPOMAQi0Z2ChuCOOYbJBVS65K67gGeftZ7X\nxVEkQgaGS5fSQqa3eSvBNHEijcBw+8a1dy/NMPvWt0hEOUe56K3j6rjOVnPGP5mqBXOKaWU/UVFh\nT7EBwNNPW7MG1agcgPatr7dHMoWgiJVzDpxOoiYDwD0ymsxTKkdh0ZQm9c0hV8EEAKe76OJTs+Gu\nKR+OD7t68cmhRdh56LSrYFJEHC4EhgAe+PxEfNQdhgAwrCSIZZs/gGlKFBdZXXJ6UbohqEhcncNX\nZ1zKUSaGyXZU+kVPryk+9zlg82br+XCY6k/UYnz6NPCv/0qvlZQAjz5K3/TdFkI1jwyIj4A4W8f1\n7fNwARwwMlELpvtt6Wm16moSRyrCBFCatqnJGvSrUCleldZTDQZ6pAqIn2NXWWmdv1vUTD2nxL2y\nO8izInCARVNaPLu1Hc9tP2QTTMpOzCmiIqaJbQcpemRoESc3qHMOMAwj5uFkSmD5Wx9gVU1VTPh8\nYfKYuHScbUadlDAMAQGqc1LddAzDZDFKsDgFUyBAM8Oczy9bRsXb1dUktkyTtl2yxJrh9dBD9kUT\noAVRn/3ljICoBVC1puuLM5MZ3Ly8/Ph7Of22ysqsfR57DFi9mgbwvvWWXfjqbNpkpfVUl93ixZbg\nEQKYNYtSt/qcOPX+blEzpwN9HndYsmhKkaa2Tix4aTciDvVjRPNwzuf1yFEiwWQIZWthYO5nJuDJ\nTa3WyJ+IRH1zKM7QUo8epTKjjmGYLEQv2lVpNn12nBO9MFftIyVFoBobKT2zdCk9VgW6qnX81lut\nhU0fDOxcFIG8XgAHBbfORCA1fy/1mm4noEanHDpkDesF3OviVFpPLxhXqd7iYhJgjz3mPTLHeW7O\n5/L4WmHRlCJbWjvihBGAWIRHpyggYAKxbjjlueSGOmQkYqKxtSPuOhdIPCrFj8dUunP1GIYZAJxt\n6qomZedOaxHUo01FRfHO4FJSBMrpKD1tmjWnbu1aah9XtgRLl9qny+t+QakKpnTd0AuJRHVBbmNU\nvH6PdXVWfZP++Zsm8PnPW9EmHS+TSq8IEn+GceS1aMq0SHh2azte23MsLt2rfJkiEjZBddvUsRha\nEsTOtk7sPXbWUzDpxxGGQEvojO35YEBg8rjhWLJ+f6yOym3MSyKPKR7ayzA5gO51o6bb9/ZSJKGm\nxmorHzfOMhp0OoOriJJei9Tebs2uU91XgHeXk7O9XRlrqnNzW8wz7Yaer3h10yUao+L2u16+3PrM\ng0FrPpyU9vo3hWG4ezkpMlF3VQCiOW9FUyZFQlNbJ55843285uG1NL5sKH7xtWuwaO0evK0Jnpff\nPpLS+1R8cihCp89Bv9Qvv/hCfOriT2Dh2j0IR6KDe4GUZ8jx0F6GyQF04QFY4qa3l6bQK6folhbL\naLC6mqJOummlGmERCADbtlFkycu7xK3Lydne/uSTtEjrNU7OxZy9nex4CYhkdUFuY1TcZr2pa0OI\n+BSuUzCp56ZNs0cV/Z6zHwpENOetaMqUSFDi63yv93Ddmhsuw/TxpaiaWGYTTYlqmIIBgQllF+LA\niY9jz7V92GXbJmAItH/YZXMCNwTw2ctHYt4tV6b08/DQXobJMP3xrdrp4Kyzf7+VjtFNLlW0ad48\nYPt2y1tp7FjgxAny87GFxgUJKj3a5PRhqq6m6IXaRkqrE8+rmy7R+JZCI5mAcEZ19GsJSD5GxRmt\nGjPG/hm7pXOBxHPg+ip6vERznkWf8lY0JRMJbqm7prZO1DeHIECmldPHl2J11FrAizuvGRcbUTLs\ngiLP7W64YiT2Hz+LIUUBDL+gCFUTy/D0Wx94bm8IoLJiBJraOmOCSQAoDhopCyaAh/YyTEbp6wLj\ntZA4i8EVQgD79tmLe1essLqfqqqoa063LDhyJF4sFRcD995Lj2trrYJzt8VU39cwSER5ddM1NpJo\nc45vKVRSibrpVhOqxiyZr5P6vOvrgdmzKb26cqX9GIDdsDKZkNXPWRflfnFLO3r9P8lhIZW3oslL\nJChh9EJTCOGIlboDgHtqG6PjT4Dnm0JYeMdkPL/jUMJapA9O/Sl2/+w5b3OwzQdO2SJPfwyd8Tyu\nAP29ejt0BkEjOntOABNHXoi5n5uYtuDhob1MviCE+CSA5wBMAHAQwNeklJ0u20UAtEQftkspv5yR\nE+hLKiqR4FKpm4ULgfXr7QW+zuhTOGx/X699haD0nV6XVFdHz3nZCejpH8MAbrmFjqtecy52ul2C\nEHk32T5lUnEBb2iwhK6qMXvjDXtXo5PGRqveraEBePxxMisF7EOdp06lz9r5vNc5q+iilJSOTbaP\njlva0W2EDGDv+rv33tTeZ5DJW9EExIsENxdvlboDEBNM6vl1u48ibFqdb7dcPRoCsNU27Tn6EZra\n6G/1ml2HPc/FmapLJMTUaz1hk2bPnfgYEVPiwMk/4Udr6O8/D+BlCpwfANggpfy/QogfRB//b5ft\nzkkpr8n4u/dlNEYywVVVRQJl0yb3USoACZniYkqJLV5sLVL6vs4ibvUNXy/w1r16Ev18Cxcm7qjy\nmnFWqKTiAl5dHe/4nkyE19VZNWw9PRRRAqzuOHUOidKAboXg995L9WsqHesVbUpUr+UWOfUyUHUb\nRJ3l5LVocqLqnPR0l0rd7Ttmnx0XCAjcOmUsth/8MJbiu2nSKDTsO2HbLhKRWN0cQn1zKGHdUyro\n1gR7HecVkcA/sXBimFkAqqP3VwJogLto6h/6MhrDj+BSs+CGDLG3jivjweuuI2Eyb158xMrLa0nd\nek2978vPp9JFDz9szTjr69iVHE7hAPDfjVZVRek09btLx0lbeXQlEiF+Uspz5lCESY1F0VPAqRxH\n/9ncrqPiYvs4mBxqHCgo0aTXOQUMga/OuDRWu7SltcPm2D157EWYNGYYFtw+Gc9tb0dJ0MDCtXti\nTt0KIYCTZ7vTEkxBA5CIN8QsvbAYH/7J6oRxWhyYEljw0m5MGjOM021MoTJaSnk0ev8YgNEe2w0R\nQuwAEAbwf6WUa9w2EkLUAKgBgIoKn19G0m3RTiZIamuBBx+0Hl9zDYkoKSmlNmZM/Dd256Kjzq22\nllzBTZMW4yVLvAWbU6S4/XyJhExHh5Vi6usiWCCdWDFqakhk+hWJc+aQoFERQ1X0rUSIW02Sn5Ry\nVRVFJlW0yZkC9nsc5zHdugfr6uzWCjnSOFBQoilRMbQSVKrj7o+hM7jnqS0wpYyZU7rx5U+Pw9oU\nrQUAGsL7F382GtWTRmHPkTN4bschRCI09uSGK0ZizS7rmJ++ZDg+7onYOu1MKdk2gMlrhBDrAYxx\neekf9QdSSimE8PpPOl5KeVgIMRHAH4QQLVLK950bSSlrAdQCwIwZM5JZqvWdRIKrvt7+eNcuWlRu\nuw149VVqR1++nB4Ho3/C3RadxkbL0BKg1FlHh7tg8yNSkm3Tl5Slk0K0L0hFhFdVARs3WsJDdTYG\nAlZN0tNP03MqUuT385kzJ3H3Xl8+Z110/8d/uI/xyXIKSjQB3sXQSlAtWb8fm987FTOQTPTX87oJ\npbhi9DAk0FSeRCTw+jvH8eZ7J/HM/TNxV2U5VjeHIGHNsVPsCp2Jey4YYNsAJr+RUt7i9ZoQ4rgQ\nYqyU8qgQYiyAE27bSSkPR29bhRANAKYBiBNNWcXs2fbhqwAthF1dVh1IJAKsWUORp/+/vXsPkqq+\n8gD+Pff2DIirMI7ig+EhJBoFV4URIdnVUUyiWcREzBpNYrKWYUMZV1JJZdekZF3NFmo2u1irVZFC\nU6Gi5iFGXVfXR0WyJNsgDNEIGiI1YcYBIjCOikHm0X32j1/f7tt3bnffmbnd996e76fKgpnp6fm1\n3fQ9c37nd06puqQNG4oH9lpWcRbJe9tKQUqQWqyRbll6hRmA1Sun1YTTtBQoFOI7NUlOfy2nri3I\n81PpeRzp81wq6E5IsOSoGDSJyIMAFgPYr6pzqr+k6Myb3oQVl5yGLbvfRv9AFvDp/O2Oj9q7ejFx\nQiNsq3jGXCl2bsCcE2QpTLH36hf+gMvmnIz127rRP5g1c+w8vMOBr5rXwiwTjWVPAvgSgDtzfz7h\nvYGINAE4rKp9InI8gI8BuNt7u9hxmg8+8IAZoZLNmovM0qVDi8OdoMiv2HfHjuL7vfrq0heoIEFK\nkNuEdREMMwCrZ94icqC4B5dTL/SDH5it2m9+E7jrLv/78tueLfe14T4ndZI9FC3VJda5gcgFAN4H\nsC5o0NTa2qpbt24NYXnRuPPp17FmY8eQE2/HeWqNHI224Jypk9A3mMXEoxrwv28cHHKbM046BgNZ\nRceB94fcr8AEVIPlumF6ft5tS+ZwIC/Fhoi0q2prDX9eM4CfAZgGoBOm5cDbItIK4KuqeoOIfBTA\n/QCyMI30V6vqA5XuO1bvX96LldMP6aWXCrf59KdNYbgTxDi/zXubG86fb25bKggJUnid9OLserRm\nTXER+Sc/ObShqdv99w/tCu69D/fWa1j1ZTGvUwv6HlYxaMrd2QwAT9Vb0FSqweXV96cDBzCO+TOa\ncOHpk/GL3+4pqj0aqZQtyGTUd3tw/owm/G7Pu0NGxHAgL0Wl1kFTNcX+/SudNkGLM5NOpFBM675g\nek+QpFKFbt0xu2DRKHk7ijvNMkUKBeKOT3wCePbZ4u+94IJC7ZtlAd/9bqFP1KpVwK23mteYbQN3\n3FG+h1TQdcbs9Rf0PSy0mqYRnT6JUKnZdJs6epCtEEgeOz6F944MFn3upd29eGn3kN56I3bx6ZPx\n1ntHisayOLZ29ppDEijuM8WBvERjgFPLsmFD8ZyyI0eAJ58sXCAbG4GbbzaF5BMmmNlk3iaDQS5g\nMb7QUY53u8y9tfn448Ddrl3ppUuLv3fDhuKMpG0Xb72GWV+WwBomr9CCppqfPhmlUrPpFsxshmUJ\nsmWqu9/3BEzV8M7hfmzfUwiY3O0QsmpO3wGFPlMcyEuUIKMNRJyLjzPt3jkx5QRMIqZRoVO/kk6b\n7IJz4WtuDrZV4s5qNTQktg6l7pWrOVq4EJg1y5zKPOccc4IynS58va3NbMk5I1juvbd6Bf51YMyd\nnnMsmNmMlG16NlmWYM87H+Q7e6tna05gghYnjgqjhaVftspty+7imXMzjz8auw4URrYsOuNEnD11\nUtFWHAfyEiVAmLUd3r46gAmYxo83E+3d3cLdFz53UW5fn+n4vXSpuaC6L4zeztPDnUdG1ZdOAxdd\nVHg9vfji0OfI6QNV6vRakFl3fN4BjOGgCUD+TWYgo3hkcxce29aNpXNbiloIiADnTW/CpAmN2LBz\nf9GoleHwnrwrFzDBc1vbElxyxonYdaAj/7m20ycXdQTnQF6ihAjrFJGTXTj3XBMkuWd5nXuuKRjv\n6zPbLffeay6c7p/jjD3JZoHnnzdtDixraCEwxdu6deZ5BMyfpQLbIM1Q3bgt6ytIy4FHYMYVHC8i\n3QD+OcgJlLjxFklv6ujBYLZQaO3UB+0/1Ff0faqmXskSQMSnF0AATsDkDZycr11z/jQcOy6Fx1/e\nA9sS7HnnSP7rlgC3X2FOyjlbdALgme37hnQE50BeogQIo0bEna1KpYDLLjOdwp1+TatWFQ+BXb7c\nfJ9zasrJLniH+3q7eV93nWl94GzPOQN/KR7SaWDbtmC3Hc7rLuYn3aJUMWhS1WtqsZBqau/sxTVr\n0hjIKBpswSPLFg7pAG7B1AdNPmZcUf2QI6sofYSzjAZboKrIZAHbAizLwuBg1pyBFiBlCQTAtOaj\ncfD9PjhTWpw2BLdfMQfXnj8N7Z29Zr0D5nt/s+sgtux+mwXfREkTRo3IunWFfk2ZjDkxN358Iahp\nazMZJncwdOONxfPgFi4sDPd1AixnELD7gmpZJuVuWSN+yFQFTmDT5/pF37ZNltHPcF53ddJTqRoS\nvz0X5Jj9+m3d+W21/oziHx99BXdddXZ+O6tpQmO+55Fz+76B8t3Ag8pmFZZlckyWZeG2y2ej93A/\nmiY0Yvved/FoezceeakL0OJaqVknHI27rjo7/5jcHct/s+sgC76Jkmw0NSLptMn+uH+J8w49XbjQ\nbMktX14cOJXr4t3cbJppurk7TvvNIaPoOIGN0wXcaTFRblhy0NcdO7KXlOhfHZy2Ad9/bic+v3ZT\nvpDby7uptuvAn3HNmjQAUxDubRJ55dwWfPzME4d05vbbnLMk1+m7hIyamikFkMlk0Xu4Hzde9CFc\ne/40TJl0FAYzKOEphwAAE3dJREFUJtPlLS4/elxqSDDkdCxvTFmwBSz4JhqL1q0bOh7Ftode3JYt\nM/O9UqlCrVJbmwm6li83/zmnqG65xVxof/Qj08Jg0aLCybnGRv/7p/Ck02ZLNZ0O/j3u58a2zefc\n26uj4QTTd9zBrTmPRGeagh6zv3JuC36y5U1kXHtuAxnF+m3deCw3uiRlW2g77QRs2Lkfg1lFY8rC\nkrNPwZOv7IUqMK7BwpcXzhjSKVwVmDd9El7pNs0mS7F8ghxni3BgMAsRwP3tV5/n3+uKBd9EVGTJ\nkkJH8FKnptyND9vaCififvjDwmkrvy2ZW27hcfNqG2n9kDdLuGJFuJkhnpjzleigyR10lMu6zJve\nhDuumINbn9ieD5wabMHBQ304MmAilf7BLJ577a389/QNZPHU7/ZB1WSSVi6ejWvPn4Z0R09Rw0mF\naQ9gixmV8vqfDvmu4awpE7Hy8tlDCrfdW4Qv7tyP/e8dwdXnTSs6Gef3eBgsEdW5UqeXrruuMNm+\noQH41rfKX9zcF79Vq4qzVO4tvVJbMrx4Vtdo6ofcz407OK7G88XTdAASHjQNJ+viBCE/3dKFxpSF\npgmNeN4VJHkpgEzudF1WFc9s3wcAGJfy39HMKPD7EgETgJLBlLNmdzfv0086puT9ENEYUC774O4I\nHuQClk6bLT3AFAk3NBQyTalUcXDErFLthVU/VM3glqfp8hIdNAHBsy4Pb+7Cyie2D2umnG0JsqrI\nKrDxjYPY6DOI163cPQ+W2T5kN28iKlIp+xD0Auk0PnROWDU2mm2c73+/cFrOjVml2otzsOpkl7q6\neJouJ3FB00iG0rZ39g47YGq0BbctmYNntu/Dr984GOgknV8fJkcWQNOERt+vBd1mJKIxIqzsgxN8\nOQYGzCw6gCfi4iSOwaq3F5hTbD7GDwQkKmgqNWTX/XW/gCrIEF636cdNwF99+HgAwLTjJqDBFgxm\nFFmUD4y8nz9mvI1DRzIATCF47+F+3zWyuJuIioSVfWhuLm5NYNtmXMrGjcVz6NzjVije/GqLqlFv\n5M52AsBXvgJMmzbmXyeJCprKbWOVC6gWzGxGypL80f9KOt8+jM7NXfmPbUsw84SjcdzRjflxKpXu\ny7YEH/Rn8h+nbAuHPhjA1fenkckqxjUUr5HF3URUJIzsQ0+P2YJzejXdcEPxiTrvqasxXKuSCH61\nRUB16o282U6n2/wYl6g+Tc42ll+PIr+AqkhuBEqZlkolZbKKXQf+jJd29+LFnftx2xLTpbvRFt/e\nTbYluPgjk/OtCQTAhaedgLW//mN+dEv/gM8aiYjC5Eywt23gqKPMhc+dlejpMfVOzuDe0fb3oery\nq3Xz+1wY2KvJV6IyTeW2sdxjUUSkqH5oU0cPBjPZ/Pw325Kink3DMZBR7Nj7Lv71M2fhyrktWL+t\nG4+2d2Mwk4UAWHTGifj7C2cBAH6Vy0g12ILJx4wr2iK0LGHtEhEN33C2YrzbfEBxVuKmm4o7hjc3\nD/9nUO2UqnWrVvfuONRaxey1mKigCSi9jTVvehNWLp6NlbleTLc/tSM/0NZbaP3lhTPyWZ+RUBTq\np5bObcHSuS1DArn2zt5cdksBEcw+ZWI+qLPEzJTjdhwRDctoj357sxIvv1zYvrMsk3ni8fL4KlXr\nFtfTd6MVw9di4oKmcnoP9yOrZvvLXfPkzVANtzDczRZgzikTh9RP3XjRh4pu585uOeNTWOxNNIaF\n8RvzcBshei86q1cXZyW8ReFtbRzWGnd+2Z84ZISqIYavxboKmhbMbIYlQNYkd4q2v7wZKifrEyTZ\nZFvmAIqTIeo93F+xr5JfGwEWexONUWH9xjzcVgTei05Pz9CshF8naQ5rpTiI4eDgugqadv7pUH5+\n22DWfFwqSLlybgsOHurDL3//FvxGxgmA6c0TsOyCWTj9pGOKMkTtnb0V+yp5R6Q4Rd8MmojGoHXr\ngCNHzG9fo/mNebitCPwuOt6shN/H9brdQ8kSw9diXQVNzqgTx0+3dA2Z4eZuTWCJIFNixm6DLVh2\nwSz0HjaN4dzbb+UK0v36MJXrLUVEdS6dNoNxnZIA2x7db8zD2YoZ6UWnXrd7KHli9lqsq6Bp9snH\nFo06eW3fe2jv7B3S6LKwLadmVEp2aOPKjAK3PWm6iKcswWdbp+LKuS1l+yr59YriiBSiMW7DBtN5\nGzB1A9dfX9uLQJgXnZidZCKqtboImto7e/NH/92yWR0SpHhrjVYuno3te9/FwUN96Dj4Z+za/z4A\n05spCxNE9WcUD2/uwvpt3WW7kPsFSByRQjTG+TUJDEOtA5gYnmQiqrXEB01OdqdvIFvUoVswtAEm\nMHRrDQBuf2oH+v0Km1y8J/LcP9vJLK1cPNu3+Hvl4tl4Zvs+XDbnZGaZiMaaatRlBA1gwgysqn2S\niVksSoBEBU0Pb+7KBx9Ocfbedz5A/2AhYBKYeiTvdhpQnBVyMkN7ct/vd4rO/SkrQBdyv7YC7Z29\n+aBsy+63872jiKhO+V38w67LCBLAhB1YVfMkE7NYlBCJCZoe3tyFb//iVQDAxjcOImWZ1gIpS5Cy\nLWQyWdg+tUcOd1YoZQkggsFMFinbQsrpEC6lO4WfNWUiVl4+u+xWn7utQHtnL+57cVc+qGNNE9EY\nUKuLf5AAJszACqjuSaYY9uMh8pOYoMl7Ms7ZTctkFVfPn4opk44q2zSyKCuUUTjjdgczWVwzfxpO\nmXQUmiY04rb/2oGBwSwk1++pnFKn6LwBmhPUsaaJqM7V6uLvNx5l1ariYCaswMr7c6MKAoliIDFB\n02VzTi46GWfnghrbEiz1ySx5ubNCIoWgK6vA7FMm5lsTONt+TgDl1Dq9uuddfH7tpiGF4H6n6NwB\nWtCgjojqQC0v/k4AUypbFCQzFJdgJYb9eIj8JCZocoKaZ7bvw+yTj8WD/7cb2cFsbr5bZe6s0N53\nPsDDm7ugACwg34vJuZ0T2Jx+0jFY/cIf8JtdB4e1vebdtgsS1BFRHYji4l8qWxSkVilOwUrM+vEQ\n+UlM0ASYwOna86fhvhd3Fc11C1on5K43Wr+tu2IbgHnTm7DiktOwZffbw2oZUK75JRHVuVpf/P2y\nRcOtVWKwQhRIooImR6XeR05QJEC+KNzbqTtoUDPSAIhz5oiqR0Q+C+A2AGcAmK+qW0vc7lIA9wCw\nAaxV1TtrtkivIJmfkRy798sWrVoF9PUB2az5k4XVRKFIZNBUaYzJNWvS6M+YKu6ft3fj+o/OwNpf\n/xGZrGJcQ2GUSamgxhtgMQAiip3tAK4EcH+pG4iIDeA+AB8H0A1gi4g8qaqv1WaJLkEyP6M5eefN\nFjU3m4AJMH828wAKURgSGTQBxZkcb1fugUzh2NvAYBb3b+zIj33qHyi/nec3CoUBE1G8qOrrACDl\naxrnA9ilqh252/4EwBUAah80BTmlFubJu54ewLJMwGRZ5mMiGrXEBk0Ov67cDbbkM03e1gFiSdm6\nJM6KI6obUwC86fq4G8D5fjcUkWUAlgHAtGnT/G4yOkFOqYV5kq2tDRg3LvpTcUR1JlDQFKu6AA+/\nrtyPLFuYr2naf6gPz7/2Vv72F39kctkgiLPiiOJBRF4AcJLPl76jqk+E+bNUdQ2ANQDQ2tpaoUPb\nCCxcCKxeDaxfDyxd6p9BCvMk23DvK8wRJhyHQnWsYtAUq7oAH+W6cgMmE/WrnfsxkFE02IKvXjir\n7P3x5BtRPKjqJaO8iz0Apro+bsl9rvbSaWDFCpP52bgROOus0oFTWIFG0PsKs4s5x6FQnQuSaYpP\nXYCPSkHOvOlNeGTZwrJBEAu/ierSFgAfFpFTYYKlzwG4NpKVxHlMSJhri/PjJApBkKApUF1A1WsC\nyqgU5FQ6KZcfeWJbuGpeC5tREsWciHwGwH8COAHAf4vIy6r6SRE5BaaE4FOqOigiXwPwLExpwYOq\nuiOSBcel87afsGup4vo4iUIgquW370XkKgCXquoNuY+/COB8Vf1aqe9pbW3VrVt926bESntnb1HH\nbwAQoKgtARFVJiLtqtoa9TrCULX3rzjX+rCmica4oO9hQTJNVasL8G6L1ZKTYeobMJ3FBYDm/uOp\nOSIKhTeAiGsQEUUtFVECBQmaqlIXEHU/JOfUnTN/7qyWiXh933vIZJWn5oho