Interactive_Spectral_Clustering.ipynb

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    "\n",
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Subsurface Data Analytics \n",
    "\n",
    "## Interactive Spectral Clustering\n",
    "\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "### PGE 383 Exercise: Interactive Spectral Clustering in Python \n",
    "\n",
    "Here's a simple workflow, demonstration of spectral declustering (for automated category assignment) for subsurface modeling workflows. This should provide you experiential learning to help you understand the spectral approach.\n",
    "\n",
    "####  Spectral Clustering\n",
    "\n",
    "Spectral clustering is based on graph theory, where the sample data are mapped to a $n \\times n$ array that describes the degree of pairwise 'connectivity' between the sample data, and then Eigen vectors are calculated to reduce the dimensionality and k-means clustering is applied on the retained Eigen vectors to find the clusters.\n",
    "\n",
    "The advantages of the method includes:\n",
    "\n",
    "* the ability to encode connectivity between the samples in the dataset. While kernel and nearest neightbour approaches are common to determine connectivity, this step could include integration of various information sources.  \n",
    "\n",
    "* the Eigen values provide useful diagnostic information to inform the number of natural clusters based on the degree of cutting of connection required to separate the dataset\n",
    "\n",
    "* the Eigen vectors provide reduced dimensional representations of the high dimensional representation of pairwise connection\n",
    "\n",
    "**Other Resources** - I found the short article with demonstration on [Spectral Clustering](https://towardsdatascience.com/spectral-clustering-aba2640c0d5b) by William Fleshman quite useful to understand this approach. \n",
    "\n",
    "These are the steps for spectral clustering:\n",
    "\n",
    "* **Calculate the Simularity Graph and Matrix**\n",
    "\n",
    "* **Calculate the Degree Matrix**\n",
    "\n",
    "* **Calculate the Graph Laplacian Matrix**\n",
    "\n",
    "* **Perform Dimensionality Reduction on the Graph Laplacian Matrix**\n",
    "\n",
    "* **Assign Clusters in the Reduced Dimensionality**\n",
    "\n",
    "##### Calculate the Simularity Graph and Matrix\n",
    "\n",
    "Spectral clustering first calculates a graph of the data in predictor space\n",
    "\n",
    "* a graph is comprised of the samples (nodes) and connections (edges/vertices) between the samples\n",
    "\n",
    "There are mulitple methods to represent the sample data graph in predictor feature space:\n",
    "\n",
    "* **affinity matrix** the connections are represented as an $n \\times n$ matrix with 0 if no connection and a measure of similarity for connected samples. This is accomplished with radial basis function kernel with a specified gamma, or other kernels such as polynomial.\n",
    "\n",
    "* **adjacency matrix** the connections are represented as a $n \\times n$ matrix with 0 if no connection and 1 if connected.  This matrix may be calculated with k-nearest neighbor (up to a determined maximum number of neighbors), epsilon-neighborhood (all points withing a radius) or radial basis function kernel with a specified gamma, or other kernels such as polynomial. \n",
    "\n",
    "##### Calculate the Degree Matrix\n",
    "\n",
    "The degree matrix is a diagonal matrix where elements $[i,i]$ are the summation of the adjacency matrix row $i$.\n",
    "\n",
    "##### Calculate the Graph Laplacian Matrix \n",
    "\n",
    "The graph Laplacian is the adjacency matrix subtracted from the degree matrix.\n",
    "\n",
    "##### Perform Dimensionality Reduction on the Graph Laplacian Matrix\n",
    "\n",
    "Calculate the Eigen Values and Eigen Vectors of the Graph Laplacian matrix. The result is $n$ Eigen vectors (of length $n$) and $n$ Eigen values.  We can interprete the Eigen values / vectors as follows:\n",
    "\n",
