Kaggle - Digit Recognizer (DL).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Read the dataset and check if anything missing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#import necessary modules to manipulate the datasets\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#read training and test sets\n",
    "train = pd.read_csv('data/train.csv')\n",
    "test = pd.read_csv('data/test.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
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       "[8 rows x 785 columns]"
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     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
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   "source": [
    "train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
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       "      <th>75%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>253.000000</td>\n",
       "      <td>254.000000</td>\n",
       "      <td>193.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>119.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 784 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        pixel0   pixel1   pixel2   pixel3   pixel4   pixel5   pixel6   pixel7  \\\n",
       "count  28000.0  28000.0  28000.0  28000.0  28000.0  28000.0  28000.0  28000.0   \n",
       "mean       0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "std        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "min        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "25%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "50%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "75%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "max        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "\n",
       "        pixel8   pixel9    ...         pixel774      pixel775      pixel776  \\\n",
       "count  28000.0  28000.0    ...     28000.000000  28000.000000  28000.000000   \n",
       "mean       0.0      0.0    ...         0.164607      0.073214      0.028036   \n",
       "std        0.0      0.0    ...         5.473293      3.616811      1.813602   \n",
       "min        0.0      0.0    ...         0.000000      0.000000      0.000000   \n",
       "25%        0.0      0.0    ...         0.000000      0.000000      0.000000   \n",
       "50%        0.0      0.0    ...         0.000000      0.000000      0.000000   \n",
       "75%        0.0      0.0    ...         0.000000      0.000000      0.000000   \n",
       "max        0.0      0.0    ...       253.000000    254.000000    193.000000   \n",
       "\n",
       "           pixel777      pixel778  pixel779  pixel780  pixel781  pixel782  \\\n",
       "count  28000.000000  28000.000000   28000.0   28000.0   28000.0   28000.0   \n",
       "mean       0.011250      0.006536       0.0       0.0       0.0       0.0   \n",
       "std        1.205211      0.807475       0.0       0.0       0.0       0.0   \n",
       "min        0.000000      0.000000       0.0       0.0       0.0       0.0   \n",
       "25%        0.000000      0.000000       0.0       0.0       0.0       0.0   \n",
       "50%        0.000000      0.000000       0.0       0.0       0.0       0.0   \n",
       "75%        0.000000      0.000000       0.0       0.0       0.0       0.0   \n",
       "max      187.000000    119.000000       0.0       0.0       0.0       0.0   \n",
       "\n",
       "       pixel783  \n",
       "count   28000.0  \n",
       "mean        0.0  \n",
       "std         0.0  \n",
       "min         0.0  \n",
       "25%         0.0  \n",
       "50%         0.0  \n",
       "75%         0.0  \n",
       "max         0.0  \n",
       "\n",
       "[8 rows x 784 columns]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "#find nan values\n",
    "print(np.sum(np.sum(train.isnull(), axis = 1)))\n",
    "print(np.sum(np.sum(test.isnull(), axis = 1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every sample is a 28*28 img\n",
    "\n",
    "The first column \"label\" ranges from 0 to 9, which also should be the output value\n",
    "\n",
    "No missing/NaN values in the datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#set features and labels\n",
    "#features = train.iloc[:, 1:]\n",
    "#label = train.iloc[:, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Try DL / NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How many processes do we need to build a NN algorithm?\n",
    "\n",
    "    1. Activation Functions\n",
    "    2. Initialization, normalization, and transpose dataset\n",
    "    3. Convert muti-class labels into one hot code\n",
    "    4. Initialize parameters\n",
    "    5. Compute cost\n",
    "    6. Set mini-batch size\n",