9FgUTVR3KgZN1aoL\niLofkvfU3crLZ+fXxVNzRDRqoymKrtYWF7fOiEYlUJ8mVX0awNNh/uCo+yGVOnXHYImIQjHSouhq\nZaiY+SIatcg6gsehHxJbCxBR1Yy0WWW1ju2zHQDRqEU6RoVBCxHVtZEURVfr2H5bG5BKmXl0qRTb\nARCNQOJnzxER1ZUwx6l4OS1mKrSaISJ/DJqIiMISVqF1NY7tb9hgtuZUzZ/cniMaNgZNRERhiHuh\nNbt1E40agyYiojDEvdC6mtt+RGMEgyYiojAkIZPDbt1Eo8KgiYgoDPWSyWEDTKKSGDQREYUl6Zmc\nuNdlEUXMinoBREQUE351WUSUx6CJiKhepdPAqlXmzyCcuizbjm9dFlGEuD1HRFSPRrLVVi91WURV\nwqCJiKgejbQFQtLrsoiqiNtzRET1iFttRKEbU5mm9s5ebOrowYKZzRwUTETxEvZRf261EYVuzARN\n7Z29+PzaTegfzKIxZeGhGxYwcCKieKjWUX9utRGFasxsz23q6EH/YBZZBQYGs9jU0RP1koiIDB71\nJ0qEMRM0LZjZjMaUBVuAhpSFBTObo14SEZHB+iOiRBgz23PzpjfhoRsWsKaJiOKH9UdEiTBmgibA\nBE4Mlogollh/RBR7Y2Z7joiIiGg0GDQRERERBcCgiYiIiCgABk1EREREATBoIiIiIgqAQRMRERFR\nAAyaiIiIiAJg0EREREQUAIMmIiIiogBEVcO/U5EDADpDv+OC4wEcrOL9R6meHxtQ349vLD+26ap6\nQq0WU001eP8araS/zrj+aHH9/gK9h1UlaKo2Edmqqq1Rr6Ma6vmxAfX9+PjYqBaS/lxw/dHi+keH\n23NEREREATBoIiIiIgogqUHTmqgXUEX1/NiA+n58fGxUC0l/Lrj+aHH9o5DImiYiIiKiWktqpomI\niIiophg0EREREQWQqKBJRC4VkZ0isktE/inq9YRJRKaKyIsi8pqI7BCRm6NeU9hExBaR34rIU1Gv\nJUwiMklEHhWR34vI6yKyMOo1hUlEvp57TW4XkUdEZHzUaxrrROQcEdkkIi+LyFYRmR/1moZLRG7K\n/ZvZISJ3R72ekRCRb4iIisjxUa9lOETke7n/978TkV+IyKSo11RJXK7/iQmaRMQGcB+AywCcCeAa\nETkz2lWFahDAN1T1TAALANxYZ48PAG4G8HrUi6iCewD8j6p+BMDZqKPHKCJTAPwDgFZVnQPABvC5\naFdFAO4G8C+qeg6AlbmPE0NELgJwBYCzVXU2gH+LeEnDJiJTAXwCQFfUaxmB5wHMUdW/BPAHALdE\nvJ6y4nT9T0zQBGA+gF2q2qGq/QB+AvOPri6o6j5V3Zb7+yGYC++UaFcVHhFpAfA3ANZGvZYwichE\nABcAeAAAVLVfVd+JdlWhSwE4SkRSACYA2BvxeghQAMfm/j4RyXtOlgO4U1X7AEBV90e8npH4DwDf\ngnkuEkVVn1PVwdyHmwC0RLmeAGJz/U9S0DQFwJuuj7tRR0GFm4jMAHAugM3RriRUq2HeYLJRLyRk\npwI4AOCHua3HtSJydNSLCouq7oHJAnQB2AfgXVV9LtpVEYAVAL4nIm/CPD+xzhT4OA3AX4vIZhH5\nlYicF/WChkNErgCwR1VfiXotIbgewDNRL6KC2Fz/U1H8UCpNRP4CwHoAK1T1vajXEwYRWQxgv6q2\ni0hb1OsJWQrAXAA3qepmEbkHwD8BuDXaZYVDRJpgfqM7FcA7AH4uIl9Q1R9Hu7L6JyIvADjJ50vf\nAbAIwNdVdb2I/C1MpvOSWq6vkgrrTwE4DqYU4TwAPxORmRqjHjgV1v9tmK252Cq3flV9Ineb78CU\nhjxUy7UlWZKCpj0Apro+bsl9rm6ISANMwPSQqj4W9XpC9DEAS0TkUwDGAzhWRH6sql+IeF1h6AbQ\nrapOVvBRmKCpXlwC4I+qegAAROQxAB8FwKCpylS1ZBAkIutgagQB4OeI4bZ3hfUvB/BYLkh6SUSy\nMINYD9RqfZWUWr+InAXzS8QrIgKYa9E2EZmvqn+q4RLLKvf/HwBE5MsAFgNYFKdgtYTYXP+TtD23\nBcCHReRUEWmEKUZ9MuI1hUbMv74HALyuqv8e9XrCpKq3qGqLqs6Aed5+WScBE3Jvkm+KyOm5Ty0C\n8FqESwpbF4AFIjIh9xpdhDoqdE+wvQAuzP39YgBvRLiWkXgcwEUAICKnAWhEdSbXh05VX1XVyao6\nI/ee1g1gbpwCpkpE5FKYcoklqno46vUEEJvrf2IyTao6KCJfA/AszAmeB1V1R8TLCtPHAHwRwKsi\n8nLuc99W1acjXBMFcxOAh3L/mDsA/F3E6wlNbsvxUQDbYNL4v0XyxzDUg68AuCdXnH8EwLKI1zNc\nDwJ4UES2A+gH8KUEZDvqyb0AxgF4Ppct26SqX412SaXF6frPMSpEREREASRpe46IiIgoMgyaiIiI\niAJg0EREREQUAIMmIiIiogAYNBEREREFwKCJiIiIKAAGTUREREQB/D/etAxET9/pKAAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ea3910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import sklearn.decomposition as decomp \n",
    "\n",
    "pca = decomp.PCA(n_components=2)\n",
    "pca.fit(Data)\n",
    "pca.components_\n",
    "\n",
    "Data_transformed_pca_ = Data.dot(pca.components_)\n",
    "fig = plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(Data[:,0],Data[:,1],'.')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(Data_transformed_pca_[:,0],Data_transformed_pca_[:,1],'.r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1130795d0>]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CZ4iG0ptJO+hEhAULoKsr+N6yZVqSGyKFJqkI2Xa55Vpuau/q4ZltB/tnowyM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\nZlaBmyYzMzOzCtw0mZmZmVXwG4n4O4r+kcy3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1198b0f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=2, random_state=0).fit(Data)\n",
    "kmeans.cluster_centers_\n",
    "Data_transformed_kmeans = Data.dot(kmeans.cluster_centers_)\n",
    "fig = plt.figure(figsize=(10,5))\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(Data[:,0],Data[:,1],'.')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(Data_transformed_kmeans[:,0],Data_transformed_kmeans[:,1],'.r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "28.4076582671\n"
     ]
    }
   ],
   "source": [
    "# But in K-means they are not orthogonal\n",
    "print pca.components_[:,0].dot(pca.components_[:,1])\n",
    "print kmeans.cluster_centers_[:,0].dot(kmeans.cluster_centers_[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# http://scikit-learn.org/stable/auto_examples/plot_digits_pipe.html\n",
    "#  Code source: Gaël Varoquaux\n",
    "# Modified for documentation by Jaques Grobler\n",
    "# License: BSD 3 clause\n",
    "\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import linear_model, decomposition, datasets\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "X_digits = digits.data\n",
    "y_digits = digits.target\n",
    "\n",
    "X_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11342fb10>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113411f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "which = 200\n",
    "print y_digits[which]\n",
    "plt.imshow(X_digits[which].reshape(8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SHH744eXNLu4JkuSFF14o7Q0fPny9j/f7/fLr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\n8pOf/KST7ubyP//zP5103/KWt5Q3Z8yYUd78/ve/X95Mkql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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a70c610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "pca = decomp.PCA(n_components=64,svd_solver='auto')\n",
    "pca.fit(X_digits)\n",
    "fig = plt.figure(figsize=(20,20))\n",
    "for i in range(64):\n",
    "    plt.subplot(8,8,i+1)\n",
    "    plt.imshow(pca.components_[i,:].reshape(8,8),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout(h_pad=.01, w_pad=.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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06CG7tQe5Xbt2slt7mJ9++mnZvWAd0+DBg2W3dk8PHz5c9pEjR8puXavWHuac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\n9dUQ0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a0ad910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=200, random_state=0).fit(X_digits)\n",
    "fig = plt.figure(figsize=(10,20))\n",
    "for i in range(200):\n",
    "    plt.subplot(20,10,i+1)\n",
    "    plt.imshow(kmeans.cluster_centers_[i,:].reshape(8,8),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout(h_pad=.01, w_pad=.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from sklearn.datasets import fetch_mldata\n",
    "# mnist = fetch_mldata('MNIST original', data_home='./Data/mldata/')\n",
    "# X_digits = mnist.data\n",
    "# y_digits = mnist.target\n",
    "\n",
    "# X_digits.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X_digits, y_digits, test_size=0.33)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.981481481481\n"
     ]
    },
    {
     "data": {
      "image/png": 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Tojg/h8c/sZzcbP0nF5HkUZ/+FHJ3fv+fNhPu7OO7n76GOaU6AUtEkkuHnVPob360i3Wt\nh3jo5ktoaqhMdjkiIgr9qfKTnUf4i5fe5ENL5nPP+xqSXY6ICBBn6JvZKjPbYWY7zezBcbbXmdkr\nZrbFzH5oZjVjtpea2T4z+0aiCp/JDhw7wee/u5Hzq4v5ykd0ApaIzBwThr6ZZQOPAzcDi4E7zWzs\nNYAfA5529yXAauDRMdv/FPjR5Mud+U4ODfOZNS30Dw7zv+5aQfEsDZuIyMwRz5F+E7DT3Xe5+wDw\nLHDrmDaLgVeD5ddit5vZCmAu8IPJlzvz/dm/b2fT3i6++tErWTSnONnliIi8SzyhvwDYG/N4X7Au\n1mbg9mD5NqDEzKrMLAv4S+CBM72Amd1rZs1m1tzR0RFf5TPQv7Ts45mfhvn0+xu45Yr5yS5HROQ9\nEjWQ+wCw0sw2AiuBdmAY+Cyw1t33nenJ7v6Euze6e2N1dXWCSppe2w9086UXtnJ1QyV/sEonYInI\nzBRPh3M7UBvzuCZYN8rd9xMc6ZtZMfARd+8ys2uB95vZZ4FiIM/Metz9PYPBqezYiUF+Z02I0vxc\n/voTy8jRCVgiMkPFE/obgAvNrIFo2N8BfCK2gZnNBjrdfQR4CHgSwN0/GdPmbqAx3QIf4C9/sIP2\nyAmevfca5pToBCwRmbkmPCR19yHgPmAdsB14zt1bzWy1mX04aHY9sMPM3iI6aPvIFNU7I/347SNc\nf3E1jfU6AUtEZra45hO6+1pg7Zh1D8csPw88P8HfeAp46qwrnOE6ewfYdaSXjzbWTtxYRCTJ1Pk8\nSS3hCAAr6iqSXImIyMQU+pMUaouQk2UsqSlLdikiIhNS6E9SKBzhsgVl5OdmJ7sUEZEJKfQnYXB4\nhM17u1ixUF07IpIaFPqTsG1/NyeHRtSfLyIpQ6E/CaFgELexXqEvIqlBoT8JobYIC8oLmKs7YolI\nilDonyN3J7Qnoq4dEUkpCv1ztP9YPwe7+xX6IpJSFPrnKKSTskQkBSn0z1FLOEJBbjaXzCtJdiki\nInFT6J+jUDjC0tpyXUZZRFKKEusc9A0Mse1At7p2RCTlKPTPwea9xxgecYW+iKQchf45aGmLDuIu\nW1ie5EpERM6OQv8chMIRFs0pprwwL9mliIicFYX+WRoZcVraIrrImoikJIX+Wdp1pJeuvkH154tI\nSlLon6VTd8partAXkRSk0D9LoXCE8sJczp9dlOxSRETOWlyhb2arzGyHme00swfH2V5nZq+Y2RYz\n+6GZ1QTrl5rZ62bWGmz7eKJ3YLqF2iIsX1hBVpYluxQRkbM2YeibWTbwOHAzsBi408wWj2n2GPC0\nuy8BVgOPBuv7gP/i7pcBq4Cvm1nKznPs6htg5+Ee9eeLSMqK50i/Cdjp7rvcfQB4Frh1TJvFwKvB\n8muntrv7W+7+drC8HzgMVCei8GTY2NYFwHLN3BGRFBVP6C8A9sY83hesi7UZuD1Yvg0oMbOq2AZm\n1gTkAe+MfQEzu9fMms2suaOjI97ap10oHCE7y7iytizZpYiInJNEDeQ+AKw0s43ASqAdGD610czm\nA88Av+nuI2Of7O5PuHujuzdWV8/cLwKhcITLziulMC8n2aWIiJyTeNKrHaiNeVwTrBsVdN3cDmBm\nxcBH3L0reFwKfA/4Q3f/aSKKTobB4RE27e3i41fVTtxYRGSGiudIfwNwoZk1mFkecAfwYmwDM5tt\nZqf+1kPAk8H6POAFooO8zyeu7On35oHjnBgc1iCuiKS0CUPf3YeA+4B1wHbgOXdvNbPVZvbhoNn1\nwA4zewuYCzwSrP8Y8AHgbjPbFPwsTfROTIdQuBPQnbJEJLXF1Tnt7muBtWPWPRyz/DzwniN5d18D\nrJlkjTNCqK2L+WX5nFdekOxSRETOmc7IjVNLOKJLL4hIylPox+HAsRO0d53QlTVFJOUp9OPQEo6e\nlKX+fBFJdQr9OITCEfJzs1h8XmmySxERmRSFfhxCbRGW1JSTm63/XCKS2pRiE+gfHKa1/Zi6dkQk\nLSj0J7Bl3zGGRlyDuCKSFhT6EwjpTlkikkYU+hMIhSOcP7uIyqK8ZJciIjJpCv0zcHda2nRSloik\nD4X+Gew52kdn74AGcUUkbSj0z+BUf75CX0TShUL/DELhCKX5OSyqLk52KSIiCaHQP4NQuJPldRVk\nZVmySxERSQiF/mkcOzHIW4d6ND9fRNKKQv80NrapP19E0o9C/zRawhGyDK6sLU92KSIiCaPQP41Q\nW4RL55dSNCuum4uJiKQEhf44hoZH2NTWpa4dEUk7Cv1x7Dh0nN6BYYW+iKSduELfzFaZ2Q4z22lm\nD46zvc7MXjGzLWb2QzOridn2KTN7O/j5VCKLnyotpy6yppk7IpJmJgx9M8sGHgduBhYDd5rZ4jHN\nHgOedvclwGrg0eC5lcAfA1cDTcAfm9mMT9JQOMKcklnUVBQkuxQRkYSK50i/Cdjp7rvcfQB4Frh1\nTJvFwKvB8msx238ZeNndO909ArwMrJp82VMr1BZhRV0FZjopS0TSSzyhvwDYG/N4X7Au1mbg9mD5\nNqDEzKrifC5mdq+ZNZtZc0dHR7y1T4nD3f3s7Tyh/nwRSUuJGsh9AFhpZhuBlUA7MBzvk939CXdv\ndPfG6urqBJV0blradNMUEUlf8UxCbwdqYx7XBOtGuft+giN9MysGPuLuXWbWDlw/5rk/nES9Uy4U\njpCXk8Vl55UmuxQRkYSL50h/A3ChmTWYWR5wB/BibAMzm21mp/7WQ8CTwfI64CYzqwgGcG8K1s1Y\noXCEJQvKmJWTnexSREQSbsLQd/ch4D6iYb0deM7dW81stZl9OGh2PbDDzN4C5gKPBM/tBP6U6AfH\nBmB1sG5G6h8c5o32bvXni0jaiusaA+6+Flg7Zt3DMcvPA8+f5rlP8vMj/xmtdf8xBoZH1J8vImlL\nZ+TGCOmkLBFJcwr9GKFwhLqqQqpLZiW7FBGRKaHQD7g7oXBEN00RkbSm0A+0dfZxpGeAFfUKfRFJ\nXwr9wKn+fM3cEZF0ptAPhMIRSmblcOGckmSXIiIyZRT6gVA4wtKF5WRn6SJrIpK+FPrA8f5Bdhw6\nrq4dEUl7Cn1g094u3NWfLyLpT6FPtGvHDJbWlie7FBGRKaXQJxr6F88toSQ/N9mliIhMqYwP/eER\nZ1Nbl7p2RCQjZHzov334OMdPDin0RSQjZHzo66QsEckkCv1whNnFeSysLEx2KSIiUy7jQ78lHGH5\nwgrMdFKWiKS/jA79Iz0n2XO0T107IpIxMjr0W9SfLyIZJqNDP9QWITfbuHxBWbJLERGZFpkd+nsi\nXL6gjPzc7GSXIiIyLeIKfTNbZWY7zGynmT04zvaFZvaamW00sy1mdkuwPtfMvm1mW81su5k9lOgd\nOFcnh4bZ0n5Md8oSkYwyYeibWTbwOHAzsBi408wWj2n2R8Bz7r4MuAP4ZrD+o8Asd78CWAH8tpnV\nJ6b0yWnd383A0Ij680Uko8RzpN8E7HT3Xe4+ADwL3DqmjQOlwXIZsD9mfZGZ5QAFwADQPemqE0CD\nuCKSieIJ/QXA3pjH+4J1sb4M3GVm+4C1wOeD9c8DvcABoA14zN07x76Amd1rZs1m1tzR0XF2e3CO\nQuEItZUFzCnNn5bXExGZCRI1kHsn8JS71wC3AM+YWRbRbwnDwHlAA3C/mZ0/9snu/oS7N7p7Y3V1\ndYJKOj13pzkcUX++iGSceEK/HaiNeVwTrIt1D/AcgLu/DuQDs4FPAC+5+6C7Hwb+H9A42aIna