    "* the number of zero Eigen values are the number of connected parts of the dataset.  For example, when the simularity graph indicates 0 similarity for all sample data to sample data combinations, all Eigen values are 0, all sample data are independent connected parts. If all data are connected, then all Eigen values except for the first are nonzero, indicating all sample data in one connected part.\n",
    "\n",
    "* the first nonzero Eigen value is the **spectral gap**. It provides an indication of the density of the sample to sample connections. For example, if the affinity is 1.0 for all sample data pairs, the spectral gap is equal to $n$.\n",
    "\n",
    "* the second Eigen value is the **Fiedler value** and the associated Eigen vector is the **Fiedler vector**. It indicates the level of graph cut to separate the sample dataset into 2 parts. For example, if the second Eigen value is 0 already, then the dataset is already separated into atleast 2 parts; therefore, no cuts are needed!\n",
    "\n",
    "##### Assign Clusters in the Reduced Dimensionality\n",
    "\n",
    "The final step is to assign the clusters based on the result from the dimensionality reduced graph Laplacian matrix.  There are a couple of methods possible demonstrated here:\n",
    "\n",
    "1. We can use the Eigen values to determine the number of clusters:\n",
    "\n",
    "* jumps in Eigen values are used to identify the natural number of clusters in the dataset. i.e. if we add another connected group we would have to do a lot more cuts!\n",
    "\n",
    "2. Assignment of clusters by Eigen vector values:\n",
    "\n",
    "* the sign of the Fiedler vector provides the 2 custers (positive and negative) if the dataset where cut into 2 groups.\n",
    "\n",
    "3. Assignment of clusters by k-means clustering applied to the Eigen vectors \n",
    "\n",
    "* we apply k-means clustering on the Eigen vectors up to the determined number of clusters. This finds the groups asessed while integrating pairwise connections of the sample data.\n",
    "\n",
    "#### Objective \n",
    "\n",
    "In the PGE 383: Subsurface Machine Learning class I want to provide hands-on experience with building subsurface modeling workflows. Python provides an excellent vehicle to accomplish this. I have coded a package called GeostatsPy with GSLIB: Geostatistical Library (Deutsch and Journel, 1998) functionality that provides basic building blocks for building subsurface modeling workflows. \n",
    "\n",
    "The objective is to remove the hurdles of subsurface modeling workflow construction by providing building blocks and sufficient examples. This is not a coding class per se, but we need the ability to 'script' workflows working with numerical methods.    \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - unconv_MV.csv at https://git.io/fjmBH.\n",
    "\n",
    "There are exampled below with these functions. You can go here to see a list of the available functions, https://git.io/fh4eX, other example workflows and source code. \n",
    "\n",
    "#### Install Packages\n",
    "\n",
    "We will include the standard packages for DataFrames and ndarrays and add scikit-learn (sklearn) for machine learning and ipywidgets for interactivity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will also need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "import copy                               # for deep copies\n",
    "import math                               # for square root function\n",
    "from sklearn.neighbors import NearestNeighbors # nearest neighbours function to calculate eps hyperparameter\n",
    "from sklearn.preprocessing import MinMaxScaler # min/max normalization\n",
    "from sklearn.cluster import KMeans        # k-means clustering\n",
    "from sklearn.cluster import DBSCAN        # DBSCAN clustering\n",
    "from sklearn.cluster import SpectralClustering # spectral clustering\n",
    "from ipywidgets import interactive        # widgets and interactivity\n",
    "from ipywidgets import widgets                            \n",
    "from ipywidgets import Layout\n",