    "    7. Build Forward-propagation process\n",
    "    8. Build Back-propagation process\n",
    "    9. Build Adam iteration process\n",
    "    \n",
    "    10. Build Validation process\n",
    "    11. Create more samples with data augmentation\n",
    "    \n",
    "    12. Run and compare the output (compute the cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Define Activation Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#first, define sigmoid, relu, and tanh activation functions\n",
    "\n",
    "def sigmoid(x):\n",
    "    \"\"\"\n",
    "    Compute the sigmoid of x\n",
    "\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(x)\n",
    "    \"\"\"\n",
    "    s = 1 / (1 + np.exp(-x))\n",
    "    return s\n",
    "\n",
    "def relu(x):\n",
    "    \"\"\"\n",
    "    Compute the relu of x\n",
    "\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- relu(x)\n",
    "    \"\"\"\n",
    "    s = np.maximum(0, x)\n",
    "    return s\n",
    "\n",
    "def tanh(x):\n",
    "    \"\"\"\n",
    "    Compute the relu of x\n",
    "\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- tanh(x)\n",
    "    \"\"\"\n",
    "    s = np.tanh(x)\n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Since we need to recognize the images of digits from 0 to 9, we need softmax activation function in the final layer\n",
    "\n",
    "def softmax(x):\n",
    "    \"\"\"\n",
    "    Compute the relu of x\n",
    "\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- softmax(x)\n",
    "    \"\"\"\n",
    "    summation = np.sum(np.exp(x), axis = 0)\n",
    "    s = np.exp(x) / summation\n",
    "    return s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Initialization\n",
    "\n",
    "Before implementing neural network, the data format should be adjusted first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((42000, 784), (42000,))"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#transform features and labels into numpy arrays\n",
    "X_train_ori = train.iloc[:, 1:].values\n",
    "Y_train_ori = train.iloc[:, 0].values\n",
    "X_test_ori = test.values\n",
    "X_train_ori.shape, Y_train_ori.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#do the transpose and normalization\n",
    "def feature_norm(x):\n",
    "    '''\n",
    "    Normalize the feature values of x\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    X_norm -- normalized x.T\n",
    "    '''\n",
    "    X_norm = x.T\n",
    "    X_norm = X_norm / 255\n",
    "    return X_norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((784, 42000), (784, 28000))"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_norm = feature_norm(X_train_ori)\n",
    "test_norm = feature_norm(X_test_ori)\n",
    "X_norm.shape, test_norm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Y (label) need to get transformed into one hot code\n",
    "def convert_to_one_hot(Y, C):\n",
    "    Y = np.eye(C)[Y.reshape(-1)].T\n",
    "    return Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 4132.,  4684.,  4177.,  4351.,  4072.,  3795.,  4137.,  4401.,\n",
       "         4063.,  4188.]), (10, 42000))"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_norm = convert_to_one_hot(Y_train_ori, 10)\n",
    "np.sum(Y_norm, axis = 1), Y_norm.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#set random seed for consistency\n",
    "np.random.seed(32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#compute first layer dim and last(10)\n",
    "def first_dim(x):\n",
    "    '''\n",
    "    Compute the neuron number of the first layer\n",
    "    Arguments:\n",
    "    x -- A scalar or numpy array of any size.\n",
    "    \n",
    "    Return:\n",
    "    m -- x.shape[1]\n",
    "    '''\n",
    "    m = x.shape[0]\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "784\n"
     ]
    }
   ],
   "source": [
    "m = first_dim(X_norm)\n",
    "print(m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#build a n layers layer_dim\n",
    "def set_layers(n, m, last_layer = 10, seed = 32):\n",
    "    '''\n",
    "    Set n layers for the neural network and decide how many neurons in each layer\n",
    "    Arguments:\n",
    "    n -- A constant to decide build how many hidden laysers\n",
    "\n",
    "    Return:\n",
    "    layer_dims -- a list consist of neuron numbers in each layer\n",
    "    '''\n",
    "    np.random.seed(seed)\n",
    "    layer_dims = []\n",
    "    layer_dims.append(m)\n",
    "    \n",
    "    for i in range(n):\n",
    "        layer_dims.append(np.random.randint(last_layer, m/(10*(i+1))))\n",
    "    \n",
    "    layer_dims.append(last_layer)\n",
    "    return layer_dims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[784, 53, 15, 10]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "layer_dims = set_layers(2, m, last_layer = 10)\n",