1/k\nBB3HT6prR0QyTjyhvwG40MwazCyP6EDti2PatAE3ApjZpURDvyNYf0Owvgi4BngzMaWfu5a2aH/+\ncoW+iGSYCUPf3YeA+4B1wHais3RazWy1mX04aHY/8Gkz2wx8F7jb3Z3orJ9iM2sl+uHxv919y1Ts\nyNkIhSMU5WVz8dySZJciIjKtcuJp5O5riQ7Qxq57OGZ5G3DdOM/rITptc0YJhSMsXVhOTnZGn5sm\nIhko41Kv9+QQ2w90axBXRDJSxoX+5r1djLj680UkM2Vc6J+6U9YyHemLSAbKvNBvi3DR3GLKCnKT\nXYqIyLTLqNAfGXFawhHNzxeRjJVRof9ORw/d/UMsV9eOiGSojAr9kC6yJiIZLuNCv6Iwl4bZRcku\nRUQkKTIu9FfUVWBmyS5FRCQpMib0O3sH2HWkV/PzRSSjZUzoj940RYO4IpLBMib0Q20RcrKMK2vL\nk12KiEjSZE7ohyNctqCM/NzsZJciIpI0GRH6g8MjbN7bpa4dEcl4GRH62/Z3c3JoRPPzRSTjZUTo\nnzopa3md+vNFJLNlRui3RVhQXsD8soJklyIiklQZEfot4Yjm54uIkAGhv7/rBAeO9bNiobp2RETS\nPvR/fpG1yiRXIiKSfHGFvpmtMrMdZrbTzB4cZ/tCM3vNzDaa2RYzuyVm2xIze93MWs1sq5nlJ3IH\nJhIKRyjIzeaS+SXT+bIiIjNSzkQNzCwbeBz4ILAP2GBmL7r7tphmfwQ85+7fMrPFwFqg3sxygDXA\nb7j7ZjOrAgYTvhdn0NIW4craMnKz0/5LjYjIhOJJwiZgp7vvcvcB4Fng1jFtHCgNlsuA/cHyTcAW\nd98M4O5H3X148mXHp29giNb93ZqfLyISiCf0FwB7Yx7vC9bF+jJwl5ntI3qU//lg/UWAm9k6M2sx\nsy+O9wJmdq+ZNZtZc0dHx1ntwJls2XeM4RFX6IuIBBLV53En8JS71wC3AM+YWRbR7qP3AZ8Mft9m\nZjeOfbK7P+Huje7eWF1dnaCSfj6Iu6xWoS8iAvGFfjtQG/O4JlgX6x7gOQB3fx3IB2YT/VbwI3c/\n4u59RL8FLJ9s0fEKhSNcUF1ERVHedL2kiMiMFk/obwAuNLMGM8sD7gBeHNOmDbgRwMwuJRr6HcA6\n4AozKwwGdVcC25gGIyNOS1tEXTsiIjEmnL3j7kNmdh/RAM8GnnT3VjNbDTS7+4vA/cDfmtnvEh3U\nvdvdHYiY2deIfnA4sNbdvzdVOxNr15FeuvoGFfoiIjEmDH0Ad19LtGsmdt3DMcvbgOtO89w1RKdt\nTqvRO2Up9EVERqXt5PVQOEJZQS7nzy5OdikiIjNG+oZ+0J+flWXJLkVEZMZIy9Dv6htg5+Eede2I\niIyRlqG/sa0LgOW6PaKIyLukZeiHwhGys4wra8uSXYqIyIyStqG/eH4phXlxTU4SEckYaRf6Q8Mj\nbNrbpf58EZFxpF3ov3nwOCcGh3V7RBGRcaRd6Id0UpaIyGmlZejPK83nvLJpvUGXiEhKSMvQX1FX\ngZlOyhIRGSutQv/gsX7au06oP19E5DTSKvRb2tSfLyJyJmkV+qFwhFk5WSyeXzpxYxGRDJRWod8c\njnBlTTl5OWm1WyIiCZM26dg/OExr+zH154uInEHahH53/yAfWjKf9184O9mliIjMWGlzcZo5Jfn8\n1R3Lkl2GiMiMljZH+iIiMjGFvohIBokr9M1slZntMLOdZvbgONsXmtlrZrbRzLaY2S3jbO8xswcS\nVbiIiJy9CUPfzLKBx4GbgcXAnWa2eEyzPwKec/dlwB3AN8ds/xrw/cmXKyIikxHPkX4TsNPdd7n7\nAPAscOuYNg6cOiOqDNh/aoOZ/RqwG2idfLkiIjIZ8YT+AmBvzON9wbpYXwbuMrN9wFrg8wBmVgz8\nAfAnZ3oBM7vXzJrNrLmjoyPO0kVE5GwlaiD3TuApd68BbgGeMbMsoh8G/8Pde870ZHd/wt0b3b2x\nuro6QSWJiMhY8czTbwdqYx7XBOti3QOsAnD3180sH5gNXA38upn9BVAOjJhZv7t/Y9KVi4jIWTN3\nP3MDsxzgLeBGomG/AfiEu7fGtPk+8I/u/pSZXQq8AizwmD9uZl8Getz9sQlerwMIn9vuJNVs4Eiy\ni5hm2ufMoH1ODXXuPmFXyYRH+u4+ZGb3AeuAbOBJd281s9VAs7u/CNwP/K2Z/S7RQd27faJPk9O/\nXkr275hZs7s3JruO6aR9zgza5/QS12UY3H0t0QHa2HUPxyxvA66b4G98+RzqExGRBNIZuSIiGUSh\nnzhPJLuAJNA+ZwbtcxqZcCBXRETSh470RUQyiEL/HJjZk2Z22MzeiFlXaWYvm9nbwe+0uYWXmdUG\nF9TbZmatZvaFYH0673O+ma03s83BPv9JsL7BzH4WXHzwH80sL9m1JpqZZQcXT/z34HFa77OZ7TGz\nrWa2ycyag3Vp+95W6J+bpwjpVYrnAAACcUlEQVRORovxIPCKu19I9DyF91yNNIUNAfe7+2LgGuBz\nwUX30nmfTwI3uPuVwFJglZldA3yF6Fnmi4AI0RMT080XgO0xjzNhn3/R3ZfGTNNM2/e2Qv8cuPuP\ngM4xq28Fvh0sfxv4tWktagq5+wF3bwmWjxMNhAWk9z57zOVDcoMfB24Ang/Wp9U+A5hZDfAh4O+C\nx0aa7/NppO17W6GfOHPd/UCwfBCYm8xipoqZ1QPLgJ+R5vscdHNsAg4DLwPvAF3uPhQ0Ge/ig6nu\n68AXgZHgcRXpv88O/MDMQmZ2b7Aubd/baXOP3JnE3d3M0m5aVHDV1H8G/pu7d0cPAqPScZ/dfRhY\namblwAvAJUkuaUqZ2a8Ah909ZGbXJ7ueafQ+d283sznAy2b2ZuzGdHtv60g/cQ6Z2XyA4PfhJNeT\nUGaWSzTw/8Hd/yVYndb7fIq7dwGvAdcC5cH1qGD8iw+msuuAD5vZHqL3zbgB+CvSe59x9/bg92Gi\nH+5NpPF7W6GfOC8CnwqWPwX8WxJrSaigX/fvge3u/rWYTem8z9XBET5mVgB8kOhYxmvArwfN0mqf\n3f0hd69x93qid8B71d0/SRrvs5kVmVnJqWXgJuAN0vm9rZOzzp6ZfRe4nuiV+A4Bfwz8K/AcsJDo\nVUI/5u5jB3tTkpm9D/hPYCs/7+v9EtF+/XTd5yVEB/CyiR4cPefuq83sfKJHwZXARuAudz+ZvEqn\nRtC984C7/0o673Owby8ED3OA77j7I2ZWRbq+txX6IiKZQ907IiIZRKEvIpJBFPoiIhlEoS8ikkEU\n+iIiGUShLyKSQRT6IiIZRKEvIpJB/j9htTBinEK2OwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114c20ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "logistic = linear_model.LogisticRegression()\n",
    "scores = []\n",
    "n_components = range(5,60,5)\n",
    "for n_component in n_components:\n",
    "    pca = decomp.PCA(n_components=n_component,svd_solver='auto')\n",
    "    X_transformed = pca.fit_transform(X_train)\n",
    "    logistic.fit(X_transformed,y_train)\n",
    "    X_transformed_test = pca.transform(X_test)\n",
    "    y_pred = logistic.predict(X_transformed_test)\n",
    "    score = accuracy_score(y_test,y_pred)\n",
    "#     print score\n",
    "    scores.append(score)\n",
    "plt.plot(n_components,scores)\n",
    "print np.max(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.968013468013\n"
     ]
    },
    {
     "data": {
      "image/png": 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sVESkWigDQomajERE9hHOgFBWgRkc0kY1BBGRKuEMCJEoGW3SaNVK8ymLiFQJ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\nEEREJKCAICIigAKCiIgEFBBERASA/w8SO7Zci3vNWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a0ad850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "logistic = linear_model.LogisticRegression()\n",
    "scores = []\n",
    "n_clusters = range(5,200,5)\n",
    "for n_cluster in n_clusters :\n",
    "    kmeans = KMeans(n_clusters=n_cluster, random_state=0).fit(X_train)\n",
    "    X_transformed = X_train.dot(kmeans.cluster_centers_.T)\n",
    "    logistic.fit(X_transformed,y_train)\n",
    "    X_transformed_test = X_test.dot(kmeans.cluster_centers_.T)\n",
    "    y_pred = logistic.predict(X_transformed_test)\n",
    "    score = accuracy_score(y_test,y_pred)\n",
    "#     print score\n",
    "    scores.append(score)\n",
    "plt.plot(n_clusters,scores)\n",
    "print np.max(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96464646464646464"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logistic.fit(X_train,y_train)\n",
    "# X_transformed_test = X_test.dot(kmeans.cluster_centers_.T)\n",
    "y_pred = logistic.predict(X_test)\n",
    "accuracy_score(y_test,y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Previous floor plan example that we had with PCA and SC "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(696, 4096)\n",
      "(999, 2500)\n"
     ]
    },
    {
     "data": {
      "image/png": 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AHGGCBQAAAACOUCKIeONZiSDgEGVXSBScq0gIlAgiQVAiCAAAAADRxAQLAAAA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YZ4FE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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10efde450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "\n",
    "\n",
    "from sklearn.datasets import fetch_olivetti_faces\n",
    "\n",
    "\n",
    "#Chairs\n",
    "path = \"./Data/chairs.csv\"\n",
    "D = pd.read_csv(path,header=None)\n",
    "image_shape = (64,64)\n",
    "Images = D.values[:]\n",
    "print Images.shape\n",
    "\n",
    "\n",
    "# floorplan\n",
    "path = \"./Data/1000FloorPlans.csv\"\n",
    "D = pd.read_csv(path,header=None)\n",
    "image_shape = (50, 50)\n",
    "faces = D.values[:]\n",
    "# faces[faces>0] = -1\n",
    "# faces[faces==0] = 1\n",
    "# faces[faces==-1] = 0\n",
    "Images = faces[:]\n",
    "print Images.shape\n",
    "\n",
    "\n",
    "# # Mnist data set\n",
    "# image_shape = (28, 28)\n",
    "# dataset = fetch_mldata('MNIST original')\n",
    "# # faces = dataset.data\n",
    "# X = faces[:]\n",
    "# X.shape\n",
    "\n",
    "\n",
    "fig = plt.figure(figsize=(12,12))\n",
    "for i in range(25):\n",
    "    plt.subplot(5,5,i+1)\n",
    "    plt.imshow(Images[i].reshape(image_shape),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(49950, 256)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.feature_extraction.image import extract_patches_2d\n",
    "rng = np.random.RandomState(0)\n",
    "patch_size = (16, 16)\n",
    "buffer = []\n",
    "for img in Images:\n",
    "        data = extract_patches_2d(img.reshape(image_shape), patch_size, max_patches=50,\n",
    "                                  random_state=rng)\n",
    "        data = np.reshape(data, (len(data), -1))\n",
    "        buffer.extend(data)\n",
    "Patch_Images = np.asarray(buffer)\n",
    "print Patch_Images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nVX/6p39azF133XUt2AbmtyuvvDKU27t3bzEzPDwcmjU6OhrKwemInOnIea4qZ5p3Ghoa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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dc8f750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,12))\n",
    "for i in range(25):\n",
    "    plt.subplot(5,5,i+1)\n",
    "    plt.imshow(Patch_Images[1000+i].reshape(patch_size),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "means = Patch_Images.mean(axis=1)[:,np.newaxis]\n",
    "Vars = Patch_Images.std(axis=1)**2 +.05\n",
    "denom = np.sqrt(Vars)[:,np.newaxis]\n",
    "Patch_Images = (Patch_Images-means)/denom\n",
    "# /"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# If we run PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110cd7310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "pca = decomposition.PCA(n_components=64,svd_solver='auto')\n",
    "\n",
    "# Be careful! it might crash with larger matrices\n",
    "pca.fit(Patch_Images[:10000])\n",
    "fig = plt.figure(figsize=(20,20))\n",
    "for i in range(64):\n",
    "    plt.subplot(8,8,i+1)\n",
    "    plt.imshow(pca.components_[i,:].reshape(patch_size),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout(h_pad=.01, w_pad=.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# If we run Kmeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "kmeans = KMeans(n_clusters=200, random_state=0).fit(Patch_Images)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fZsrK5icVGKSB7ZDvoRrshDHHo8C1a9f6/GVeZyKmu/BxdzPzdJFNepgHA3Fg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4H1y2Uwc4raEVoxySkzKdtZWzV9qd3ejJZHmS1ZW2MfYnlqVz/mYSbuXHc0ZbN2RVOa2uHb8jOT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2PpQpDO+dIyhV8rPymeeANp5UxLGR6TTfE+uBERgjpu147ty5nv7mN785TOf8TJrATt4r03GF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r\n+p/+6Z96+T/96U/XNK67uHbgdfv6Mxkek08wWWPWSxCuj9hXfq1j8g+s/9q1a2v6R3/0R3v5MbDH\n//zP/9Q09uXFixdr2gdFacnCFvG4kmHRoBjziOqL/YumfqyLl7Tgb/OkJNPptHoKwb714w/nBq4P\n2H/4vZcfbd68uaZxbF26dKmmo7GJ5WHdsCz0VOU5c+ZMTWM7/tu//RvNg+jOI4QQQgghRo8eioUQ\nQgghxOgZHLyjvK6Pdhwy0wMzGUfyBWamiSQaGRNS1nl6y1m8p5i7ss7FWZ2iXaZZx+8Fb3plbZJx\nGO7JmOWm02n1GhF5U0AH77/5m79Z0z/3cz9X0+jQ/Tvf+U4v/7Fjx2oapRUoYUBTC5r3zPomGTTj\noSkLy8XzmfVNNSU/7qBmRMEH2O7ZbECRofKHaPc+zmWcf2zHuv9tnhkSg1REDvPH7O0i63UHYX3g\n+wP7NLN+ZXfPZ6QYZsOc689ms2oOxfnpzb8soAkb116WcO7cuZo+cuRITaP3CVwTMLiQ/7yIRxAk\n0z6z2axeQ7SGs35AUzqa5/06z7wmYXs999xzNY3eJszMNm3aVNNf//rXaxrXd6x/5D2j9HnG+0Qk\nVWO/ZftnqOTL15d5+sGy8BjvQYGtzy2m02mVJrCgar4cJo3B+7aXHz3++OM1/da3vrWm8V6L48zn\nR0klep7CemL74PgxM9u/f39NHz16tKYlnxBCCCGEECKJHoqFEEIIIcTo0UOxEEIIIYQYPYMj2hV9\nTaTbzWof2fdMQ8fKilyyZTR4kX43Q7neKHpYFBWqwDRFHtSZMfcl3p1ORi/IosN5Mu1z69atpv7P\nnxv1Upj+7Gc/W9Of+cxnanrfvn29/KjtYy7HIvcx6PII2wjdAWG7ogs4s77Gq+TxxyCl7SKdGhvz\nmbngf8tE44s0ycylVcbtYavs6Bjvbuh2ko2qdqfyDwXXWlYPXxemmUV99gMPPNDLjzpBVhaOAe9u\nkLkuZFpLP0dba3Xk+q+lnfXjj2krWXQ77zIS5z66kfrKV75S03hN3/3ud3v5UePo9catunjweqLI\nY0g5jkXtM+u3C/7GXGZ6l2h4HLufPfvsszXwhgUmAAAgAElEQVSN+y3M+mPvwIEDNY3RAfG+Fel/\nW+dmRO2Jn1lbR/siMvt7ov0jeG9k6yu2ie8r7Aev4fbMZrM6HvG8fv8GtgOOAawH6sj9PfX555+v\naeZSENvK52duItn64nXaXmM8FL0pFkIIIYQQo0cPxUIIIYQQYvQsHNEucsnEXnmz6FbepMDMscyE\nmY2oh+nITVHrt8hkWq43e02Z6HS+DdDEwUzXkUyA1Q1NDxlTkFlsDmqdk40Bs755EaNEvfTSSzX9\n+c9/vqa9SzQ07zCJCLaFNxWhSQ/7Hc1U6ErGu8TB9muZdj0Z0zsz17H+icpkx0VyAOb6JuO+yDPP\nfR+6k2J1MJvvbmgeQ6NURpHX3gz5RNd1TTlB5BKNrXsoS9myZUsv/2OPPVbTGIkKTaUnTpyo6Zdf\nfrmXP4re2CLjfjOST5S1BI/x5lMWOY65ofJrGJpf0Ux8+PDhmsY29RIJjMrGJAfRmjg0euhsNqvX\nzKJ6+jozSUskNWBzHtfglovKApOhYf5IFhO5EYtgsiL/mT3TRH2QWRfwez/W8De8N+GaiPUqEekK\n2KcoVWiRfX5DsB7Z8YtzBo9jUfo8mXtWdP7IXWMGvSkWQgghhBCjRw/FQgghhBBi9Ax+t1xeoWdf\nf7Pd71nzBHvNH+2yZRGNMtHtzPpmjPL6PTKNlN8wX7STntUpa+bB4zBa286dO2t648aNvfxobkDz\nIJpGI9MZk6FEEYVa0hN/XWhiO3XqVE2jGQ5NtH5HNDMtZ7wm+DysL9AcG8li5pnV0XzFosOV41rl\nZ6JjZX/D6/DnZyaryLS5HEpdIkkGM5dl1xHWpmwdG2KevRNg9CnmNcCMXwuuRRghCqNNmZn9yq/8\nSk2/973vremzZ8/W9Oc+97ma/u///u9efjSJsp30UR/hmCrX6SVKBZw/iF+DsE2wHSJ5G6sTOw5N\n1VHkN7ZjPhvRMivVaUnVPOw3/D671kUSl0K0rmUlE0g2YmyULyufWKRsRvQMgudk147z3z9XzJNM\n+HqUto7qhL8xKRI73oxH5mXPDdkomSx/NOYzEQ89elMshBBCCCFGjx6KhRBCCCHE6Bkkn2AmvWiX\nKDMTM3O8z4+v0tFUEO36ZL+xcr1JAr0VzDOpTCaTaqJDU4o3azAZCdvd6b1HoAcE9Jiwd+/emn7f\n+95X008//TTN/9xzz9U0mkO/9rWv1fTJkyd7+bEfMY1eIjylXyOzOGszJmXw5qqhgSr8+ZkMB68x\nMtXg54xXg5ZHgShf1mMEktlxm50/zDyf9U4yT2aBJr1swBjsDyZZiq6JzWnmIcbnX64njAyTyaQp\nwfLXxTydsPXNO/jftGlTTT/88MM1jbvc0SuFX5fwPMwTTBS4KDumfP7s/GFzJvJGMtTLSzRWGNEx\nWc8urfJwPkTziV1Xdg5m2sh7+mHyCSQT5OoHDXZfMetfLwuigvlbnnoKvr1blP7J3reGShl8HiZj\nRKJ7OpPKRfMnGsMZ9KZYCCGEEEKMHj0UCyGEEEKI0TPYDlhebUe7BxF8lc3S/vU925mbDYCBr9yZ\nOSa7k3Ve7PnpdFrlDNFOxyjWdyHyZMDM2GgaXbVqVU3v3r27l3/79u01jZ4d1q5dW9NoWo3MNJkd\nr+hoP9p9zvqBmU28iYiNA7bj2PcnM6szKUcUe76kI08lpb8i7xNsbmTNiaxNs7vaMT+rJ5NY+N/m\nmZJns1n1LsIC0fjfsEwcp5FHjcwu5MzuerP+nGOmumzwnIhM8A4mBcE+xGs/fvx477ivfOUrNY1O\n99G8vW/fvppGzzVmsbeCFlGgpyHyo0jWxsZBdv1n4z9rymVjNStZYJ6GIspx0XUxLw+s36L7asas\nHq31LBBElH+5ZvHvF9ju/v6DcxO9LGE74PfLCWqE8ldcN7NSOPZclfVexAJBZYO34b0/kugt1zOS\n3hQLIYQQQojRo4diIYQQQggxevRQLIQQQgghRs8gTTFqIrMunZiWjulLIlh0rUiLxo6LtJot7SSr\n42w2qzrT6DpYlBfU6UT6vMuXL9c0ixyF2qODBw/28m/ZsqWmX3755Zr+6le/WtOvvPJKs1xP1uVX\ny0WM1x+hPhOj8D344IM1vX79elovppPLaLDN+tphHJPokorpVtn5h7pk8to5pnPGdo80+ZkokpFO\nFfuNRUlj+i4PHtcaUzdu3KhjNXKpxlxAsrnk+ymjh8zC3F6xSGqLnLPruqauP2prFvkO9cE4x836\n9f/6179e09hXGN0Odcdm/bmRiXLmiVyjZYn2pGTGvJ9/bHxhfuzfRTSMWe1sdi1prbWRHjnjni57\nXUyL7/sl2kfRKitaF+92WFQ4vycF7x94/8bvMb/fzzO0v1ptmNVqMx1w5GZ13rnNYpe8bDxFmmYE\nf2Mu7zx6UyyEEEIIIUaPHoqFEEIIIcToGSSf6LquvtrG19LR63Mmk4jkF5iHmVQzLmV8WVnXL0PM\nNLdu3arShsh8y0wb2I5ZN3VoskTTCn5/+PDhXn6MgofHoXs2NC941zHLcXMSue9i5nn8Ht1bYWQ+\ns36dF3G514oa5s+PRGWV+mdc3EQm0qzrs0I0fjPygmxEyIyrxCh/i4sXL9pnP/tZM+v3hR//zAUk\nk3RE8h90QzgvYmWLjGugSP6RkR/NZjO7du3akjpGYwXXAtZveIxZX5bFJAU4x6J1LXKJx2CyMkap\nVzYiasYNqD8vu59kyvWfmRwgap9oHDFa0UN93ox8MJI1MkkaErmawzmZcTUZ3dfLb3cq6l3kknQo\n7B5t1pc2XblypaaZ28lIksJcvWLeUpfo+Ym5ScQ8OG8jmU6mf6LnPyaliKLX4vXMc6nbQm+KhRBC\nCCHE6NFDsRBCCCGEGD2DvU+UV92RWZeZqdB8wl7Fm3GTNnuVH50/Q5Q/Y74qxzOphj8HptG0kjWb\nMfNCMbf6tNnSXeMF5h0kMp1ld0S3TJ2RqQNNudgukemZySSyO12ZeQV3AqP5GE1cvrxiUmQyh8lk\nUo+JoqLhNTLvKcyTSzlPK83ye9AMt8iOX2Se7Obq1av27LPPmll/Z7XvJzQzItiOkXwC64HnQVlR\nawd/CxbZKWpTJmOJKG3cGmMFZobG87F118P6F8e/b9fsmszq38oTmVzLMdFYZGOW9VsWVpa/VjZ/\nWZ0j+VGGruvqeSJvBBnJBBJJ3Zikhx3jz4lzDecjk1j4+txpTxQ45rF+i5w3MufjfY6Nj2hdwXrO\nW78wyuwishN2r43Gb8YjjT8migib+Z554cmiN8VCCCGEEGL06KFYCCGEEEKMnsHeJ8rrf7Yr0Iyb\nY9iuxshMwoh2H7LzIFmH8sWMEb26L+aVyCya2eEb5WfmVzSzRG2KZinmhSDaXcxMh8wh9mw2qxKE\naFc6yhFOnTpV0yj/wGMuXLjQy487czOm0kgqwzxhRGbhlvwiGlulLpH5l41fZqr3Jm02VvE8kfk4\na85kZDxmFG7cuGGHDh0ys9gkjWZGZrrF/H6XN/MCgP2MspHIow5KNrJBiLLeUFpEspfMzv1oXcH+\nZWM+Mv9iHhYgJap/S2oXrdmlvmzd83VkczcK5sIkCFlZXsZ7Ejuf/5w957y2M+Nm5azXHjaOmNeS\nSGLF2j+aQ3fK08S8c7H5ns0fycLwN7yXskBAUVAgJjtFWuNpES8liG8TdhyTDEXeL3CcMK8/0Xo6\nVEprpjfFQgghhBBC6KFYCCGEEEKIQfIJs7aZJhvYgZkeoh3J7PV91sySMeN5k2Dr9X1GbhF5P2Cm\nJBZkwLdVxrQZmZ9Z8I+Mo3n/W9b8W8qI5Ad4/eh9AuUTaFbywQeGOv/PmiqZB5LMTvchQQhaZeI1\nZky50e5fbN+spw4cH9gnbF5lvV+0TFm3bt1qekaJgm8wMxzOET+nmUcctls+uia2yzsy6UVyL1ZW\nSyoQnTPjiSK6LjTlsnNGUjW2fkSeUvCzn9uZ85vF5t9o7jKy3hQKfqwNNT9H58/mad2XfVtlggKx\ntcMsZ4rO3huiQFWZsuZ5+mHnerNgcw693Zj164/yB/x+3bp1Ne3XnqHrSjlmESlQNngGwvowkrhm\nntkiD2FMPpVFb4qFEEIIIcTo0UOxEEIIIYQYPXooFkIIIYQQo2ewS7ai5UC9kddUZfRokUu3TDSm\nrOuZodFV2G/RMS19TqRfi/TMBa8dYsdlXcQw11UZl04+f0bnhq7qsI6oWzTjblaw/VBr5d0CZTTn\nkdaT6ekyrtrYObPtw+rE9FLMzZwfa2zssfaNXOqgmzymdfZk3ZRF9fPjPeNGEPsmuqaMe7QomhfC\ntJlsvprlXCdh2ZF+bxHN3O0ko+mPtKHZNb2UU8ZBFPGLzS025n0bMjePSKSJzbhUi9bgIZr8Qiv6\nYbbdM997Mm7Y/JzBa8YIlWzPSWatzqy1Q8bYnQBdPfo+ZO3A3EYu0qcFdKmb1fmz/og0wcy1Kz7L\nZecPG/+R+1i2jyaL3hQLIYQQQojRo4diIYQQQggxehZ2yRa572KRb/C1eOQ+LDItt/JEboYyrtCi\n1/dDTOGR6YjJQJhp1LchmimZuYqZ2s1y0WiybteYSypPMXeg2cO7XcJ6lQh4Zvx60RRlxscaM5lF\n0XOYSSiSjrT6HN3JMdBE69uEmUkXcfUUucNj+dEFHkYQZOMucv83xHwVuQ5DmGu6bPQ9Ns7ZXIpg\ndY5M3dk1peXS0NcrI1nISnWYeRPHZyQLQVgf+X4d6j4pYzZHiRaTt0QmdZS3oAstLDcyiWfcUEXf\nD3Xfyc6djRSL58tI68xil1gsP6tb1u3qIpH+zPpjzLchfsZxzuShi5jjMb+PAIvnxPTq1aub+X2b\nRs9RLVp9lY3um5WaMTexGfeGZvx6s5ETh7pp9ehNsRBCCCGEGD16KBZCCCGEEKNnMmQ35mQyOW1m\nR+5cde5q9nRdt8V/OfI2MVO7tFCbtFnSLmoTjZUGapM2apelqE3aaK1dSnOseAY9FAshhBBCCPHD\niOQTQgghhBBi9OihWAghhBBCjB49FAshhBBCiNGjh2IhhBBCCDF69FAshBBCCCFGz6CIdtPptCvR\nQ6LIM1FUnQyZPBh16OGHH+79dvTo0ZrGyGHZurSioMxmM+u6bskPk8mkK9FVovJZ5DRMRxG9WHtn\nI/uwui3X+8hsNjtDXOI0C44izCwSfeZ2ko3Yg7QiHM1mM5vNZksKm06nXSYiEou2tdx5lc2f6YdF\n+vHWrVtLxgrOn2z/38415c3yvhO0fXP+3HPPPV2JmrZz5876/cmTJ3vHYfTEoZE4PWyssahwZv1o\nUhj9be3atTV9+vTpmo4iWpbzsLV2xYoVXYmQtci1LnJcZkwuMpeicll5rfnzf2V1rfIWOQfmwXus\nmdlDDz1U06+++mpNX79+fW65EctZ96P7cuZcLIppdr0YWnd/fKYfojYNflsyVvD5zX1Py2TlR/fE\nTBS8RZ7FWL2yUT5v3rzZnD+eQQ/FK1assPXr15tZPwwiPnia9UP74UNbdqBlwvTt2LGjpv/mb/6m\n99tHP/rRmt6/f3+zLhGtB1Wc+P7YcjOIwnBiWNA1a9bU9KpVq2oaByyGeTTr30zwRsjC8PpBi/lZ\nuMzsQMf8165do34PWyGYfX+yEKOZyWA2PEx1tKix0JM4vn25999//5LjL1682CxnOp32HhYKvt3x\nfCzEaLbfWDjMaF5iP7A/bVGYTgwDjnW7ePHikrEynU5rG7L+95/ZteN1RGHWMX9mffK/sYfE6GaA\n9cGybt682Zw/9913n73zne80M7OPf/zj9ftPfvKTveOeffbZmmZhaqO+Ym2BefDhyK/1uE69613v\nqun3v//9Nf1Xf/VXNX3s2LFefqxnaTMfCrewcuXK+geBhcf1dcf+weOyoa+xLPaH1p+fvdzIhhRn\noa9b86fkxxDU8+prxsM04xzctWtXL8+nPvWpmv7d3/3dmt63b19Ns/uMPw+C60X0sNNav9h92ax9\n//FtwsIps3u5/56tWSy0ua8T62ucc9FzC7a3WwuXjJUVK1bYxo0by+/1e38Pw9/82C5cuXKlebxZ\nPxw69i22A87x6I8KprEuLJS02dI/c4VTp06lfDQPeiieTCb1hNHbgyh/K509DhsIHyy3bdvWy89u\n6myx87RidLOFejabNScmDgZfJ+y0devW1TQ+IONDdDlPAc+HZWEd/c0r80eDPWD4z9n+xnMW/KLE\nxhG2F1s4zPoTkD1gRw8+2H74Gy5+bJL6c5b8mTc00UKH9WDnxnaIbn6sLlEedk7Wvh5s08xYKXWM\nHvTZ+Vj5kfWKrQnR2xnWjuxh1+dn54koZWN9/VqDn9kNDM/n16XMWhuNFfbwjWXh/PVrQqvNordT\n5WaM5fi5xB6K2YOOvxdgHja+2Prky2MPedELjOjaGKXs7B879rCO1+XvQXivYn+wo/nO8mSvESl5\nojet5RqxfN9X0YssLKvg1yH2RwePi/4AsXtu9q3o0Dfdrf6J2gSfKfA68PkiWh9azwC+XN+m7E8S\nawefP2rvDNIUCyGEEEKI0aOHYiGEEEIIMXoGySfM2q+j/evzzGYiZsL0v7FX5mg237x5cy9/JI0o\nRFKB1m/MHLFixYpqVmL1M7Oq5TEze+tb31rTTz75ZE3v3r27prdu3drLf/ny5Zr+9re/XdMHDhyo\nadyEc+rUqV5+psFjpsKoTTLta9YeKz5vxtQR6fqYLAW/R3NQJL/A8zNdr9crYf4yjjPyiaxJLNp8\nWYikAozIzMmkMqzOWf3uvLpgn2W142yt8LA2Ze0byYcym0R8+zLTNWufruvqGMR28fq/1vgz45IF\nXy/sq8ymTi/RYG2GpnecM35dbEmbmAwE6xX1R1be1aqDWawBLURrIGu7jNbYk7mX4nmi9SKzQRvX\nPX+NeA/Dccjmrb8uNIvjmGRtudwNv61jfJsw/Wm0PwFh9y+2Ri2yQS2qCzt/aw51XVfPzyQ+vo7s\n3ruITAfTbN3y18G+Z1JH/9vQtcBMb4qFEEIIIYTQQ7EQQgghhBB6KBZCCCGEEKNnsKa46DUitzXM\nX182OELGiTyW63VBzEUM06T487eujWlo7r333qoFRh1d8edcQAf873jHO2r6p37qp2r68ccfr2l0\nhG9m9tJLL9X01atXa9r7/WxdgxnXsDFNldf5MDd3zFWdWU57zHwmLxLIgblei1wcMZ0U6pQiTWbL\ntVDGLVHUNplrWkTfldGs+d9adffn90Ta9BatsnwdmG6R9ZOHaSjZ95Eek7V95JoKj4vc2WH+MrdQ\nf+fz4mfmfgznuB93TO/Ixl2kP8Q0rl/4vV8vhqy1XdfVPm75N55X38y9wIyPCczvXdshmT0B2KfR\n/Wc5wSGiMczGc6RfR5dsrF2jOcj6Nev+b4iuH/WzrN3N+vdp5o8+ch/H1kQ2ViJXk8wlaeT+jN3b\nWpriyWTSdPPo2wQ/s71IUZ9l3MRF+na2z4GRDd6RRW+KhRBCCCHE6NFDsRBCCCGEGD2D5RMtIvNT\nxiSedamTibRlxl1CZdxL+c/zXsXPZrMqZ2BuvMz6oX/Pnz9f00eOfC/y4KZNm+h5MJzzt771rZo+\nevRoTV+6dKmmMQyjrxuC7RhFnkITUMbNFkYUikzHzLUXSlEi8xUzqzPJQyQVwLZgYygKCZtx/9Jq\nO29+Yq61mGnRlxlFeWoRzd/IdU+rjtlz4u/FXBe558Pxh32TiUjl68jM24tEjmJ9no3YyZhOp3UO\neCkVwsY5u0bfV/g540opGv/MvIqSiazbPMYi7vBa5Ufyo0yUxGhNGBqRMuseMaIla4z6mo2VKPob\nC9kb5ckw5H6bZTqdNqPv+rn00EMP1fTx48drGtsd751RX7E+jeQwLPonroVR6OyMe0c8tkQCxnUT\nQ137Mq9du9asa7bP8TqY+1OfH39DCQ9+H8k28Tx4LfgMFaE3xUIIIYQQYvTooVgIIYQQQoyehb1P\nRGZj5qkAYbubfXnMpMlMdWY503lkKkXmma9u3bpVo82hqQAj0Hkw2tyhQ4dqmpmIzfptimYAPA/b\nKVrq2SITPdAsb+5DWtHbfF8xyUM2KhrbfZuRePjzIxkPJmZxn7XOVc4XRTlikhB2rij62nKj2zFY\n9Cb/2zxPC5PJpB4fSaLwNxzbrJ+iyE/s++yufza2spKJbJSyQuSpAMcBi0YWyYcy5vloLuJnPD8z\ntUf9Os/0PplMml4fsnOd9UHk/QHJRHqMjmNSpKykJaJcD+t3XxarY9QuLDIhzvFIApWJXId9Gc2T\njAeXkh/rvWHDht4xP/ETP1HTzz//fE0fPny4plGK6M32WI/Mc88ia633DsFAqQF6qCps2rTJPvjB\nDy451kfPLRILT2YNNuuvF9gma9eurWlcK86cOdPLj9eL0g4csyhB9dJQPA7b4fd///ctg94UCyGE\nEEKI0aOHYiGEEEIIMXoGySfQIXZk1skE6YhMlczMg6/lI/lEZnd4xNA8xXwQmc/RxIA7OlH+EO1o\nRhMQnifjcN+M74KOzGXI0Dbtuq4ZzML3FZpX2I7WyDyacZ7OHKSb9b1coNkGy8W64PHsOO/5A8m0\nXSY4RFZ+xMpFFjH/Zk3W80DvE9hP3mSY8WYQrSlM7sHWsUxAH19utIt+qKQFQVNn5L0lIx/y15sx\n+TITsc+DwR02btzYLMuvkRnvJgWUT0SBHDJjIgqew66XycD8WMGy2fXd7rGSkaoNrUsUQIdJUVgw\nKH/+jEQl+i2zjraCd2zevLl3zNNPP13T6AkKz4X1joLn4LWz+7Uf/5k5x2SFZv21cJ6kZOXKlXVe\n4lx99NFHe8dt3769pjG4CXruQBmTlzRlpIf4vZd64DXiObHc69ev1/S5c+d6+ZmkNIveFAshhBBC\niNGjh2IhhBBCCDF6BnufKK+wox2ymRjl0c7SyLG6r0frmOi3QtZheMssFZXFvmMygWycbxZkgJnL\nvHkw44Uj025DaAXviMzSrP6tHecFlDNgG2G7rlq1qlmuWd90hKY1Zh70dUFPIGUXrTfnIK12zc6f\nTB9myUqEWCAPJsHxZc87z2QyqXMjkgkgGfO4b5PMjv6orsyjBl47M7X7srNBKkqd0YToxy/z8sBM\n2lFQEoSZbL2nBJx/aJLFuYTH+H5tmanZejyZTOq1RN4b2JrI+j1aK9mciwKasHnCJAu+TfB6IpkH\nltXqR/9dRtYYSfjwOJSIsfGRHWvZoFpRm3tw/kSBHnbv3l3TaJLHPJj25nhWd2wHzBPJ91i5SCTR\nnLfWHj9+3P7oj/7IzPpjztcB24FJD/H6IkkVeoZg9xIvuWHBUlido4BCWc8diN4UCyGEEEKI0aOH\nYiGEEEIIMXr0UCyEEEIIIUbPYE1x0W9ktE5my3MvY5aPuJYpK6MvzuYpzGazJRFVWmXidbAIUVk3\nPUybxSLORGT1lUPd4Uyn06rnifScOI5Q/4P6UqbRM+vrGFFfia5k9uzZU9M7d+7s5ceIRm9/+9tr\neseOHc3zYyQdM7NvfetbS9IYDQlB/Ww0f3B8ZFzOeTKa84hM5Cnmnsnnj1w0lbyl3zGyks+H2m3s\nZxYBy7dPZh3JarNZHhZJ0x+XjcZVtPBsjJvxKGPYB6i/89eI6wRzQxWNITwnRsJ68MEHaxr79fjx\n47382H/l2pgGFOcPzpHoXsD6Hb/37uvYfgLmUiqbP1Mvs36fZO+zrbKi6IFsruD4wghkZn1XomzP\nR9QXbNyzvSx+rA9xlYouQSNNPN5ncNxl3YNmouRG+VlER5zXWTd189b3ruvq2MJr9c8v+Bv2AbZ/\npNPGurMolVFdWXthm+I+IT/msL+j/UgMvSkWQgghhBCjRw/FQgghhBBi9AyST2BEoazrFXx9nXXP\nlok4lTFB+rotEkVnHl3XNd2kRO5w2PkWieaTiRgTHcdcsg2p25A8kXkNxxSa6iL3RfiZmcnQHHnq\n1KlefnQttG/fvppGl1Loogaj5ZiZnT17dkka647cf//99uSTTy75PjILMvMtRgHy44+508pETzLr\nm9uxbixiU9b93xe/+MUl57733nvtoYceMjOzp556qn6/evXq3nFHjx5tnu/kyZM17fsGYa7LmMkz\nkj8wd2fZKIwZ6Re6lMI+9NEScWyjKZi5evRjAOufcZnkTa14TmaqxL5Esyc756VLl5rlMLKyINbX\nUURU1lfMraaHSQuY7Md/ZuZnT2m7yFUik+cxF3D+2nHs4RqB4yOKKslM8ayOfl1p9Uvkvq8lVfNr\nHY5HHNs4BrNSROZ2MeprbHvW19FYY+7LWP3K8dGxbB1j9fD9hHXKyCeyEYnxPNF9rSXJGoLeFAsh\nhBBCiNGjh2IhhBBCCDF6Bsknuq6rr7OjndbMPMnM/lFEH2a2Z+bxiOxO85ZpLSMfiI4ZGhnJmwTY\nbv/IdJepWzaaEDO9MTPxbDbryQ7m1cP/FpWLoEkPxwGOjyjC3P79+2ua7cjGnbaR94ySh5l/d+/e\nbX/6p39qZn15ho+6gxHM0DyNZkqskzeps13USLRLne14xzEY7Y5GScmxY8dq+n3ve9+SMu+77z57\n7LHHzMzsZ3/2Z+v3e/fu7R134MCBmmbeWxAvYYk8mBSypkgc/2hGZp4c/OeM9GsymdQ6oyzE14uZ\nOln0KU/khaGA7e3XWmxXrCfOuWh9bv3G2n42m9WxjWM8imjH2iGS6GW8cGTHBxtrkaehTBQ+X1ap\nZyQVYJ4SWIRG3zfoOQTHCubPestg7RdJYbDsedEPzXLRaHGtxfsVk8D5NmWSAnYdUftkotZ6Ihlb\nq/xSryj6LbsPZqJ6+jysrKwcMyM1jZ4/F0FvioUQQgghxOjRQ7EQQgghhBg9g4N3lNfWkRQBzVQZ\neYDPz0xLLfOJT/vPmVfp3iTS2vEYmSCLCSUy5bAgBsxMErVJRorh24TtImV1idota/oodYgcsmPb\nZ8wuvu7M8TuawrHtvNNxDArBTMnR7qAlArwAACAASURBVOHW7n3WvkeOHLEPf/jDzXIQJh/CtsLr\n8/IJzI95MM12nJvxXeJ4rWh29HMDr78V2AZZuXKlbdu2zczMdu3aVb8vHikKKEnZtGlTTePu8azM\ngM0zlLFEARmYzChak6Jd9YxyDThWsN3NuKSGeY+IggIhTK7l2xX7F+cS1iXySNAy/zL5EQYfyEpC\nMmuKvybWV2wnfCR1Y9IC5rHBf8a56Oc51reUx4Jq+LqgPIAFjfBzF4MS4TVjcBnM76V97JqZvCYK\nlDEPlHpG6zfOJyYPi8YKwuZ/lIfJSDP3e0/k8abkLX2d9VTF7q/zzjMkT7ZcJoXKylaz6E2xEEII\nIYQYPXooFkIIIYQQo2ewfKLlNDtyvhyZLgrZV9zMPODlDxn5BZJxch5JI1oyAf9Kn5nemGnEm54y\nQQYijwKsbqxNMrt6zeabbHwdM8d7ss7PWcCCaCc+21Gb9VTSagt2/I0bN+zIkSNzy2ReNJjXj2j3\nPQtawTwV+DxsnqNXjOj887h+/bp94xvfMLO+J4cvf/nLveO++93v1vQLL7xQ0ydOnKjp8+fP0zqx\nNQb7PKp3xktDRNZzAZ6jyEGYFMGMe+Jg8zfytMAc6kfzB4/D3ftZk2/L40fG3ByVP7SvIg8+i3gK\nYmsHa0cvH8h6U8JzlOtcxKsTu59cvHixl//rX/96TaNUhq3PkSyLEcnKWuv7UO8Tfjzg+dhcivIz\n7yTMK0xWYrmIlHFRqUJWPsTuGVH+jEeNrKQrKzVla1cWvSkWQgghhBCjRw/FQgghhBBi9OihWAgh\nhBBCjJ6FXbJl3YxktG2+rEhv0vrea25QG8Q0mREtTQzTuWA0oUi/xjQ4LE8U5ShDVufD8izXJdt0\nOq0urpiLMLO+ZimjRYrc9GAe1K9FkcqYTpeNT6+Ta2n4ojFfxmY0RzJRyrIaVXZcNBfwnExzHmmS\nM/O3cOPGDTt48KCZ9V1xeReG6G7tzJkzNX369Omajtz0ZMZ25CYy0/aR+6KovVpMJpM6nrBeXpfJ\nroXNUZ8/4z4T8f2COnAsm11v5NIwE52zjEdcR3w+Ns7ZuI4icjGdaLSesjxsXnid9tB7Ft6Dsu4r\nM2Pw6tWrvc/79u1r/sb2dUT6c3b90Vqb1dn646MIrKjfjiJS3i6i6Gt4/kz7+M8Z/XxrPPm2ZHue\n2JiJ9ilkIzKyz2zMRO4v2d6grFZfb4qFEEIIIcTo0UOxEEIIIYQYPbfFJVsUXWi5MJMJe0Ue5Wdk\nzL9ROeWYyKTDTKvMDOdNIcykl4muZRZH62p9H7kZGmqGQyJTCysrig6EJhEWCSpy35SR5yBRpDMW\ntRCPLe0a1Wmo+Ski4xLRX2tGZoFm0kiSMo+bN2/a2bNnzazv5ilqS+b6K5I/sDGfdVPHxiC2QzR/\ncY3MuqYqbu/wWlCu4D9ju+D6iMfgOmDWlxaxtQSv0efHz3hONK9jvXyUtCH3DmyTSP6QkTxEbikz\nEVEjSQhzbYfpaHwzkzFGoUO6rqvtmjW1szUG6+UjC7744os1jf2I4yOST+BYYc8PuJ77NmqNlYyM\nM3LRheOUSQWyEXKHyMYKzI0oW298uUxG0JIioXwPj/XtytY0JCPH9L+xuRBF3824jI3kH9nooYje\nFAshhBBCiNGjh2IhhBBCCDF6BsknJpNJfW3tvQhkWMS8wF6zezMignVjEavYq3yztrki2tm5HBM3\nkzxEZqGM/CGqE4tSE0kZWNQjRtd11SyT9VSAZKNHIVg2iwrnYSZVHDdY/0g+Uc6Zafus5Cez4zqK\n3sZMScw8Hp2fHRN5SplnHr9161Y100ZSFJQcYN9mPBZ4MtHWIu8TGSlU1nQd1bFEsivyEn+OCGx3\nNLtnI/0hzDxuxiOCYZ2Z2X8o9913nz3xxBNm1h8DXpKBYDRAvHaWNsvdpzCPN9GyPLimPPDAAzXt\nd8Wj3ATLPnfuXLPc2WzWXHuitZataUwa5Oviz1/IRqRj+bGNorJK+2dkjexcZv3xwTxRRPdlVl8m\n5YrWw+g+w84fyWValHpFEoOMl4lslFd2/4raBK+dyWQznnLMlsq9MuhNsRBCCCGEGD16KBZCCCGE\nEKNnsHyitWs22uE3NGiFWW6XPNbD7+bGV+5MKhDtnsTyWg7APeW6siZlhJkxovZhJphs8IGsTAPJ\n7jZFWiaWaKxEQTrYudmYYrKIqDzWFln5RiZ4RzGNRrvf8TpYcIWoHuzas2bOzO75yNMJy4NmYSyn\nHBOZTjMeW7L9nA0+w/JHu9lZ/kWC7xTT7smTJ+v33gSN6yAzFUbjl3lsYUEnIq8eTKqA51y9enUv\nP3o4mCe12bVrl/3xH/+xmZlt27aNlomfsX44/ph3DF8PZlK/cuUKzY9yDiwL2wfzYGAaM7OLFy82\n83/sYx+zFpPJpPZdJOtgawGOocirFAuClJUAsvnN5mPkwSUjnyjnwHHtZZeZgBDR3MXjmKQ02yet\nuvtj/PMXk8HNC+SRndPsXpZdzzLeK6I2yUg2ojUN51wWvSkWQgghhBCjRw/FQgghhBBi9Ax2IVFe\ndaNJImtOZ6bqyNMB25GJr8z9K3Jm2smYgv3neaZW9LKAZGUCTOrhJSH4GwtYEfVDRpKSbRPmmcFT\nrjOSzTBTdHa3PusrZiqMxloUfIF935KlRB4Nym+R+ZBJBZi8JOv9JOOUPapbJrhKVNY8IlMZk5tk\nzLBmXDqySH42FxYJEhNRyjt//nz9zntaYJ4XUEqB1+jNx2jGZ2M+WuvxtxJYw4x7WvBrNdanXAtr\nqyNHjthv/dZvmVksJWJrCrtneO8PbB1k5mlfX7x2JiOJZGtYt6ynn1I3HHf+uhD8jfVvNAeRrASQ\nyQjmmfoLQwJFodQzklrib2vWrGmmo3WJecfKrtWZZ5VI/pQJzoTllLEZXVNGKpn1RJF55vP9z+YW\nXl+0JmXkHxF6UyyEEEIIIUaPHoqFEEIIIcTo0UOxEEIIIYQYPYM0xdPptOmSLdKkZPSRWZcnTLt4\n4cIFmp+5GYp0M5G7LE/XdVXDEmkKmQYO64SaNa+fwnbPuIuJdDasXlH9sxqiVh0inRrTWzFNVtZV\n1iLXxfRHWU3yPDdBk8mkGdEucjPHxn/kvm5olMDIpRojcp+W1emW38v1RvlYe7GIR1mdGotslnWp\nuIjLyaHzB/Wf2fGPRHVhet+MVt+srwnGvkCtc+QSC885L9rj9evX7Vvf+taS8rPRB5m7sOxazdYq\n74oL12p2fsR/j+Mwq7ctx0VzAPshUxd/XWxNzazBvuzMHpVoDs5zlYrRdxG/fqNen90LIv1zZp9F\nNvpaph0X0f/i76055l0aMjdmTK+e3aeTXVMy15Td0yZNsRBCCCGEEAugh2IhhBBCCDF6BsknZrNZ\ndeHDom6Z5cyDmCd6/c5MD/iK//jx40vqyerfKmueRCICI3L579lnVr+MKd+Mm9EXiXKGRPkjCUGm\nnixvJDVopSP5Q8alW2RqZe0fudQZ4r4P3QRFfc3KQTNj1n0Yko2Ix8YXiygZnWee+Xc6nVb3YZHp\nlkkemEnWtw8re5E2YeMsmuPs/MylGotS5stl8gUmr/H9gXmYRAtlXatWrerlR9MrSjHQvBrJn7Lu\nHc367i+zcxLJunlka0rGPVUEa4esmy/mYg0lfNF4ZtefkUKYtSO9zsuDMHkSe5aIpHaZiHal7fD6\nMJKhmdmrr77aLJ+tEX5dwj7J3JcjqVxGPriIHABpRQ/1kTCZ/Ii1T1aSmIlu58/P8uNYzI7zLHpT\nLIQQQgghRo8eioUQQgghxOiZDHm9PJlMTpvZkTtXnbuaPV3XbfFfjrxNzNQuLdQmbZa0i9pEY6WB\n2qSN2mUpapM2WmuX0hwrnkEPxUIIIYQQQvwwIvmEEEIIIYQYPXooFkIIIYQQo0cPxUIIIYQQYvTo\noVgIIYQQQowePRQLIYQQQojRo4diIYQQQggxegaFeZ5Op10mpDGGAMTQhyxcqQ9dmgkjHIU7zIQO\nzlLyzGYzm81mSwq45557uijkbQtsEwyNiun777+/l2foORZhkXCl+/btO0P8RNax8v12+7fI+RcJ\n6VqudzabWdd1SwqYTqdd6fso9HQm3HcUPjMTZjMKhcny4JjcsWNHTR87dqyXH0Owu3ClS8YKjpOI\nTH9Ebbrc8KisrOzYYm3aahMzPlY8bK1c7vUuMv4z58yENGdr7WQy6Ur+KLx9Zv2P8kf1nVeWJ9M/\n2TE0m83oWptpl8x9Fe9NDz30UO83DPd94sSJmmbhubNjMHu/bh3XdV1zrcU2yZJZdxchs75FdYlg\n46g1VtatW9dt377dzPrPaBgy2aw/BrB8fH7DNR6/979hmoWMxnHly8uu78jQtdYz9KHY1qxZU9MF\n/8C2efPmml61alVNnzlzpqavX79e09euXevlx9/YQMWO9JM9M8lYnHJPOe7KlSvN3++99157+9vf\nvqQe0URYu3ZtTT/55JM1/c53vrOZNjPbvXs3LW854LXj4Iza5OLFizW9d+/epjPw6XRq9913n5nF\nizFODuyTReKss/bHScYWcJ+HndPnxzFVYsjjQoCsWLHCNm3aZGb9tn799dd7x+E5sE5Yj9K2/hh/\nHM4TrCue0y9KWB7mL+PczOwP/uAPavr3fu/3evlffPHFZtkXL15cMlam02ldI9h1m/X7A68Dy48W\nWiyP3UiiBwrMg7/hOXH8YX3NeD+02sTs/4+Vso5iX/nxz8YaW+siWP3Znymz/tzCa2Tzx9+AW3Pz\n8uXLzfpNJpOaH+vh7z+sT/DcWCd8GRHVl7VP9FLnxo0bzXLZy6LouEuXLjXHCrYLluVfrLC6IOX+\nbmb2sY99rPfbyZMna/oTn/hETeO9MZoDmXmH+HHbeqnm5zmeq7RJ9qGUjWW8Jv+w7B66ahrPiWu1\nhz3f4JyPnlWwnti/165dWzJWtm/fbp/61KfMzGzLlu89G27durV33Lp162q63NPMzE6dOlXTuMaf\nPXu2l/873/lOM43PDRcuXKhpHFdm/edEvCb2UO3bhD3wnz9/PhW4ZNBDcdd1tbOwsfxCh4OA3cAQ\n/33mn2f0cIOwCRH9ExxyQ+m6rt6Y8Fw+H+tQ9iDmF2pc+NkNPntN7Pvo7T17eGVMp1NbvXq1mcUP\nlfiZvQ2PFgWsJy5q2Ydi1mfsnL5dMH+ZE6dPn25eR9d1tS7RQuvztM6N1+Hzs7nJ3g77a8Jrx7JK\nf5r13xRHD+VD3h6yPwBm/HrZA5CH/eFj9VvkQTJa6/C4bNnl2qLryjxcRH822Pxn62Y0fzMPH/4Y\nzF/uLew6uq5rtkn0p5L9mcFz+D8W7JrY+uDbhD0Usz+bUf4MrF2y1hK2Pvv7OltTo3qxz+yceI5o\nPJX2Z88UeI7syyp2L43mK2tv9oaV1dHXDb9n97WoLi3OnDljf//3f29m/XutH394bpxbmMYXmfiS\nz6w/n44ePVrTOBew3/AlqL8OthZE94rsMxFDmmIhhBBCCDF69FAshBBCCCFGzyD5xGQyqeZU1J28\n5S1v6R1XxNwR58+fr2n/+pwJrZmmODIJMvNq9Iq9pf+LTE/lHJFmi20+QjMEXrc3CWLZaM5B3RgT\nyGeJ5ClDpSu7d+9eokkzW6ozQzMO6qZR54TjKTLp4ThC/RKmI6kBjmmUCly6dKmmcdya9fVP5beP\nfOQjthzYOM2YHM36pikmL8Hv/fxjpmHMv2HDhpr2feLHbsRkMqljAsuPdJaZPQOR9o+tKcvdyBGR\nlXu1zoNzJpqXCJP/RKZGtn5EJttI6jDvGH+eeW05mUyapuxo/WZ7XyKTOpOUYD8wCZsZn39IViIx\ndLNapP/O9FWk1czIcyI5U0YegG0crQHzpDr/twFvST2y7RlsYKPHZWRR0fxl0pGoT4ZIba5cuWJf\n/OIXl5Rz9erV3nHY7lg/f+8u4L3SrD/P8N6C8yKSNLL7AJtzy5XvefSmWAghhBBCjB49FAshhBBC\niNGjh2IhhBBCCDF6BmmKf+RHfsQeeeQRMzN7+OGH6/c///M/3zvuPe95T02jvvArX/lKTT/zzDM1\n/cILL/Tynzt3rqaZf2DUgkZOviOdYiHyMzkvaMbNmzer/75I58nKZL77MG3G9a7LhWl7In+kzDcq\n8tprr9mBAwfMrD8GfLmo/8NrRh0x6nYjMP8rr7xS0+j31Otf0Y82uhnD9sbrPX78OD1n0Ydn2gfx\nY4X5U2U+V73Wi+ntItd47DimI8T2uV2BZSKdGNPVZfWCQx3oLxKkYrkBIXxZZc6x9cx/xnMuV0eZ\ncWXmj2MuAxE//1p9GWlfWxrKSGeZGfO+fXA8M9/guJfDl4vrDXNxFvkpzug4/fF4Pyz4eZnxqYvl\nFJ/qBdSH4vWjVhTTvl0zfujZ2ufzLIqvU8b9V+YY/xvTB2cDvWTm0rzyWseWsRatT2wdYW4lo/nH\n/LNHewnY8wLz3x21QcZ1oEdvioUQQgghxOjRQ7EQQgghhBg9g+QT99xzjz344INmZlVGYWb2xBNP\n9I5729ve1stTYOZtH+YPJQXMJBG5nsmYOyL3KVjnYoJi5obZbFbdpTHXMh5mbsK0N8Gj67ZW/TwZ\ns5tZ3vzCXHMxzp49W6PnZMNHo7nOm1kLXk6D5j50W4djDb/3phqMHIjnx3JxPDE5j9n3xgiGw0Qm\nk0nTxV8UUSga563j/XHMzMTcs/njmKSGubeK8g8hGw0rE77ZE7nTYgx16ebXiyja5bxzRrKSbOS5\nVn3NcibjaD0dYr4dcp4WK1eutPXr15tZ3qUTtg9KpTCcMcqmzKze48zMNm7cWNO7du2q6ccff7ym\nfThlvJ9hCFw2BrxLLFz70R3kJz/5SWuBruqi9mRu6JhcAyVSZv17EK6PLemGL8ufE9dkJivJrGtR\npNZyTBQlj62vGYmU/5xZF6Iw5+z80Xo1xOUYi0gcyVSYVC0KPY/3hozLy2zkxegZDJFLNiGEEEII\nIZaJHoqFEEIIIcToGSSfuHHjhh08eNDM2rvuC1/96ldrupi7zMxOnDhR07iLH01EZnwHK3uV7835\nzAyB5hy2k9HnKXWJzIz++n0Z/hxs5yXWL9rRj+Y1ZsaKogmx79Fsgn1gFpsrW2C7RNGjsCwcU8ys\n5dsazVFYFrZRVr6BYF9kIlRh2VH7lOuKog+y/L5PCpFJEM/DdtX782VMq5gfTaFmsWnNM5lM6vnY\nrufW53n482bkRNlzMJlEFPkKGRqlLJJlsHmSjd7JYGMg2r2f3V3OzjPPJI5RyrLm18xa603aKBt4\n9NFHa/qpp56q6Z/8yZ9slmVmdvr06ZpGzzm4huJa7e9f6H0J5RdMPoFRVSNZFM7zTMRC7+Uo4/Uo\nkipk5ldUr6ERW0v+bHRFRtbjBPueeTAx63sqyawr/lklK8XyZUUeTrLR9BhYJya5QPz3TFrI7n/R\nuBrqdchMb4qFEEIIIYTQQ7EQQgghhBCD5BOvv/66vfzyy2bW9xCB5iKzvpkWd/zi63dmIjLrvyZH\ncxC+VkfzeNbJNzM1+NfvLW8FkUm85Y3BmyTwGGbOx3bzO3qxPKwvk5r487MdmaxNol2ufrd1CzTp\noXkkMv9iG0XO7ZGhDs+zgV6wnsxs48ubF3wAwfpF8gVmUkOTr29Tdn4cExmJh1l/TLJdxd78zBzw\nt9oRx0kkcWBm1axjfVZWZJpEWHtlJRO3I/BA6xzs/JlAAj5PJHMqZGVhbL2J8s8zBd+6daved5gU\nwNcdy8TgEzgW8V5mZnbo0KGaxiBT//Ef/1HTO3furGnvPQk/ozSQeVZYu3ZtL3927UNaa0/WUwk7\nxsslUFbC7tHROMf7AObPBPUwy3niwWNL/sirBJNh4Lmj+yXrHzwOPRzhuDHreyrC5w7m9cf3IdYT\nnxlYAKlyfPSsgPVg7RCNpaw3kla59v/aO7OYva6r/K/z2qW1HY+1HTuJM7hN2qYtoWraogrIRQcJ\nIQSol3CBUJnEIAQXbUFcAQJUQSUkJAR3FVLpFSAkpNIWSqEtLWSgaVqnSZzJ8fh5HjI03/v+L/rf\nO89Z337Wu8754iT4PL+bbL/f2cPZ0zk569lrGZfGZmWFmWdFhL4UCyGEEEKIyaOXYiGEEEIIMXkG\nySfMXjLPoCkk8h6Bn9Lx8zk6LPef+tkne2YejbxPINmTlC1z33qd1CPYXvSmgH0aecRg8cSRrENs\nhr8eTef+BC3LX9qZPYmO5Y4JqsDMTMw85/Mg7PS9n2st83V0Irlcw8yPvu7MWvDmo4yMBPNEkhac\na1guyp+yp/8Zpf7IpMdMoKyvI5PcGM8MGflE9Pt6HcoXsl4tso7yGZE8AWHSjEwAgGV/i4hM2vhv\nZl5G/NiizIJ5sUFPOehJyaz/PGSegvC+fUCglvejZZTysoFpWIAfTGOAE7P+s4rNqegZm5G0RW2O\n9nHPbDar/R1JUHB+YPk4VliXl4qxfQXzoweu22+/vZcf5wfKeJi8zvcptnmZPGY2m9XnOHuumHEZ\nIasrCrKSeeeK2s0Cu2Tzj5Ei6UuxEEIIIYSYPHopFkIIIYQQk0cvxUIIIYQQYvIM1hQXvUikFWER\nrdA1SaRzY1FMmC5vjE4t434I6xmqKY50llgf6lyYyyDf3pbLOI/X/UaubgqRPom5xovI9B3TITKt\nYtalFJtfUb/i/XvtWCFy6bYsIlfXdc2Idh68R+YSDdNR9DcWGTFyr4P3znSY3o0iwuY3a0fpi8id\nFM5ZVmakTWR/i7RxjKyOOds2VkeZqyzCk1kuylN0X2z9ZPWDCHNjGO3VrfUf9W9r/fi1FK2NVr1+\nPrH82Pe4B/szMUxjy9yQZaJkLqPcT9QveJ9MU4pprylGzSuWxVyJ+fozURIjF1qtfo36p9xjds6O\nmfMsyic+f/fs2VPTb3nLW3r5H3300ZrGcxqZ55pn2VxZLBZ13HD8Ik0wqzty78lcqrGx9RFR2fsb\ne1eIIjeOQV+KhRBCCCHE5NFLsRBCCCGEmDyD5BMYJQaJpAJoimWmhsilDjOVRuYN5kKLmakiU3Yr\nKs4YMtGEEG9SuHjxYk0zc2RkZmVm9DFkTHpoFo/cJzEzWkYK4cvLmOf8/GWSiWz0npa0g5nH5/N5\nlRZl3Y9hmsleIvMXgveKkSZRtmPWN/2xOr0bKgTnGvYPunQq4DyJ1nQmQlokv8jIFyK3acwkGEXL\nGlo/gi6lcNz8vpDZ37J1M9lOdlyYKZpJkczaZnyU37Hro4iKTGrD1nT0/MF+QPlf1j0YtgXTuMaw\nXN/mjBsplNpEe2WmL6Loo0jU/61rfHlMYpKVkix7HmOfZCNNMjeE0XMV+4vlx3Z7+cSXvvSlZrsy\nY2XW7/tlz/j5fF73j2w/Y5ko/4nkp6xP2R4aSRpZlFsWHdJsfS4vzfSlWAghhBBCCL0UCyGEEEII\nMdj7RCEyGbFP4+zEoi8r8jZQyJ7CZOnoRDSS+RTfMjFHJj00SeB1mPbeI/BveB/MzBKdUs9IKfx9\nR6eaGaWdkacS1n7W79G8y55iRoZG5IrmXaZfWvkjSUjmniITa8a8H8kv2Cn1o0eP0vqx/ZmIXOW+\nIjM7k1Thyf8xpldmxvX7DpsDbEwi03FmT9m0aZPdddddZtZfr15agF5AsK8znlwimITG9zGOBY4f\nW6dRRMjS/sOHDy9tX1Y+x+432