    "from ipywidgets import Label\n",
    "from ipywidgets import VBox, HBox\n",
    "cmap = plt.cm.inferno                     # color map with tone and intensity change"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Declare Functions\n",
    "\n",
    "n/a\n",
    "\n",
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"d:/PGE383\")                     # set the working directory with the input data file"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Specifying Data\n",
    "\n",
    "Let's specify a small dataset with arbitrary $X_1$ and $X_2$ features. \n",
    "\n",
    "* we can easily edit the data to explore the behavoir of spectral clustering\n",
    "\n",
    "* the can run the approach fast enough to itneractive with the system in realtime\n",
    "\n",
    "We will also calculate the:\n",
    "\n",
    "* **adjacency matrix** - we will asumme a radius to efficiently find the linkages\n",
    "\n",
    "* **degree matrix** - the sum of connections for each sample data as a diagnonal matrix\n",
    "\n",
    "* **graph Laplacian matrix** - the adjacency matrix subtracted from the degree matrix  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# specify the sample data\n",
    "X1 = [100,150,170,150,270,360,440,470]; X2 = [400,320,200,90,420,350,420,270] # made up small dataset, 2 paired features\n",
    "\n",
    "\n",
    "radius = 150                              # specify the feature distance for pairwise connections\n",
    "\n",
    "adjacency = np.zeros([len(X1),len(X1)])   # declare the 2D matrices\n",
    "degree = np.zeros([len(X1),len(X2)])\n",
    "\n",
    "# populate the adjacency matrix\n",
    "for j in range(0,len(X1)):\n",
    "    for i in range(0,len(X1)):\n",
    "        if i != j:\n",
    "            distance = math.sqrt((X1[i]-X1[j])*(X1[i]-X1[j]) + (X2[i]-X2[j])*(X2[i]-X2[j]))\n",
    "            if distance <= radius:\n",
    "                adjacency[i,j] = 1; adjacency[j,i] = 1 \n",
    "\n",
    "# plot the adjacency matrix\n",
    "plt.subplot(222)  \n",
    "plt.imshow(adjacency,cmap = plt.cm.binary); plt.grid(alpha = 0.2)\n",
    "plt.xlim([-0.5,len(X1)-1+0.5]); plt.ylim([-0.5,len(X2)-1+0.5]);\n",
    "plt.title('Adjacency Matrix'); plt.xlabel('$X_1$'); plt.ylabel('$X_2$');\n",
    "plt.colorbar()\n",
    "\n",
    "# populate the degree matrix\n",
    "for j in range(0,len(X1)):\n",
    "    summation = 0\n",
    "    for i in range(0,len(X1)):\n",
    "        summation = summation + adjacency[i,j]\n",
    "    degree[j,j] = summation\n",
    "    \n",
    "# plot the degree matrix\n",
    "plt.subplot(223)  \n",
    "plt.imshow(degree,cmap = cmap); plt.grid(alpha = 0.2)\n",
    "plt.xlim([-0.5,len(X1)-1+0.5]); plt.ylim([-0.5,len(X2)-1+0.5]);\n",
    "plt.title('Degree Matrix'); plt.xlabel('$X_1$'); plt.ylabel('$X_2$');\n",
    "plt.colorbar() \n",
    "    \n",
    "# calculate the Laplacian matrix\n",
    "Laplace = degree - adjacency\n",
    "\n",
    "# plot the Laplacian matrix\n",
    "plt.subplot(224)  \n",
    "plt.imshow(Laplace,cmap = cmap); plt.grid(alpha = 0.2)\n",
    "plt.xlim([-0.5,len(X1)-1+0.5]); plt.ylim([-0.5,len(X2)-1+0.5]);\n",
    "plt.title('Graph Laplacian Matrix'); plt.xlabel('$X_1$'); plt.ylabel('$X_2$');\n",
    "plt.colorbar()\n",
    "    \n",
    "# plot the sample data graph\n",
    "plt.subplot(221)\n",
    "plt.scatter(X1,X2,c = 'red',alpha = 0.2,edgecolors = 'black')\n",
    "for j in range(0,len(X1)):\n",
    "    for i in range(0,len(X1)):\n",
    "        if adjacency[i,j] == 1:\n",
    "            x1 = [X1[i],X1[j]]; x2 = [X2[i],X2[j]]\n",
    "            plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "plt.xlabel('$X_1$'); plt.ylabel('$X_2$'); plt.title('Sample Data and Graph')\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=2.0, wspace=0.2, hspace=0.3)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eigen Vectors and Values\n",
    "\n",
    "Let's calculate the Eigen vectors and values with the NumPy package\n",
    "\n",
    "```python\n",
    "vals, vecs = np.linalg.eig(Laplace)             \n",