    "layer_dims"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#initailize parameters W, b with regularization\n",
    "def initialize_parameters(layer_dims):\n",
    "    '''\n",
    "    Random initialization with Xavier Initialization\n",
    "    '''\n",
    "    #set random seed to keep consistency\n",
    "    np.random.seed(32)\n",
    "    #set dict to store parameters\n",
    "    parameters = {}\n",
    "    L = len(layer_dims)\n",
    "    for l in range(1, L):\n",
    "        parameters['W' + str(l)] = np.random.randn(layer_dims[l], layer_dims[l-1]) * np.sqrt(2 / layer_dims[l-1])\n",
    "        parameters['b' + str(l)] = np.zeros((layer_dims[l], 1))\n",
    "        \n",
    "        #assert(parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l-1])\n",
    "        #assert(parameters['b' + str(l)].shape == layer_dims[l], 1)\n",
    "    \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "parameters = initialize_parameters(layer_dims)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Set Mini-batch Size and Build Forward and Back Propagation Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Mini-batch\n",
    "def random_mini_batches(X, Y, mini_batch_size = 256, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- one hot vector , of shape (10, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation]\n",
    "    \n",
    "    assert (shuffled_Y.shape == Y.shape)\n",
    "    \n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = m//mini_batch_size\n",
    "    # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[: , k * mini_batch_size: (k+1) * mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[: , k * mini_batch_size: (k+1) * mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[: , mini_batch_size * num_complete_minibatches: m]\n",
    "        mini_batch_Y = shuffled_Y[: , mini_batch_size * num_complete_minibatches: m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Forward Propagation\n",
    "def forward_propagation(X, parameters):\n",
    "    \"\"\"\n",
    "    Implements the forward propagation (and computes the loss) presented in Figure 2.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input dataset, of shape (input size, number of examples)\n",
    "    parameters -- python dictionary containing your parameters \"W1\", \"b1\", \"W2\", \"b2\", \"W3\", \"b3\":\n",
    "                    W1 -- weight matrix of shape ()\n",
    "                    b1 -- bias vector of shape ()\n",
    "                    W2 -- weight matrix of shape ()\n",
    "                    b2 -- bias vector of shape ()\n",
    "                    W3 -- weight matrix of shape ()\n",
    "                    b3 -- bias vector of shape ()\n",
    "                    W4\n",
    "                    b4\n",
    "    \n",
    "    Returns:\n",
    "    loss -- the loss function (vanilla logistic loss)\n",
    "    \"\"\"\n",
    "    # retrieve parameters\n",
    "    L = len(parameters) // 2\n",
    "    cache = {}\n",
    "    \n",
    "    # LINEAR -> RELU -> ...... -> LINEAR -> SOFTMAX\n",
    "    cache['z' + str(1)] = np.dot(parameters['W1'], X) + parameters['b1']\n",
    "    cache['a' + str(1)] = relu(cache['z1'])\n",
    "    cache['W1'] = parameters['W1']\n",
    "    cache['b1'] = parameters['b1']\n",
    "    for l in range(1, L-1):\n",
    "        cache['z' + str(l+1)] = np.dot(parameters['W'+str(l+1)], cache['a'+str(l)]) + parameters['b'+str(l+1)]\n",
    "        cache['a'+str(l+1)] = relu(cache['z' + str(l+1)])\n",
    "        cache['W'+str(l+1)] = parameters['W'+str(l+1)]\n",
    "        cache['b'+str(l+1)] = parameters['b'+str(l+1)]\n",
    "    \n",
    "    cache['z'+str(L)] = np.dot(parameters['W'+str(L)], cache['a'+str(L-1)]) + parameters['b'+str(L)]\n",
    "    cache['a'+str(L)] = softmax(cache['z' + str(L)])\n",
    "    cache['W'+str(L)] = parameters['W'+str(L)]\n",
    "    cache['b'+str(L)] = parameters['b'+str(L)]\n",
    "    \n",
    "    \n",
    "    return cache['a'+str(L)], cache\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#build cost function\n",
    "def compute_cost(aL, Y):\n",
    "    \n",
    "    \"\"\"\n",
    "    Implement the cost function\n",
    "    \n",
    "    Arguments:\n",
    "    aL -- post-activation, output of forward propagation\n",
    "    Y -- \"true\" labels vector, same shape as aL (10 * m)\n",
    "    \n",
    "    Returns:\n",
    "    cost - value of the cost function\n",
    "    \"\"\"\n",
    "    m = Y.shape[1]\n",
    "    \n",
    "    cost = (-1 / m) * np.sum(np.sum(np.multiply(Y, np.log(aL)), axis = 0))\n",
    "    \n",
    "    return cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#softmax derivative: \n",