s9YRDwmKfF7NdvTWFTQSD4RSUmQVn9nzchsPfixZuZzVmfWrM3G\nIlrP5bpo72vttZH3ExxrtmaivZKVhWN98ODBXv7rrruuWXamXH/dsvHuuq65HnwfsnczlG4xr0S+\nHRnZadTuyHMUq2PdUtd15RZCCCGEEOIaQC/FQgghhBBi8gyWT5TP79mACuzTeGSSyJxyzJrEs14M\nkKzngXJtSz7h7xvNEOzEeOaksVnfxITmNTQlb9q0qZcnMne08Oa4MQ6xW472fb+zU+DMg0h0+pbN\nKSY3MePm0ewcwH4p+aM5X8ZlyEnqZURO8pn8gQVqaP27cPny5Zp+5JFHatoHL2CmQ3T+j5R2Yf9v\n27atdw2OG3piYfKHrEkwI0XysD3p5RzT2267zT796U+bmdnOnTvr735ds4A/TMIWmY8zHj5wDkR1\nYrswKAGOnVl/Tpw9e9bMzD71qU8Zo4wdjqGX3bD7YGb6yCMOG1Oc435McD1kPKVEEqOs3KUVKCla\nA628Pk8k62KSmsgDDKuT/e7zYz+1vG14WvcbrctMIBvfp/j8xT5BTzuYx+9rKEnANYPlRrJI740m\nAr1PME8ZZjl5WOSlJBOQKwr+wbzgsDGJZDoZT2YefSkWQgghhBCTRy/FQgghhBBi8gyST2DsbPxk\nHZnmx5xSZfIC5jUh8pSAecY4CW/dLzKbzaqJmMUG93VH5pDWPZj17yPjEH7dDqwD01cmeAdeF53q\nZ87HWR2RqSTTriioA7aT9bE3dWb7olxb6shKMtj8iORHSCSTYDCTGZq+H3zwwZo+depULz8zH7fA\n4B1oWvRO7rHfn3zyyebvaEr095qVRmRgko2IocE7Hn30Ufupn/opM4tNlSzQAzMVZqUCzATpzbVs\nnTAzvu+vlsn65MmTzbZ3XVf3iyj4DZNOZWQzUX5mEvfBb7CPWJCqaC1G/bUeMlJGJNpXsvtPpn4m\nj8uY9TMypUiiyIITsfb5/Z+9q+B9YJ6tW7f28uP44jpnZUVSg8w4DL0G0yy4le/DTHCxSArL9q4x\n8tcx6EuxEEIIIYSYPHopFkIIIYQQk0cvxUIIIYQQYvIMdslW9B+oA/GaqkwUuUykK1a3LzfSqY3R\n/yHLNDhd11UtLNOPmfFoRsxliNfuRdHuClu2bKH1D9XZRNrdTFld11WteTbSF/YRpiNNF3PNhGnM\nE7kZYmOEefy4YP2lrChyXNGNZXTlZlwzFrnUYRo9plWO6sexYy7Pzp0718uD2stlOuYNGzbY9u3b\nzczs1ltvrb//8A//8JrrCl/5fqfOyAAAIABJREFUyldq+tKlS0vb6vMz3WLkTirjhi2CubPy7uwK\nzz//vD322GNm1t9fo3ZltLRe/5dxKRe5NWJrdowrTFYH5i1/a627AtOJsjMfPj9zh8WiJ3pNJFsn\nbN7hemmVl6HcA5un/m9sXTIXl2bc/R7Tavv7yOhTWXv9v0tZGW1pRjdsxl2CRn3KNPWYxnu9/vrr\ne/nxmZ1xBRi5VFzmcgzPb2BdPmoiW7sseuUYN3fR84+5Bcw8C6P6s+hLsRBCCCGEmDx6KRZCCCGE\nEJNnsEu2jOyBfX5nkXOybq7YZ3JvNmDuPpgEwOdn7ohaoEkich/HzH14r2gm9W6uionZrG/aZ+bL\nSKaQwednkXei/MWExFw1+X9nzGhRfmYqwb73c425hGOudjzMzLbs+siknInCFbltYmZiZrL0c5yZ\nzFCqEJnUh5jLX//619vBgwfNzOzd7353/f3DH/5w7zqc/3i/aHp+6qmnavr06dO9/ExawSRP2Yh2\nGZdKZnEE0Ba412L/elNwxtVc5JKKtSUyGTOYy8us3CQjVStjFJmKmck1E1XUrL9HMDeRkXtPtg+w\ndeWvZ5IuRtd19T6jtceehVgHulf1cw2fAays7Pgy+ZaPToi0nsXsnQClNpH8gD3fWZ7IJRuba5gn\ncl+GbWHyuChS7jJQvhftdZn5m4la7POMcamWkeJG+ce4Z9OXYiGEEEIIMXn0UiyEEEIIISbPIPlE\n13XVdB/JKFjkEjQdRJ+1mWmYnX6MTBJDIzb5Ni8z6S0Wi6ZHjihKH8oP2IlefyIZTbNoxmKnQLPR\nyxiRSTAjE0BTDbY3MvfgvTCz9LITtq3rIrNNxgsDK6v1b/Zb+d2f9G1dz6RFzOtIFBGIzYOoHzMy\np8ikPsR8tWHDhhrJDiPaoVzCrH9q+8CBAzW9Y8eOmkbJhJdPMPkC66tI/sDWGZNFjQGjHyK+PzMn\n1n250b9b+aO9nq0tzB/JpzJtQVqeBPxcZJIDtodF3iOYJ4pIkjVUPuHbz8zoDIz0F0WEY5IW5hkl\nKwFidUZeoTJ7RBTRbkhkNiaXMuP74yiz+zo9BbH3k0iqMETqie8q/nf2b/Yul40oyd6JonnK5jyb\nv9FYRTI/hr4UCyGEEEKIyaOXYiGEEEIIMXkGyyfKp+pIYsBMilkn3b7OAjPZ+M/3zFzBTppHp//L\n35gJkXnk8CYAlAbs2rWrpnfu3FnTaAres2dPLz/+jQX/iOpHMnm8qWGMNKM1VyLzD5o9WbCFyHk6\nM09i2ssXsC/Z/Mye8F3mUB5Pz0flZ077R87TWXvZifnIfMa8G0SSlqhszwsvvGDPPPOMmZndf//9\n9XdvAt+7d29N33vvvTV97Nixmj5//nxN+yArGRlXVv7AzLgsEM0YcK7guPm5wU68s2t8/syezPZg\nTzTvM3lKnVHfl3uMpCLMJM1kAlFAk0y7o+fHmOABkWckRmlzVHcmgA3Wt7Ky0st/5syZ5nVs3UTj\nyAJqZJ/L2QBS/tqoTZlAGH7/ZiZ9Noe85ybmsSYjW2j9exnl/rN7NLsPHL9oT8oEQYnWCJP5RO8g\nQz1trcm/rtxCCCGEEEJcA+ilWAghhBBCTJ5B8gmzlz5bRye1mWSCndiNzF+M6PRwxqQwxvk7u7bc\nCzo+j05EY/9s2rSpprdu3VrT3tNANrAAIxOwgAUl8HmylDxo6s+Wg3nQFO7z498yJ6Kz5icml4lO\nRBeTEisTT/9mPZywtkdjxdrHvLpEfcKuiwJVsLJaPPfcc/bwww+bmdmJEyfq7ydPnuxdh5Kjo0eP\n1vThw4d7ZRW89xa2prMBUTJBILIyg8z6xX0lGuvMPIjmPztpnnWaz+RLrC2R+ZnVgbRkApH3Bubl\nAa/xey0L4sPG1AecwOtwnWTlf0O9T5i1pVv+GcfmKpNPXLx4sZf/woULNc2ev9lxyex/vl+ye14p\ns9xLJD9ieyqTF0Rme5YHnyW+T5mXlowsakjbfLmR16XMMwPTkVQNyUowM14qov11jMcJRF+KhRBC\nCCHE5NFLsRBCCCGEmDx6KRZCCCGEEJNnsKa46D1Q3+E1VczlEdOneE1Rxl1IpJ1iehVWbqTpXKbT\nwWhCWL7X2eD9bt68udkm1CTjNWY82huLvuTHBMn0bxQlMAPqZzORtsx49LQoD2s/0w9G7mPY760o\ndMvyt8CIdpFmjGn08F6zLtky7oii+rORAVl5y1xSzedzu3Tp0pq6/LrDCHWXL1+uaVxnkf4zE5Ex\n0s5Gf8sw5JyCvy7aK1vX++vGaOozEc/8dUwfGbkJG3p+o+jGo7nCzl8wTa2f/xlNItPX+zyZiGXR\nfWejh5b9MnKVxZ5lbKwjLSvqsDPnDko7C9gvTCuMz0N/3bJ+6bqu3leku830CRLNfza+eE/+rATe\nB9vTI1dv2WdraVO53zGu81gUO18vO2eQPeeT2Z/x/cDP02zkZIa+FAshhBBCiMmjl2IhhBBCCDF5\nBssnWmQ/6TOzsDdhZNwBRVFeMmRN8i0XQMhsNqtmnsjNDH7Sv+6662oaXbJFphA0F2B/FdOzWd/c\nFElKMq5bIjNnxs0Jmmoikx6CrpBYpDl0u+XLZm3Ecv24oMkqYzLzJsEhUZbQpBdJOpgMICMV8TBz\naNZ8y8xkkfksGxnO1x9F8kLJBOsfbJM3qTFpTsb9nK+HrdMoSlPWXNlijPyB5YnmaMZsmY0ex/rL\njwuOBYtyhuW0Itr5/szMc2a+N+PRCJlLqch1GJYVzS/W/sxc6bqu1hM9A9hYMfxeh2PFJCJRVLhM\nxFDsV19/tv8KZVzGuLjLSpxYO5gEB91JmvWfZ8x935h2tcD1g2OZiejr6x6zp7D1k42SmXEfaZZz\noxihL8VCCCGEEGLy6KVYCCGEEEJMnm6IKa/rulNm9uTVa85rmlsWi8Ue/+PE+8RM/dJCfdJmTb+o\nTzRXGqhP2qhf1qI+aaO9di3NueIZ9FIshBBCCCHEtYjkE0IIIYQQYvLopVgIIYQQQkwevRQLIYQQ\nQojJo5diIYQQQggxefRSLIQQQgghJs+giHZbtmxZ7Nq1y8zyEUlYJDVM+4goGAVoPRFcXk6eeOIJ\nW1lZWRO6ZTabLUobI08eLALLq+H9g0WgGdOWxWKx0nJzsmHDhsWyCFW+zkzEtmg+4H2xSDq+DlYn\n+933XSvKznw+t/l8vqaTu657RQb75ptvrulz587VNPYDRv3xUQIZ0ZrN8OKLL66ZK13XNddPFFEO\nyURhW1b2UFiUtCjyW7C2mutnNpstSn+zSKBRuWPWMpaNESVvuummmn7qqad6eZ5//vmldWb7G9fP\nYrForp9lEUZL/hZsrKK+YlG8duzYUdM7d+7s5XnyyZe8XrEociP3/aVzhe2B/t+ZiJa+jSw/e7ZF\nczWzHqMxLn9bXV1dutfic+jgwYO0TThuLHpedl9h6QH7QgoWcW51dXXNXMF3lWyZmShy0V6N6c2b\nN2P7avrKlSup+tcLe1fxDHop3rVrl/32b/+2mZlt3bq1/o4bqGf79u01jZvHtm3bXmqEe3m69dZb\naxo78tXk7rvvbv4+m81q2OZsmFgMsYjpKKRvJjQzbsBR6FFWVtR+Fg73hRdeaPo93Lhxo91www1L\n24wPVWwj1oFhsTHdqrPw7LPP1jSGwvahR30o0Vb9Ud+1NqWLFy/SNr4S/N7v/V5N//3f/31N4+Zz\n8uTJmj506FCqXFyzGE42y/Hjx9fMldlsVvcPtsGb9cOhIzjOCK4rs/54srDjLGRzq82F7EbPwgrP\n5/Pm+tmwYUN98YrCv7KQpv7+W3Wb9fscx/SOO+6o6U9+8pM1/eu//uu9/I8++mizLbhfRHsXtrlc\nx8YU99oolDiGBMd24FhhP+Ae5NuEH2iwf376p3+6pj/ykY/08v/yL/9yTZ8+fbqmcRyjUM5sHbz4\n4ot0ruzevdvM+vfr/2cX5ySuAXyWY7v8HMJ+wnpYaGk/V9n/lLOPJ/73Vkh37F9PaSP+D8xf/dVf\n9a7BMfmVX/mVmj5//nxNs5DNZnzPeN3rXte8j2zobNYnfv3ieOE4nDt3rrnXlrGOwjSzZzJ7uffj\njOtsy5YtNf2ud72rpvEZ+cADD/Ty4/r3/d1qS/TijGP37LPPpnw0vzY+wwohhBBCCPEqMuhLMcLe\n4D34Ro//B4L/h+PB/8N9rXwpZszn8/p/f1kzIf7fITPze1h/RdIAVif+3xP+H+nLabbYtm2bffjD\nHzaz2KqAXy/Yl2q0NvgvhvjFE+fNsWPHavrIkSM1feHChV5+/KqU+T9U/9ULvySVrwNY5qvB/v37\naxq/FOMX83/8x3+s6Y9+9KOpct/3vvfVNFp9/FfjG2+8saYPHz5c05/5zGfWlLlYLFJzjcm1cM6w\nr/tm3FycNR1jfvalmX2d9WT2CewXvC8/L9lXRfxSFe0RrF+wv9FCgOVG+bMm8dbXvyhvuYbNASwn\nItrr2P6Iv2M/+D0JrVm4v7F5Ho1phq7ranuwjX4NYD24ZvEZG83hjFSArQ0zvr/jHsqeR2b9+yn3\nG82Vcg3eK85ls/6eyMYd8W1iew5rl5+rTHLFvqp7ss//Qmu/8/mY9YyNeWRVa42ZWbxGWXnZPkXG\nvMfoS7EQQgghhJg8eikWQgghhBCTZ7R8AgXj3kzDPn+jfAJNzJFJA03nmcNmrzRd19XP+mgS8H3C\n2p45yd4qr5U/87svix2O8fmHeh7YvXu3/fzP/7yZmb31rW+tv3v5BDOpoBkP+8JLE5555pmafuKJ\nJ2r63nvvrWmUb6A536xvekH5RdbcnvXC8kryT//0TzX9zne+s6Y/97nP1fR///d/Dy4XD0ccP368\nptE7gZnZL/zCL9T0b/7mb4Zl4vrJyndw/jJzb2RyzHgpyY4zmycZE75ZzvQXHSqLJFeFKD+Cbcb0\nnj0vHdj28onMvpY9vV/uJePFB6/xcwD/xg5JRYc62f6GfYIHiLz3CTTXZzxeZKU60aGjzN7D5if+\nztpulpMXROB9MpkESik8+M6xTGpj9lL7mRTI/w3nNt471uvHANcvk65gnmiuIuzQeXS/mfejUi6T\nSPj2sj2R7RW+He6gaPP3jKTKE70rRTK6DK+Np7gQQgghhBCvInopFkIIIYQQk0cvxUIIIYQQYvIM\nEgYtFoumrsnrZFCXxJzmo37T60xRe4x6HubA/9XkB37gB2qwEWyf7xP8G7r+YoEhIp0Z0zFiWV6L\nMzSilx9npg365je/2cx/7Ngx+6M/+iMz6+vvIufjTN/JnN77dmEa9a/Y316TzAIjMB2kb3/LzeCr\nEaUQ+fSnP13Tt912W03/7u/+7rrK/cpXvtL8fWVlpffvo0eP1rR3zN6izNX1RoSMdGaZ/JG+l7k+\nYjq+7DyPKHlYgJ+orDGR/pjmDzWzvv6Me7zoPMKQ6ILoZityCYXrnWlyo+AiTGeKz7USLMOsr7n2\n1/n2t9rs92r8N2psWeRJDMoQwdYXCyCRDb6RiURq1p8TOEbY3yyYklnbvWt01qb0I17j+4nppNlc\nzp4bybha8/X79reuiXTDy547i8Wi3ks28uGYvZJp4pHonjLnEaI9JXoOZNCXYiGEEEIIMXn0UiyE\nEEIIISbPIPkEun6JPp8jLCIKmtT9J240fbMY8UPMbleTAwcO2J/92Z+ZWT+SkXddhPHX0STGTA3e\nBMeiTWFZkZsTZtLD/sV+R7d4Zmbnzp2raYwi94EPfKBZ7pUrV6rpPJor2GaUIjDznDfHoPQGIzOx\ncn2/DDUJRubn14p8gkXhulpE5ucMpd+jfmNmVbY/ROOUMc9lI0+xNeflR5m55esr10WmdtYvWReO\nTD6B+XFd+XJZdM5s9Kuh8omWKy7fB9gmvI5J+SL5Att78Pnl5/v58+dr+uzZs836I/P1yxVZNIqU\nh32E/YdpL2tkUVGzz2iWB2FuOX15GalAuf9IgollojwF00xi52Fz2b8L+HYuA+eHd1kXuZHMlunn\nScbNaDTO7G/sHcaPM/Y369NojUg+IYQQQgghxDrRS7EQQgghhJg8g+QT8/m8nhqNPC0w08yFCxdq\n+sqVKzXtIwLhJ288pcqi3UTRda52lLEjR47YJz7xiaV1YdvRXOFlCoUxEYOQ6PQ9gmbAKPIO/i06\nIYz1t07Pe1MjM6mw06WRSY5FFIzM4kxqwDyB/F+QT1wtbrnllubv119/fe/fQ+4fzZyRSS4zntE8\nGTomWe8vUZ0Im08ZGVokP8hEj8pGT8M+RskR5vEeEFhEQWbCzMgnsvKSQnR6nvUv5o/kF2j6xmcR\nM6+b9T3cMEkKi3627G8tFotFbXM0B7EtmGZ7beRpJBOJLRrHzBhHz8DSzuh+W3/z7xA4P1AmhNIR\nJg/x/2Z9l/X0wO4liuAZSStalPZGci7m0Ym11d8TiwyIv0fjlvH2wTymRG3Ooi/FQgghhBBi8uil\nWAghhBBCTJ5BNvrV1dUqgUCzP5qVzPqeFtC0hN4ZIpMcmnPwbywoiD/diWaE7Cf7sTz//PN2+PDh\nNb97kwS2CT/p+2ASjCiwR+YaZtZiJ8u92TEyIbWYzWZ1vNgJcLP+/MB5lHVejm1BSQ87XYtmYV8P\ntgXNM9H9tvr1WpVP/NIv/VJNHzlypKb9KXUW0GUZkZmdnVZmazqST2SdwLPyMmbOrHP7iNLOrFcL\nttdlvfYw7wRR4JFMkBAma1rWnqjc7P7PyAZ6Yb9HJm0WZCNzkt6Me8lgvPjiizWADvMy5GEn/LMB\nbJiHjsiszsrG35kcx5ft95zWtWVtR2ON/8Z5g/3IPLREYP5Ibsj2IuzfrNeNzFpqrZ9sQB+2h/p6\n8X7xnvx7YsGPOZPEMSlFJMkaI6XQl2IhhBBCCDF59FIshBBCCCEmz+jgHRFM5oCSC/Q+EQWqQN7x\njnfUNEo0vCmFmXCuVsCPYmKIykeTAouFHpl5MvKFKMY6M02z09GeyCzWAr0KRI66M+ZXvMabSnHu\nsJOueI+RqSVzkt+bz1qmmqyJ7f8aW7durenPf/7zNe0lQBjoJUPmJHnG8X9k5l9Wt09HZkpsC5Ms\neJlOZv15Wm2I5AtsLTNzZFQf26+yQZtYuf6ehgR6mc/n9bkRBS1gZeJ1uA/5PYntAyy4kO8T9sxh\np/qzkgUGSgXGyBeya4Dto9lALUOJvHKUsiNJSmlv9A7ApJq4p+Hv0XhgWey5FD3XM8/CKCDLkOdO\nZj/N5o88BSFMphPtSWzNRPN86LvKmjoH5xBCCCGEEOIaQy/FQgghhBBi8uilWAghhBBCTJ5BmmLU\n6Zw5c6b+/tRTT/Wue+ihh2oadYi7d++uadTc+IhYqOFB10+o30P3Kfv37+/lx3rQDdzVACO3MR1r\nua6QifqTdQ8V6fUy5WV11kOjLM1ms6r1jlyqZSLyMA2nWX8eoRsbLAv1S35cUE+IeTJu73z7S/2R\nW6H/y5w9e7amcV0yF1QZNmzYUM8HoGbTz0tcx6gtQ+0rpiOdJ5tPkSYP5xm6MWSuqfz8YW6ZvPYY\nKfcZ6e+Y/hXnYPZcRWYv8v2acTMW7RdD3Bd2XVfHK9pDmaaQ6b8jTTKbKzgf8Rnn87C2ZCO/Zei6\nrum6zf/Gooey54nfj/E6FrUM553vV1xDTIccuVBl7WeUuRrpz5nuORPd1P87c09RuzOuE317h56Z\nKvVH65O1Hdd+1uUkziFcM8wl4LK2Fdi+6/OMOUemL8VCCCGEEGLy6KVYCCGEEEJMnkHyieeee84e\nfvjhmi5En6/xOjS/YvQx/4n7+PHjNY2mqfPnz9f0zp07m7+bmd144401feDAgWa78PP79u3bbSzo\nDidyj4JmiKFuyMxyLnAidzosP/ZDFP2FRVZipnOUlUQmDOwnZqZl0bHM+lFy0HSHv2Pajwsz4zCz\ndsZ90rUa0e4//uM/anqMq5sWN9xwg33sYx8zs76bRm9mRInUbbfdVtMsspWXsKAZb8uWLTXNzLXe\nTSS6gMSyUEaGkS2/8pWv9PI/+eSTNY1z6C/+4i+a7WdEey3CXA2OMVVm3aZl5v163GIyN4/ZPsG1\nj/uWX9O4xzB5Cv7u5RMor8F5xNy4RfKPbH+VtkVjwOrMRgpj8iAmC4mkPixSWvQMGhLRrlW/2dp9\nHfcc5oYQ25eN9IrPHNxjsqb+Mc+QIe4Nsd0+XyZiZzTOuH4wzfohmmfMDWA0JsgYt4D6UiyEEEII\nISaPXoqFEEIIIcTkGSSfmM/nPbNAwZsqMRoMmidOnTpV01jO/fff38uPpso9e/bUNJon8fcbbrih\nl//o0aM1jZ/v0WyKJlBvPkBpR8YkUcwHTJ7hy8mcjsxGfsqYwaK/MZOYb9fQqDerq6tV1hJJR9A8\ngiYx5gkgMrWgSRT7H8vyXgCYTIKdWI4iBZb0tSqf+MIXvvCyl/ncc8/ZoUOHzKy/J/hxeuyxx2r6\n8ccfr+ldu3bVNI6535My5lYcZ3891vPGN76xpnH+rKys1DRKxczMTp8+XdOZ+bFYLOo9RBGaMmbs\naI9YbwQyZtLMnMr3+cvf2NpH+QSOr99rsW4ms4hkCbjX4XMCpRAomfB7M7YN9yRmCo72NOa1BEEJ\nXxR9cKhsLoq+xsY08j6B94/rBvNEEd5abWZrCecK9mHk7SUbZY21iUkMs95j2DqNnr2RNMrTdV29\nhskpo79Fz0GEzV/Mz9aVGZdZsLZE72jyPiGEEEIIIcQI9FIshBBCCCEmzyD5hNlLn83xs7g3FV68\neLGmL1y4UNP4KfvSpUs1jRILs76ZxZ/sLTCn0mb9E+EomcBT6xgwxH++x8/xKKVgtMyO0Wf7jLkq\nOiXOyo7MNOxkKzNVRvVnzb9ljkSmFtau7OlfbD/Lw04Vm3GTcdbsst4Tw69FcM1g/6DHl6effrqm\n13PfZ86csc9+9rNmFstcsJ+Z6Rr3BJRw+TYyE3MUuADlFNu2batp5skCpRRmfemYD0CzDCaL8G0e\nE6AnY55EIolFZh5E+TMeTcp44b4ceW9gzwkcz8g8jXMNJTRYvx/PzDODyRd8e/Be2F69urrae+Yy\nmOSEef2J5Bcv577H6mTBnMyWS30woEkUPAPlFEy6Ec