    "vecs = vecs[:,np.argsort(vals)]\n",
    "vals = vals[np.argsort(vals)]\n",
    "```\n",
    "\n",
    "Note, NumPy's [argsort](https://numpy.org/devdocs/reference/generated/numpy.argsort.html) returns an int 1D ndarray iwth the indices that sort on value. This sorts the Eigen values and Eigen vectors in order of ascending Eigen value.\n",
    "\n",
    "* i.e. first Eigen vector and value has the lowest Eigen value\n",
    "\n",
    "* code taken from this [article and demonstration](https://towardsdatascience.com/spectral-clustering-aba2640c0d5b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# calculate the Eigen values and vectors and sort by Eigen value\n",
    "vals, vecs = np.linalg.eig(Laplace)\n",
    "vecs = vecs[:,np.argsort(vals)]\n",
    "vals = vals[np.argsort(vals)]\n",
    "\n",
    "# plot the sorted Eigen values\n",
    "plt.subplot(221)\n",
    "plt.plot(vals,c = 'red',alpha = 0.4); \n",
    "plt.title('Eigen Values of Graph Laplacian'); plt.ylabel('Eigen Values'); plt.xlabel('Ordered Eigen Vectors')\n",
    "\n",
    "# plot the sample data graph with 2nd Eigen vector\n",
    "plt.subplot(222)\n",
    "plt.scatter(X1,X2,c = vecs[:,1],alpha = 0.8,edgecolors = 'black')\n",
    "for j in range(0,len(X1)):                 # plot vertices \n",
    "    for i in range(0,len(X1)):\n",
    "        if adjacency[i,j] == 1:\n",
    "            x1 = [X1[i],X1[j]]; x2 = [X2[i],X2[j]]\n",
    "            plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "plt.xlabel('$X_1$'); plt.ylabel('$X_2$'); plt.title('Sample Data Graph and $2^{nd}$ Eigen Vector')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('$2^{nd}$ Eigen Vector', rotation=270, labelpad=20)\n",
    "\n",
    "# plot the sample data graph with 3rd Eigen vector\n",
    "plt.subplot(223)\n",
    "plt.scatter(X1,X2,c = vecs[:,2],alpha = 0.8,edgecolors = 'black')\n",
    "for j in range(0,len(X1)):                 # plot vertices\n",
    "    for i in range(0,len(X1)):\n",
    "        if adjacency[i,j] == 1:\n",
    "            x1 = [X1[i],X1[j]]; x2 = [X2[i],X2[j]]\n",
    "            plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "plt.xlabel('$X_1$'); plt.ylabel('$X_2$'); plt.title('Sample Data Graph and $3^{rd}$ Eigen Vector')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('$3^{rd}$ Eigen Vector', rotation=270, labelpad=20)\n",
    "\n",
    "# plot the sample data graph with 4th Eigen vector\n",
    "plt.subplot(224)\n",
    "plt.scatter(X1,X2,c = vecs[:,3],alpha = 0.8,edgecolors = 'black') \n",
    "for j in range(0,len(X1)):                 # plot vertices\n",
    "    for i in range(0,len(X1)):\n",
    "        if adjacency[i,j] == 1:\n",
    "            x1 = [X1[i],X1[j]]; x2 = [X2[i],X2[j]]\n",
    "            plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "plt.xlabel('$X_1$'); plt.ylabel('$X_2$'); plt.title('Sample Data Graph and $4^{th}$ Eigen Vector')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('$4^{th}$ Eigen Vector', rotation=270, labelpad=20)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=2.0, wspace=0.2, hspace=0.3)      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Assign Clusters by k-Means Clusters on Eigen Vectors\n",
    "\n",
    "Now we will apply k-Means clusters on the first k vectors where k is the number of clusters.\n",
    "\n",
    "* code taken from this [article and demonstration](https://towardsdatascience.com/spectral-clustering-aba2640c0d5b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 2                                     # set the number of clusters\n",
    "kmeans = KMeans(n_clusters=k)             # instantiate k-means clusters\n",
    "kmeans.fit(vecs[:,1:k])                   # fit k-means clusters\n",
    "clusters = kmeans.labels_\n",
    "\n",
    "# plot the sample data graph with 2nd Eigen vector\n",
    "plt.subplot(222)\n",
    "for j in range(0,len(X1)):                 # plot vertices\n",
    "    for i in range(0,len(X1)):\n",
    "        if adjacency[i,j] == 1:\n",
    "            x1 = [X1[i],X1[j]]; x2 = [X2[i],X2[j]]\n",
    "            plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "plt.scatter(X1,X2,c = clusters,alpha = 1.0,edgecolors = 'black',vmin = 0, vmax = k-1, cmap = plt.cm.Dark2)\n",
    "plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "plt.xlabel('$X_1$'); plt.ylabel('$X_2$'); plt.title('Sample Data Graph and Assigned Clusters')\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label('Cluster Index', rotation=270, labelpad=20)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=3.0, wspace=0.2, hspace=0.3)  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Interactive Spectral Clustering Method\n",
    "\n",
    "The following code includes:\n",
    "\n",
    "* dashboard with number of clusters, variogram model sample locations in the feature space and the radius for connections \n",
    "\n",
    "* plots the Eigen values, 2nd Eigen vector and clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings; warnings.simplefilter('ignore')\n",
    "\n",
    "color = ['blue','red','green','yellow','orange','white','magenta','cyan']\n",
    "\n",
    "style = {'description_width': 'initial'}\n",
    "l = widgets.Text(value='                                              Spectral Clustering, Michael Pyrcz, Associate Professor, The University of Texas at Austin',layout=Layout(width='950px', height='30px'))\n",
    "ncluster = widgets.IntSlider(min = 2, max = 8, value = 2, step = 1, description = 'nclusters',orientation='vertical',\n",
    "                          layout=Layout(width='100px', height='200px'))\n",
    "ncluster.style.handle_color = 'gray'\n",
    "\n",
    "radius = widgets.FloatSlider(min=0.0, max = 1000.0, value = 50.0, step = 10.0, description = 'radius',\n",
    "                        orientation='vertical',layout=Layout(width='100px', height='200px'))\n",
    "radius.style.handle_color = 'gray'\n",
    "   \n",
    "x1 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[0], step = 1.0, description = '$x_1$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x1.style.handle_color = color[0]\n",
    "y1 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[0], step = 1.0, description = '$y_1$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y1.style.handle_color = color[0]\n",
    "\n",
    "x2 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[1], step = 1.0, description = '$x_2$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x2.style.handle_color = color[1]\n",
    "y2 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[1], step = 1.0, description = '$y_2$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y2.style.handle_color = color[1]\n",
    "\n",
    "x3 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[2], step = 1.0, description = '$x_3$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x3.style.handle_color = color[2]\n",
    "y3 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[2], step = 1.0, description = '$y_3$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y3.style.handle_color = color[2]\n",
    "\n",
    "x4 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[3], step = 1.0, description = '$x_4$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x4.style.handle_color = color[3]\n",
    "y4 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[3], step = 1.0, description = '$y_4$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y4.style.handle_color = color[3]\n",
    "\n",
    "x5 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[4], step = 1.0, description = '$x_5$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x5.style.handle_color = color[4]\n",
    "y5 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[4], step = 1.0, description = '$y_5$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y5.style.handle_color = color[4]\n",
    "\n",
    "x6 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[5], step = 1.0, description = '$x_6$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x6.style.handle_color = color[5]\n",
    "y6 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[5], step = 1.0, description = '$y_6$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y6.style.handle_color = color[5]\n",