1L9ixnXo2ioF44Jqwtfi3j3zJBo1r9Fj1T\nM89Hn5/JGdg6y3qPyMg6PGPmpr4UCyGEEEKIyaOXYiGEEEIIMXkGySdefPHFKpVAyYQ3LzzzzDMv\nVUC8P0TmFzR9njhxoqbRKTqatbzpCE+xf+c736lpbPOb3/zmZllmZrt3767pYmZjp4C7rmt+vvcm\nBGYiyJo8M6aryFTATray/FGM+Gzghla/RCeKM5IFb37C093MvMJON/vrohO5BT+uLfMzM3O+Uqw3\nsMZHPvKRmkZPC29961tr+td+7ddqej33O5/P6xhiX3pTIJM2YN04Nn69snmO9UTBW1iQGGZqRNmY\nWRysoQWeFI8kEpmgPkh2j2B1rBc/N1lwDNaO8gyJTq+zE/nMi0fkEQc9Ie3du7emUUrk8+PzBNMs\noIMH+wGv80GqCuiphHlAaLWzwDwg+DXEgo/gWER7KBsL5pkpegYtY7FY1LIiWSHOHSyfySr8GmGe\nTlhQqmj9sb0s8jAReRvxoEeOaM/GMlndWS8lOB+xr3Et+HnJ5gCTfUZjMuZZqC/FQgghhBBi8uil\nWAghhBBCTB69FAshhBBCiMkzWFNcXA2hltODmg7UVF133XU1zdzmmPU1e+i6jdWJGmCzvnYFI0lh\nuahDvvXWW3v5Ubu1ffv2NXkzRK6TstFqGOvVzGR0dv5+M3pbf30Zh8j9ENN6Mjc0fq5kNMX4u9dS\nMc1SNspTNkrWyw22z2vicf5HGsOCb/fHPvaxmr7zzjtrGiNF/uqv/mq+sUvqLvVH7qAy2lnUAUaa\nuUx0R18/01oybZtfl0M1xdjOrPuhrGutTH6m+Yx0omPcuGV00NiOouXFee33BBZljLlx888V/Bu6\nYcPnDOpocV2Y9c/O4NrE31nETTPuOo1piruuq+3Bvoj6Ha/DOvB5612iMR02m2tR9MTomdC63qw/\nD8tZn2jOlfbjffhIlTj2kZ65EO3/bC8Yo8ln7uj8voJ9hPs+jiNe22qLv6fMmaMxUfpwzmU1xZkx\nifKPQV+KhRBCCCHE5NFLsRBCCCGEmDyD5BMbNmyoEgiUQqBEwazvxgbNAPhJPzLVYx5m+kOXR9gW\ns/4nezSZoXkD8z/++OO9/AcOHKjpEm2PySfQ9Uski8iYGSPXLUOjCXmTIsufde8WSQiWwdzTmOVM\nNVEEPmayRhN31pSVucfIfPZKRrRDU+5P/MRP9P42VJLj2/2Hf/iHNb1nz56avueee2oa55d3XzaE\nruvqGkVTpm8TM5ez+RNFLmTp7PhlIkJGrseytMyAkfujMa4amfslZgKNZCWsnmxEywyl/kgihH9D\nN574nMA2eZM67vXe3VvhgQceaKbN+jKHTMTA6FmRmZMbN26s+0H0nMG+wGcsGwPfLxh5NtMuLwHA\n+tmegXl8fhyL0rZjx44tbUc0f7FNKG/B9wPsR++mLiMZwv0qchWJ48DcTq5HvjebzeoawL3W72Fs\n7TMpg19/+M6FkYPRDS662vXzDF3yZlzWRlK5Mc9nfSkWQgghhBCTRy/FQgghhBBi8gyST5i99Kkc\nP7GjWcWsb+ZAUxSTTHhTCpob8NM6RqTbt29fTZ87d66XH+UbaAbBdqH54MyZM738GJHvpptuWnM9\n0nVdbW/koYF94mem3KwJnJlls6YClt+bhZi0gJnB5vN5NRVFsgR2CjlbHzsZz077Z+UPrP8i8/Er\n6X0Co8t5+cSXvvSlmv785z8/uOzPfOYzzd/RFIbjth75xGKxqPnRtBjNf9bnuG9kTyRnop+Z9ecm\nM91jWZFHg+zp6NKGrDkd28gixWWlDCzSZBTRkZUdSZaGrJ/5fF5Nq1n5HY4Vi7zm5y/OPTSvY54j\nR440fzeLo70WWHQ4T2ZSBzdWAAAgAElEQVSu3HLLLfaXf/mXZtaPtOdlhfgsxeh8uG6wXb7ukydP\nNq/DPs5KbdBEjs9vfJdADwX+urJX4Dj4ukr9OD+8fIHJFPDecX5EXqUQJkuKZIksImc0JlEUUM/G\njRtrhFK8J98m7BM2ntgOL3PZv39/Tb/3ve+t6R//8R+v6fvvv7+m0cOLWd8zGJOqsSiIZnwfyXoQ\n05diIYQQQggxefRSLIQQQgghJs8g+cRisaifoKNP+vhvvI6ls6AjdPyUf+rUqd51Xk5RwE/uaD5C\niYVZ3+xUpBSR94lyL5GZkEkjWPCM6EQy+x3vL2vmH2NazYBBGaK8zPE7k09EXjkwD5p/s6b4zO8R\nr6T3CRzrf/iHf+j97W//9m+vSp2ZQCBjKHMwmn9sbeD8jbzWMHMkO4Xv1zL2N+uHKCABk0lFtIJ3\nsGs8YwJ+RCfK2e8ZrzbZvaP0MdtrV1dXqwcjHN/IJM6C+2AdkdQFT9JjHpxDvk/886SA/YDlRvKN\nTN8tFovaZjbPo7+xABB+PRbTu8/PvJZ4qQ2axVnwEpRyeA9KKK0o6Wj/Lv3KZJNmfdM9etphgVIi\nrzZMysWCVvj2M8lTNB/wb76/PJs3b7Z3v/vdZtafy75MlAzh/WLf4fjh9WZmt912W02///3vr+k7\n7rijpg8dOlTTuBbMct7HsP7ouYF9KvmEEEIIIYQQSfRSLIQQQgghJs9g+UT5/I+ftb1JAM0h+Gmd\nnfT2Jg38HI6mKPysjhIH/4kdT9liWeicG80W/vM/UuqPTPDlfqOT1NEJ1AwZzwjRKfWh8cB9+8e0\nudwz9l0UfCNzyj7yHjHmd+aQPCNX8f9+Jb1PIFdL1vBKE0le2PxnXkb8PGOn/Zn50p+ojuRirXK9\nqY5JPhhd1zU9w2Q9OWAbI+8Rvs4CGwsfzAL3WiYviOpsmYzZOkL5HjO/+/YySRW21Y8V1o8meyb5\ni+QPfh4Vor0msw8hjz/+uP3sz/7smt/9Xseey0zu6PcVts8wDwqRhAjB/ou8CuB7RsnjPV8hpawo\n+Aa+XzBPWZGnEBb8B8vCvo6ef5lyfZ9k5hrmLRKWyPsK9hHzrhPJLlHO+l//9V81ffTo0Zr+z//8\nz5r2cle2v6I8JHofYpK6LPpSLIQQQgghJo9eioUQQgghxOTRS7EQQgghhJg8g8SIGzdutN27d6/5\n3WuyIncdLU6cONH7N2pC0F0HRqrDtNfEoI4ENUOoSYm0edjmZZoujGjHtGz+bxl9cDZyFXNVFUV5\nYdpH5qYn22Z/fSkv0ooy/RDL48ctiqDE2sVg+SM9dksT/Uq6ZjNb7opnPeA8QP3oy3WP6Lov0qkx\nXSzT6vt5wtY+c6Pm8zO9IcPrL6MIUi0Wi0WtJ9Kts3tm+rsoP3M7h233/ZJxaRe5imyNRaTnb+21\nkZvGjA7YX8N0rez8gc+f0WZHc5XVyVhdXa1R9LJRGdkzAH/3WnCmyWa6bX9frG1YVrQHtNyIRedr\nSluwTH/+Cc8zYZvwHQD7hEW2bbW3VW6kf2VEz/Uhz78rV67YAw88sKacSOeM17GIof4emPYc3x1x\nLDFSotla3XerXObK1bdtTLRVfSkWQgghhBCTRy/FQgghhBBi8gyST2zYsKFGtWHmNbO+mZWZDdGk\ngJFy/HXoeg2vu/7662vam0QQ/BtKMVjarO92qLSTuRVCM2fkOsXnaaWRbJQWJDLTZFxavZzyCSwP\n54NvOzO5MvNiZGrMmJIiU2smOljUr+W6jIzj5WT//v1XrWxc5zfddFNND3Xxx1gsFrW/siZxJhNg\nEiGz/txG0x2L4OVNgDhvsU68DsvykpasdKvApAJ+XWbGIZq/GdeDp0+frmlvamVrM+M2z6wtFYhM\n4qUO7E8/1pELuVZbI5dxzPVbVpLC5iSWFckMMuOLaygCpS7sWZU1x7M8kXtIJp9gbfGyzKFRcEsd\nUUQ7NNXjPMBnFhJFdGTPLOz37HtBdn5GMobWtcWFHfatX29MrsGiw/n5n3GDxtzz+n9jf2Oayb7M\n+PMhi74UCyGEEEKIyaOXYiGEEEIIMXm6IafIu647ZWZPXr3mvKa5ZbFY7PE/TrxPzNQvLdQnbdb0\ni/pEc6WB+qSN+mUt6pM22mvX0pwrnkEvxUIIIYQQQlyLSD4hhBBCCCEmj16KhRBCCCHE5NFLsRBC\nCCGEmDx6KRZCCCGEEJNHL8VCCCGEEGLyDIpo13VdylUFi5I0BhYdKKojioi0rFyzdmSm+Xxu8/l8\nTaVd1y1K/ihyFGtH9hoWQWhMHS+zx5EV4hLnqrg1iaL2rPe+2JzAiDlRRLvCfD63xWIRzpUxbWKM\nWW/RWsL7xXmXjdTH+nGxWKyZK7PZbFEiFUX3yiJBZe+dXZedM0Pnlp+nW7ZsqWmMDPjQQw81189s\nNluUMta7l0R73XrzsLaNWYulHrZ+ZrPZoszNqHzse7ZvjumTMWTmXbZ/5/M53WtbZWTHgEWLjCKF\nIRhpDK+JIpVln+XLuHTpkj3//PNrCti+ffti3759Zma2srJSf79w4ULvukyk1qERTZflYWVj32GU\nXYzke+zYsV5+FjHYGs9l3FOiyHqZKJfR75l7j67JvOuMfNY3149n0Eux2UsLIJpMuJhY6M8ovC57\nEGOeKJQg61RsF5br69+2bVtNlzCQ58+fb9bVdV1tCyvfw/onCmeMk58tBCzXh6NkoVZZ/w4IXUr9\nHmYeYCwMKgsX6kNy41hjGFAWnjLa1LB+nF84H3yoUR821IyHHe+6rt5Xdv6zcJzYP9H/1LExxT7x\noXDxBQ7nGj5Qoo0L/4Z1fu9731szVzZu3Gh79uwpf6dlYjhWLB/HKdpoWZ+w+e/HmYU+ZXVgeHoz\ns/e+9701/ad/+qc1/ba3va25fmazWS0D2xKFSWf7D/ZrFPYU87M6/b2zEL04Xtgvfl9shXRtranS\njp07d64px89/3CMuXrzYrDvqU2TMwxfLY2VHY4L9hevv8uXLzbnSdV0NS4zt9WGS2TMJ1xDOWz+H\n8d/Y5zt27KjprVu3Nu/DrB86mYVnH8rnPve55u/79u2zv/7rvzYzs7/5m7+pv3/xi1/sXYd7NVvX\nuNfieJj15xEL+e7HgZW9efPmmr7rrrtq+ud+7udq+o//+I97+b/73e822//iiy+umSuz2aw+y3CN\nRe9vLBwzjq1/VuN8YnOO7TVmZpcvX65p39+tNvs62F7f6pMWkk8IIYQQQojJM1Q+Ud+8I/NPxozA\nvjCY8a8y0Rc/hH2dZuYf/3vmqxBS6oj+jzdjooryY57M/4lFX3rZdVFb2Ne/jEl9jPmV9Xv0VRL/\nj3OMVSJzj/gFzOeJvjj5a8Z81cyOVcZSE8lQ8H7ZPUXrb8jXtcViUfsQv6j48WdfkXEtRF8kWfvY\nnMl+EWX4a7Afd+3atTQ/fv2LvjSxL/bZPSxjxm99zW3Vw8qKxnWI2R+tclimn8tsvbP1HcHyRP3G\nnnPMEujvl61zxo4dO+yDH/ygmfXHJ9or8Uvt3r17a7p8iTdba43FL73YLiwrui+8jlkCI1pz/Wtf\n+1rz2tlsVtuP9+GtYtjX+PWUWVo8zPKS+ULq82M7sa9xTPBrsr8O+xstJIWu62r90f7P5hDuldhu\n/zWXWdywXOwH/0zNSFKyUr4x6EuxEEIIIYSYPHopFkIIIYQQk2ewDaN8wo7MJMz8mzEL++vw83v2\n9GN0MKR1jTcltEyyly5dapaD5t/o8BEzbTIzRsYjhk/jPUUHEZGMqdyDbYlMS4XIbDlUPhGZTZiZ\nF3/PnrrNmr+Y+ZiVX/ouKylBMxUzK3lTJJrU2FyLzGfsoF+mvVE7s/lb+dj8zxxqMst5IchKspDA\n00bvOmYOjShjl5U/oBkSTZrRXGF9yUzdfj5E3gZa+HtpyY+iOVfqi54/Y2QSrTqy+aPnD/Yjm6t+\n3g5t/44dO+xnfuZnzKw/z/xY4yE4TON165U4RLKu9XqcaB2kxkPByGw2a/7N18sOx+Fawvnon6vY\nX9g+zB+9wzCZE9aJciscNzMuD2qxWCxqfZFEJyPpzB6ex/5i71xegpKRRkT1s+eAP9DH0JdiIYQQ\nQggxefRSLIQQQgghJo9eioUQQgghxOQZrSnOakrGaLKQSDvGfs+4hIo0lZk6lxFp91j/RPUyt0ZM\nL+jrZw7xkayWLTumRU8UaZ2YpopppSL3Sxl9ZOT+hWmeon4ZortD/XmkBWNuwli7PUOjv0X63Uyg\niuhvUUAMs+/fR5nbLPiKWS6ICaZ9XUxXHgUMYWTmrO/TK1eu1HQUQAPbUtqTOYPgYc71o/nL2hVF\nNWTnN5iO0q+XzFzHv5d9LJorqA3F9rJxizTJGS25vybjvi/SsrMgI4wtW7bY3XffbWb9e9++fXvv\nOtQbszUezRU2PtmzKOulNebexVoLDDqEgSGwHJ/GuiKXggzm1iza67FtmI6CcmXd1Ja/l/qwXr+m\n2Z7AdPBZfS9zw+bneGbNZF1OjjpTMDiHEEIIIYQQ1xh6KRZCCCGEEJNnkHwCTZ2RiYmZC5irjcgE\nzWLcZ92fjZEqtNocRVkqZUVmkiiq2rLfzbiJiskHIpMCMx9HprOhboK6rqvljXF7xcyy0VxjfRGZ\nIDNRqqI47a35lZGeROtiqMuwyM0Pu471tf93xiVPtP4y5v6MS0Nm5mT7g5fJsPWTjZyYmU+RSz+U\nL2Xc3G3evNne9a53NduCZKJ/ohsnHxELwfafPn26ptH8fPbs2V4elIWgGzg2B6JIgcUUzvqHmX8j\nl6CZ3yPXYRmy5ltsZxSRL7tfYv7rrrvOzOKxHiprXO+6fjVh0Q8j+QJel3GV5vPjmmMSmCh6IZP9\nYF/76HG4zy0bU/ZMjvZ/dk+RVIw9Z9g4ZKOjMhlWVtKS5bU9s4UQQgghhHgF0EuxEEIIIYSYPIPk\nE13X1c/pWVNM5mRqZIrBz+TsRPWYz+fM1GjWP3HZigDjKe2KIj8xkxiaJKKT4BhRj0kesh4B2Jhk\nTWJjTumz39g4ZE2YmRPl7AStGT/FnonEyOrMmLuz5iPWD1GbmIyGedfw8iUWbYjNj8gknqFcn/VC\ng2TnPyuL9WMUeS2D7wOcZ88+++zS/Pv27bPf+Z3fMbPvRywrRCZxBM3oGBFr27ZtvevQHHvu3Lma\nfvDBB2v6gQceqOlvfvObvfyPPPJITR8/frym2fz27cX5VczH3kMAUsrC/ozGPSOJysqPsp5YmDQv\nu6dlIrL664uniUgeM5QoUt9rnY0bN9ob3/hGM1sbBQ4ZapLPjiF7fkTekzACX2m7mdnevXtretOm\nTb38KLnAslHyxOpjvzEZGL53RF57sB3YXvbe49+VMvI/Vpa/bgz6UiyEEEIIISaPXoqFEEIIIcTk\nGRy8o+VpwZtVmKmemXXHmI+z+Zn5mAUAaP07YjabVRMBmgK9SQBPibK+Q+fq3uRz8eLFmmaO8SMz\nTcYkFznkjuQmLTD4QGRCZKbGjAnF5/f1F3Bc/H2xscY8aNbyQVBYcABGSyqQ9Z7CronMxyx/FCAA\n/8Y8CjBvEMv+lm1jdEo7uq4w5kT/mFPQbM769g4JUmFmduLECfvUpz5lZv178dILLBfHCvPg/PWy\nLLwOTbFYLnqcQBmXmdn58+dr+syZMzXN1kI0LmVtRabr0v5MgA1fftZTT8bTTmSiZXWy52LxktC6\nLgN6FRDfp+u6Op+j8cwExomeqwiT5ETvKlge84Th5wfLv2xfQY8c0X1nZIyYJ5IvYNvxuuj9KxOQ\nK9pr1xt8TV+KhRBCCCHE5NFLsRBCCCGEmDyDg3e0Ts97hjr8zwZ0yH4WZ/Uzs4D/fF8coZu9dJ+R\n4/di0ssGecD68HTm/v37a/rgwYO9/Gi2RHMmM8N5kwtzHM9O7/v+ZaYPBvNUst5yI+kGczqOfRE5\nb8frcFxuuOGGmsYT9mZt5+kZbyxRn7DgEBkPDFiHB++dSXB8eRkn9FlT8pBrIkkJ+515FzDjXkbG\nBO9AonFEhs7zZ5991r7zne+YWX+9evkElsskWjiefq6gnALlW8xU6fuVBSUZI1Uo7c/uL620zz9U\niuTbxMzgWU8prB+i5190Mp+x3hP31xpd19U+wTXj5T9MZsdkDX7+susY0VhjflxXuK79+sW/LZPv\nbdq0yd72treZWf9evccS3AeYxwm275hx7zEotcL789fjeLG1EHlfYu+MmfEx05diIYQQQggh9FIs\nhBBCCCGEXoqFEEIIIcTkGR3RLnIJxfReGfc0/jqmE2VRVzysnagZxYhPZmY333xzTZ8+fdrMvu8i\niVHKZZHAfHuxbtTv3HTTTTX9oz/6o738jz32WE2jhifjns0spxGMxjRya9YC50qk4WTzgGk9vaYK\n+49pbrFcdFvl/1aiQpmZ7dmzp6bf8pa31LR3yYZ6qCHuXyI3PZG7mdbvkX6dlYV5svkz7TLj49ga\nU3Tdl3VdxOYMzo0oP5Jx+ej/zbSl0TmFoetnPp/blStX1lzvx4ppZjNp/2+mb4zanqknu/7L3zJn\nTKKIjJlnxhiXhmPc/7HrIp11xjWliOm6rj5n8awIPi/M+FpmWt0ooikDr/FnfXDu4t/wXBM+l/D3\nKD+6cC3s27fPPv7xj5tZ/5mGZ2bM+usddcAY8RIj5h09erSX/9ChQ82/YXplZaWmDx8+3MuP/YU6\nYhyTaP1HZ0sy6EuxEEIIIYSYPHopFkIIIYQQk2ewfKJ8oo9Mhcx8ytzQRBHlvAyh0DK7tcpm5vG9\ne/fW9F133dXL/453vKOm7733XjPrmwQ8pb6oTSxKGDPNoHnDrC+5wLKxrMhUwCLYsLHyJkEck6zr\nmVb0Nt9GZsZkc8CbnzKRDbG93hzJXL7s3LmzpnEsnnzyyV7+Y8eO1XTGJdsQE7EH24r9E5n6M67E\nIjd1Q03BvuzITaHPnzFFsrxmsZsgZtof4yaS1R+Z4cdEWSr3g33o62BuklieSFaF64yNhZcPRa79\nCln3YxlafRfte2yeR27mGMwNVCQfZO2MIsIyN2HeHZ/goHwP+9e7uGN7ajaqIBtHtodGLvZwrKP9\nGYmkUZ4zZ87Y3/3d35lZXzLhJSUojUAXdjj/8D5QVmHWl1wwN3NYls+P12WkUJFLxqwbNkRfioUQ\nQgghxOTRS7EQQgghhJg8o71P4Cd9b/7JmAHw87uXSKAZA8v2JtGonQWUHWDklhtvvLGm3/e+9/Xy\nf/CDH1zTzi984Qu0rmJqyZrUMiabO+64o5ffe8goMPmDN0uy8cpG9MpGc8JrMt4nWKSvMSYQLJv1\na3RSHNuyY8eOmn77299e01/+8pd7+dEMVOZn1Kflb1mpCzO1R+MRzQPWLpaf3UtWDpD1tODr8vfE\nZEbsFH9kcmTSE7wn32+sHjZ//J6GMqesTKTMES8vY7A+ikyNLNodiwQVyS9Q2pSNytaaR5locZFX\nCOaRg41htFdmvL9ko8kxU3C0RrJzRRHt+szn82qGZx50zPhzhsmiIq82bJ3i/I+kaigbKJ5nzPqe\nJHz9kccdz4ULF+xf/uVf1rTb58NnGptXmN+vbybJYu9HfkwyEemy62KIR6ha5+AcQgghhBBCXGPo\npVgIIYQQQkyeQfIJs/YJ++j0OftMnj2RyeqJzFdYXsa8gZ4GzMwOHDhQ08VjBTN3z+fzahqNAiKg\n+ZSZB9D8uG/fvjX1FNC0kg1ywUyCzGNGZJIfKp+InJ9nzNJMdmPGg5KwtkdSDLwOT+TeeeedNb11\n69Zente//vVr8kcm18ypZjbXMqfa/XUsjXn86ePMmh0TEGIZWY8WmfkXyZfYnIlMkWxuZk+pY9nZ\n9VOuY3uELxf/Fkm5ELY/Mu8Vvl9wPTL5U1a+UYjmTPlbdA3b05gpNRrrzPhG3l8yHjl8HdF+J3LM\nZrMqnWSyFTPuPSVr6mcynOx+xeQbzNODb3/UNs/q6mrPM0TBz18255i8yq8f3IeYl7EoeI1vcyET\nHMiXPUZWpC/FQgghhBBi8uilWAghhBBCTJ5B8onFYlE/Z0efqDMnFrMmOWb+wlONkfkJTRIoOzhx\n4kRNP/zww738X//612v6W9/6lpnFjtNbARm8CWKo/ADN8mbcjMD6NDsm2dOZGZmCr68V6CUyB2K5\nWRMm86rBzL+RqQav27ZtW03fdNNNNe1jz7eC2GTGN5oPGdNzJF9iwVmYGd7LJ9h4MelJdL/LAiPg\nPEGiIA/MYT6a56I5yqQM0fph5bExiQISZWn1nV8LmX0h8srBTnSzsnzwDpwf6B2IScn8PbWkbpHM\noZSF+aL5l/FuE5lf2X6RlQ9l9udI/pRlzCn7a53SJ7i/+ecqG5NsoDE2P5isIpKFMfnS5cuXa9rv\nwcz7DaMVaCwK1MX6YYwkkvVDdE/MS0tWEjkGfSkWQgghhBCTRy/FQgghhBBi8uilWAghhBBCTJ7B\nmuKiG4uixOC/mR6UaVX8vzMuT3wdqG3Dv6E258yZMzX9v//7v738qFd76KGHzGytlg7bWq7PaoqZ\nHg7r8Fol9jem88nqcJFIUzmGUl6kH89o9qIIfMylFpsDXhvOdLaoWWcR0Hw9ZYwyuuWsW6+MSyh/\nDcvD9LeRJj/j0iq634zWMRPJLKOtjnTaQ7XZPj9bG1nXS0M1+VhetNeyaHNM0xvdF9P+ZiNCsnkT\nRT9tXTckCqJZ392lWdtNoi+XuZIzy41ptH6zOnX2+5hoedkIX68mmUiD0VmJIfeIz+VIf8qeE1n3\nfRn3X9F5gsz8uHTpUk3je4tZ/3mWWTctN4++XzMuOaO+ylyH4xC9K+FzGK9j54/M8u4oGfpSLIQQ\nQgghJo9eioUQQgghxOQZ7CeofAKP5A9DTb6RWYSZHfHzu68f/4amCzQ1YLmPPPIIzX/06FEz65tZ\nEHRTF5ma2d+wTefOnatpL9dgEW6YyThrsmFurCI3RRnQfIXlRuZT5vqGuWXx+dn9ozk1chGG16HZ\nJjJfDzXPtEznY9znRWZGFgGJubrxLtGYmy5mqvd9MFQqMMTs569nprrsuLA+icDrsiZxxJv7WbvK\ndUxC5v+dkbr4fmm5wzPj/R1JBZgbxagvWuOUMZNHY83alJX/ZFyKZqOUMUlb5PaNrb+ovoz0JNoz\nWr+v161nZJZnazhyMRa9c7TqLi5Yx0hdmAk/kgpkIjp6+Qb+DZ8/7Fm0efPmXn7ci9g7Squ+rGQv\nE0XV9wk+e5n0MJIvZfoxqn+MZKKXf125hRBCCCGEuAbQS7EQQgghhJg8w8MsJRh6+jBLxoRqxqUD\nLU8BZmtPdGL+8rcoolXrc31kEmBko60xM88YjxHZk/Tr8UaRNTsy7wiR+QrHNGMe9LDrLly4UNMo\nrzl//jzNv8xsg2bOyFTPxjTjqcOXjX2HpnJmnvPlYTQo5sUgmivL5BPslHgUJSmTjuQ/zKSXOX3u\n25YxL/rymCcbf33pu6g+thdkT8+zfTgTCS5bz9WOtub7hHm+YLKxKH+mzkh+gf2L6yxa/2P6rtQT\nSdVYG5lkIZrDzKNItAbZ+spKkLKSy5K37HfRus7IW7LyH9Y+lAr4vZZFH8XrcK+O9vplUTNns5lt\n2rRpTT6/R7O5zeRz0ftX5vkVzbPM/M96X8qiL8VCCCGEEGLy6KVYCCGEEEJMntHyiazZnplpIlPf\n0IAfkUN5ZhpCbw6+/RcvXqzpcoKVffpfLBbN4ANZh+zMTOJPmaLpm51+Z6czffszwQu8KSby9sFo\nBR+IZDNoZsIxxX7xY42maGbSiYJ/IDgnDh8+XNPf/va3a/r06dM0T7lP1j9d19W2RKbAjKQlMpXh\n33DebNu2rab37t1b01u3bu3lx/nP5hSOo/emwILsLGOMJIOtpehEPzN5Rm1lHkgya8msP7dRmhNR\n6onamDE1Zr3iIMwE6k+4Z/aFqF9a9bA9YjabVTlPZDbOnF6PAh0x+UUkuWAwzwEsOJAZ9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x116741f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10,20))\n",
    "for i in range(200):\n",
    "    plt.subplot(20,10,i+1)\n",
    "    plt.imshow(kmeans.cluster_centers_[i,:].reshape(patch_size),cmap=plt.cm.gray);\n",
    "    plt.xticks([]);\n",
    "    plt.yticks([]);\n",
    "plt.tight_layout(h_pad=.01, w_pad=.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Here, overcomplete transformation by K-Means seems to be very helpful, since each of the centers are like a informative feature!\n",
    "\n",
    "# We will talk about this later on \"Dictionary Learning\" and later in \"Deep Learning\" algorithms, where the main problem is to find an appropriate representation of the data\n",
    "\n",
    "### Further reading\n",
    "* https://cs.stanford.edu/~acoates/papers/coatesng_nntot2012.pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Another view to the original problem of clustering\n",
    "\n",
    "\n",
    "## Are outliers bad things or good things?\n",
    "\n",
    "### Examples: \n",
    "* **research communities and those research topics that don't belong to any group?** \n",
    "* ** Can we say outliers might be those who are ahead of their fields?** \n",
    "* ** What if we set our criteria based on the above clustering definition?** \n",
    "\n",
    "* ** One tricky recent application of ML in peer review process: Quick pre-assessments of papers for their potential popularity!!!***\n",
    "http://www.ariessys.com/views-press/press-releases/artificial-intelligence-integration-allows-publishers-first-look-meta-bibliometric-intelligence/\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# What if we say each obsevation is a potential communiy itself?\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What if we increase K in K-means drastically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "1ca0c4005b7645a4aaf69eca8c512bac",
       "version_major": 2,
       "version_minor": 0
      },
      "text/html": [
       "<p>Failed to display Jupyter Widget of type <code>interactive</code>.</p>\n",
       "<p>\n",
       "  If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n",
       "  that the widgets JavaScript is still loading. If this message persists, it\n",
       "  likely means that the widgets JavaScript library is either not installed or\n",
       "  not enabled. See the <a href=\"https://ipywidgets.readthedocs.io/en/stable/user_install.html\">Jupyter\n",
       "  Widgets Documentation</a> for setup instructions.\n",
       "</p>\n",
       "<p>\n",
       "  If you're reading this message in another notebook frontend (for example, a static\n",
       "  rendering on GitHub or <a href=\"https://nbviewer.jupyter.org/\">NBViewer</a>),\n",
       "  it may mean that your frontend doesn't currently support widgets.\n",
       "</p>\n"
      ],
      "text/plain": [
       "interactive(children=(IntSlider(value=20, description=u'K', max=300, min=20, step=10), Output()), _dom_classes=('widget-interact',))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from ipywidgets import interact, HTML, FloatSlider\n",
    "X = Data1\n",
    "interact(visualize_Kmeans,K=(20,300,10));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This is the origin of the idea of Vector Quantization.\n",
    "### However, K-means is not scaling perfectly. For example, most of clusters overlap."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <a></a>\n",
    "\n",
    "# If we look at it as a kind of indexing of the space, we need to sort the indices themselve!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# In order to do so, we invert the whole game of data clustering\n",
    "# we create an aribitrary ordered set of indexes and try to fit them to data, while having a \"topology preserving\" indexing.\n",
    "\n",
    "# This means, if two indices have similar label, they should index a similar area of data space and vice versa.\n",
    "\n",
    "# This is the original idea of Self Organizing Maps (SOM) and manifold learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total time elapsed: 0.418000 secodns\n",
      "final quantization error: 0.040090\n"
     ]
    }
   ],
   "source": [
    "import sompylib.sompy as SOM\n",
    "msz11 =20\n",
    "msz10 = 20\n",
    "X = Data1\n",
    "som1 = SOM.SOM('', X, mapsize = [msz10, msz11],norm_method = 'var',initmethod='random')\n",
    "som1.init_map()\n",
    "som1.train(n_job = 1, shared_memory = 'no',verbose='final')\n",
    "codebook1 = som1.codebook[:]\n",
    "codebook1_n = SOM.denormalize_by(som1.data_raw, codebook1, n_method = 'var')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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E3QrP57N3b8X6+QawrcGiZDtu4hQyUiXCgf5Kv7vOJbONFnhXzBjec2sqMuMN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\nFS5FURRlWfH/AT2nXMGhxC2aAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112c59750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(X[:,0],X[:,1],'ok',alpha=0.5, markersize=4);\n",
    "K = som1.nnodes\n",
    "for k in range(som1.nnodes):\n",
    "    plt.plot(codebook1_n[k,0],codebook1_n[k,1],marker='o',markersize=10,alpha=1.,color=plt.cm.RdYlBu_r(float(k)/K));\n",
    "fig.set_size_inches(7,7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now from this point of view let's think about linear regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 50\n",
    "x1= np.random.normal(loc=17,scale=5,size=N)[:,np.newaxis]\n",
    "x2= np.random.normal(loc=0,scale=10,size=N)[:,np.newaxis]\n",
    "y = 3*x1 + np.random.normal(loc=.0, scale=.4, size=N)[:,np.newaxis]\n",
    "\n",
    "# x1 = np.random.uniform(size=N)[:,np.newaxis]\n",
    "# y = np.sin(2*np.pi*x1**3)**3 + .1*np.random.randn(*x1.shape)\n",
    "\n",
    "y =-.1*x1**3 + 2*x1*x1 + 2*np.sqrt(x1)+ 10*np.random.normal(loc=30.0, scale=4.7, size=len(x1))[:,np.newaxis]\n",
    "\n",
    "\n",
    "degree= 2\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn import linear_model\n",
    "X_tr = x1[:].astype(float)\n",
    "y_tr = y[:].astype(float)\n",
    "poly = PolynomialFeatures(degree=degree)\n",
    "X_tr_ = poly.fit_transform(X_tr)\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X_tr_, y_tr)\n",
    "X_pred = np.linspace(X_tr.min(),X_tr.max(),num=500)[:,np.newaxis]\n",
    "X_pred_ = poly.fit_transform(X_pred)\n",
    "y_pred = regr.predict(X_pred_)[:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/SVM/anaconda/envs/tensorflow/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class RandomizedPCA is deprecated; RandomizedPCA was deprecated in 0.18 and will be removed in 0.20. Use PCA(svd_solver='randomized') instead. The new implementation DOES NOT store whiten ``components_``. Apply transform to get them.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n",
      "/Users/SVM/anaconda/envs/tensorflow/lib/python2.7/site-packages/sklearn/utils/deprecation.py:52: DeprecationWarning: Class RandomizedPCA is deprecated; RandomizedPCA was deprecated in 0.18 and will be removed in 0.20. Use PCA(svd_solver='randomized') instead. The new implementation DOES NOT store whiten ``components_``. Apply transform to get them.\n",
      "  warnings.warn(msg, category=DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Total time elapsed: 1.649000 secodns\n",
      "final quantization error: 0.008065\n"
     ]
    }
   ],
   "source": [
    "import sompylib.sompy as SOM\n",
    "msz11 =20\n",
    "msz10 = 20\n",
    "X = np.concatenate((x1,y),axis=1)\n",
    "som1 = SOM.SOM('', X, mapsize = [msz10, msz11],norm_method = 'var',initmethod='pca')\n",
    "som1.init_map()\n",
    "som1.train(n_job = 1, shared_memory = 'no',verbose='final')\n",
    "codebook1 = som1.codebook[:]\n",
    "codebook1_n = SOM.denormalize_by(som1.data_raw, codebook1, n_method = 'var')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Y78GDIIJ75EjmX3cd7hEj6mRbb++kdAnLm8Uc96c//SlXXnklzzzzTHSfzkg2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\nxgEAAAAACNn/B5jk6JgTINDMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e548390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "fig.set_size_inches(14,7)\n",
    "plt.subplot(1,2,1)\n",
    "plt.title('data points vote for the line')\n",
    "plt.plot(X_tr,y_tr,'.r',markersize=20,alpha=.4 );\n",
    "plt.plot(X_pred,y_pred,'ok',markersize=3,alpha=.4 );\n",
    "\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.title('each data point creates its own community')\n",
    "plt.plot(X[:,0],X[:,1],'.r',alpha=0.5, markersize=20);\n",
    "plt.plot(codebook1_n[:,0],codebook1_n[:,1],'ok',markersize=3,alpha=1.);\n",
    "plt.tight_layout()\n",
    "font = {'size'   : 12}\n",
    "plt.rc('font', **font)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think about it in terms of structure of our social ties and identities. \n",
    "## One is the product of 19th century's idealization and the one is 21st century"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Next session we discuss SOM and its applications"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}