    "\n",
    "x7 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[6], step = 1.0, description = '$x_7$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x7.style.handle_color = color[6]\n",
    "y7 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[6], step = 1.0, description = '$y_7$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y7.style.handle_color = color[6]\n",
    "\n",
    "x8 = widgets.FloatSlider(min=0.0, max = 500.0, value = X1[7], step = 1.0, description = '$x_8$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "x8.style.handle_color = color[7]\n",
    "y8 = widgets.FloatSlider(min=0.0, max = 500.0, value = X2[7], step = 1.0, description = '$y_8$',orientation='vertical',\n",
    "                         layout=Layout(width='30px', height='200px'),readout_format = '.0f',style=style)\n",
    "y8.style.handle_color = color[7]\n",
    "\n",
    "uipars = widgets.HBox([ncluster,radius,x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6,x7,y7,x8,y8],) \n",
    "uik = widgets.VBox([l,uipars],)\n",
    "\n",
    "def f_make_spectral(ncluster,radius,x1,y1,x2,y2,x3,y3,x4,y4,x5,y5,x6,y6,x7,y7,x8,y8):                       # function to take parameters, make sample and plot#\n",
    "#    text_trap = io.StringIO()\n",
    "#    sys.stdout = text_trap\n",
    "    X1_local = [x1,x2,x3,x4,x5,x6,x7,x8]; X2_local = [y1,y2,y3,y4,y5,y6,y7,y8]\n",
    "    \n",
    "    n = len(X1)\n",
    "    adjacency = np.zeros([len(X1_local),len(X1_local)])   # declare the 2D matrices\n",
    "    degree = np.zeros([len(X1_local),len(X2_local)])\n",
    "\n",
    "    # populate the adjacency matrix\n",
    "    for j in range(0,len(X1_local)):\n",
    "        for i in range(0,len(X1_local)):\n",
    "            if i != j:\n",
    "                distance = math.sqrt((X1_local[i]-X1_local[j])*(X1_local[i]-X1_local[j]) + (X2_local[i]-X2_local[j])*(X2_local[i]-X2_local[j]))\n",
    "                if distance <= radius:\n",
    "                    adjacency[i,j] = 1; adjacency[j,i] = 1 \n",
    "    \n",
    "    # plot the adjacency matrix - optional\n",
    "#     plt.subplot(222)  \n",
    "#     plt.imshow(adjacency,cmap = plt.cm.binary); plt.grid(alpha = 0.2)\n",
    "#     plt.xlim([-0.5,len(X1_local)-1+0.5]); plt.ylim([-0.5,len(X2_local)-1+0.5]);\n",
    "#     plt.title('Adjacency Matrix'); plt.xlabel('$X_1$'); plt.ylabel('$X_2$');\n",
    "#     plt.colorbar()\n",
    "    \n",
    "    # populate the degree matrix\n",
    "    for j in range(0,len(X1)):\n",
    "        summation = 0\n",
    "        for i in range(0,len(X1)):\n",
    "            summation = summation + adjacency[i,j]\n",
    "        degree[j,j] = summation\n",
    "        \n",
    "    # calculate the Laplacian matrix\n",
    "    Laplace = degree - adjacency\n",
    "    \n",
    "    # plot the Laplacian matrix - optional\n",
    "#     plt.subplot(223)  \n",
    "#     plt.imshow(Laplace,cmap = cmap); plt.grid(alpha = 0.2)\n",
    "#     plt.xlim([-0.5,len(X1_local)-1+0.5]); plt.ylim([-0.5,len(X2_local)-1+0.5]);\n",
    "#     plt.title('Graph Laplacian Matrix'); plt.xlabel('$X_1$'); plt.ylabel('$X_2$');\n",
    "#     plt.colorbar()\n",
    "        \n",
    "    # plot the sample data graph\n",
    "    plt.subplot(121)\n",
    "    \n",
    "    for i in range(0,n):\n",
    "        plt.scatter(X1_local[i],X2_local[i],c = color[i],s=60,alpha = 0.9,edgecolors = 'black')\n",
    "    for j in range(0,len(X1)):\n",
    "        for i in range(0,len(X1)):\n",
    "            if adjacency[i,j] == 1:\n",
    "                x1 = [X1_local[i],X1_local[j]]; x2 = [X2_local[i],X2_local[j]]\n",
    "                plt.plot(x1,x2,c = 'black',alpha = 0.2)\n",
    "    plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "    plt.xlabel('$X$'); plt.ylabel('$Y$'); plt.title('Sample Data and Graph')\n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=2.0, wspace=0.2, hspace=0.3)        \n",
    "\n",
    "    # calculate the Eigen values and vectors and sort by Eigen value\n",
    "    vals, vecs = np.linalg.eig(Laplace)\n",
    "    vecs = vecs[:,np.argsort(vals)]\n",
    "    vals = vals[np.argsort(vals)]    \n",
    "    \n",
    "    kmeans = KMeans(n_clusters=ncluster)             # instantiate k-means clusters\n",
    "    kmeans.fit(vecs[:,1:ncluster])                   # fit k-means clusters\n",
    "    clusters = kmeans.labels_\n",
    "    \n",
    "    # plot the sample data graph with 2nd Eigen vector\n",
    "    plt.subplot(122)\n",
    "#     for j in range(0,len(X1_local)):                 # plot vertices\n",
    "#         for i in range(0,len(X1_local)):\n",
    "#             if adjacency[i,j] == 1:\n",
    "#                 x1 = [X1_local[i],X1_local[j]]; x2 = [X2_local[i],X2_local[j]]\n",
    "#                 plt.plot(x1,x2,c = 'red',alpha = 0.2)\n",
    "    plt.scatter(X1_local,X2_local,c = clusters,s = 60,alpha = 1.0,edgecolors = 'black',vmin = 0, vmax = ncluster-1, cmap = plt.cm.Dark2)\n",
    "    plt.xlim([0,500]); plt.ylim([0,500]); \n",
    "    plt.xlabel('$X$'); plt.ylabel('$Y$'); plt.title('Sample Data Graph and Assigned Clusters')\n",
    "    cbar = plt.colorbar()\n",
    "    cbar.set_label('Cluster Index', rotation=270, labelpad=20)\n",
    "    plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.5, wspace=0.2, hspace=0.3)  \n",
    "\n",
    "# connect the function to make the samples and plot to the widgets    \n",
    "interactive_plot = widgets.interactive_output(f_make_spectral, {'ncluster':ncluster, 'radius':radius, \n",
    "                                                      'x1':x1, 'y1':y1, 'x2':x2, 'y2':y2, 'x3':x3, 'y3':y3,\n",
    "                                                      'x4':x4, 'y4':y4, 'x5':x5, 'y5':y5, 'x6':x6, 'y6':y6,\n",
    "                                                      'x7':x7, 'y7':y7, 'x8':x8, 'y8':y8})\n",
    "interactive_plot.clear_output(wait = True)               # reduce flickering by delaying plot updating"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive Spectral Clustering Demostration\n",
    "\n",
    "* select the number of clusters and the data graph (locations and connections by radius)\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1) | [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy)\n",
    "\n",
    "### The Inputs\n",
    "\n",
    "Select the variogram model and the data locations:\n",
    "\n",
    "* **nclusters**: the number of clusters\n",
    "\n",
    "* **radius**: maximum distance in feature space to form a connection\n",
    "\n",
    "* **$x_i$,$y_i$**: sample data locations in feature space"
   ]
  },
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   "execution_count": 7,
   "metadata": {},
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       "VBox(children=(Text(value='                                              Spectral Clustering, Michael Pyrcz, A…"
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       "Output()"
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   ],
   "source": [
    "display(uik, interactive_plot)                            # display the interactive plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some observations from these spectral cluster assignments:\n",
    "\n",
    "* as expected the method is able to devide the sample data into a specified number of clusters\n",
    "\n",
    "* the cluster group index is arbitrary and will switch as you move the data\n",
    "\n",
    "Things to try:\n",
    "\n",
    "* make a chain of all the data (i.e. sample 1 connected to sample 2 connected to sample 3 and so on)\n",
    "\n",
    "* make no connections\n",
    "\n",
    "* make a ring of data\n",
    "\n",
    "* make connected clusters\n",
    "\n",
    "#### Comments\n",
    "\n",
    "I hope you found this tutorial useful. I'm always happy to discuss data analytics, geostatistics, statistical modeling, uncertainty modeling and machine learning,\n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
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