    "#https://stackoverflow.com/questions/40575841/numpy-calculate-the-derivative-of-the-softmax-function\n",
    "def backward_propagation(X, Y, cache):\n",
    "    \"\"\"\n",
    "    Implement the backward propagation presented in figure 2.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input dataset, of shape (input size, number of examples)\n",
    "    Y -- one hot matrix for multi-class labels \n",
    "    cache -- cache output from forward_propagation()\n",
    "    \n",
    "    Returns:\n",
    "    gradients -- A dictionary with the gradients with respect to each parameter, activation and pre-activation variables\n",
    "    \"\"\"\n",
    "    L = len(cache) // 4\n",
    "    m = X.shape[1]\n",
    "    \n",
    "    gradients = {}\n",
    "    \n",
    "    gradients['dz' + str(L)] = 1./m * (cache['a'+str(L)] - Y)\n",
    "    gradients['dW' + str(L)] = np.dot(gradients['dz' + str(L)], cache['a'+str(L-1)].T)\n",
    "    gradients['db' + str(L)] = np.sum(gradients['dz' + str(L)], axis=1, keepdims = True)\n",
    "    \n",
    "    for l in range(L-1, 1, -1):\n",
    "        gradients['da' + str(l)] = np.dot(cache['W'+str(l+1)].T, gradients['dz'+str(l+1)])\n",
    "        gradients['dz' + str(l)] = np.multiply(gradients['da' + str(l)], np.int64(cache['a'+str(l)] > 0))\n",
    "        gradients['dW' + str(l)] = np.dot(gradients['dz' + str(l)], cache['a'+str(l-1)].T)\n",
    "        gradients['db' + str(l)] = np.sum(gradients['dz' + str(l)], axis=1, keepdims = True)\n",
    "        \n",
    "    gradients['da1'] = np.dot(cache['W2'].T, gradients['dz2'])\n",
    "    gradients['dz1'] = np.multiply(gradients['da1'], np.int64(cache['a1'] > 0))\n",
    "    gradients['dW1'] = np.dot(gradients['dz1'], X.T)\n",
    "    gradients['db1'] = np.sum(gradients['dz1'], axis=1, keepdims = True)\n",
    "    \n",
    "    return gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Setting Adam algorithm for optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate = 0.01,\n",
    "                                beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = beta1 * v[\"dW\" + str(l+1)] + (1-beta1) * grads['dW' + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta1 * v[\"db\" + str(l+1)] + (1-beta1) * grads['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l+1)] = v[\"dW\" + str(l+1)] / (1 - beta1 ** t)\n",
    "        v_corrected[\"db\" + str(l+1)] = v[\"db\" + str(l+1)] / (1 - beta1 ** t)\n",
    "        # You can't repeat the formula again since the value of v[\"dW\" + str(l+1)] has been changed!\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l+1)] = beta2 * s[\"dW\" + str(l+1)] + (1-beta2) * np.square(grads['dW' + str(l+1)])\n",
    "        s[\"db\" + str(l+1)] = beta2 * s[\"db\" + str(l+1)] + (1-beta2) * np.square(grads['db' + str(l+1)])\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l+1)] = s[\"dW\" + str(l+1)] / (1- beta2 ** t)\n",
    "        s_corrected[\"db\" + str(l+1)] = s[\"db\" + str(l+1)] / (1- beta2 ** t)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate * v_corrected[\"dW\" + str(l+1)] / (\n",
    "            np.sqrt(s_corrected[\"dW\" + str(l+1)]) + epsilon)\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate * v_corrected[\"db\" + str(l+1)] / (\n",
    "            np.sqrt(s_corrected[\"db\" + str(l+1)])  + epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer = 'adam', learning_rate = 0.0005, mini_batch_size = 256, beta = 0.9,\n",
    "          learning_decay = 0.001,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 300, seed = 10, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    #seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 3\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            aL, cache = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(aL, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, cache)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 10 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "            \n",
    "        if print_cost and i % 1 == 0:\n",
    "            costs.append(cost)\n",
    "        if np.log10(cost) <= -9 : break\n",
    "        learning_rate = learning_rate / (1+learning_decay)\n",
    "        \n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.yscale('log')\n",
    "    plt.xlabel('epochs (per 1)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate) + ', ' + 'mini_batch_size = ' + str(mini_batch_size))\n",
    "    plt.show()\n",
    "    print(np.log10(cost))\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.5 Run NN!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since there are many problems while implementing mini-batch, try whole batch first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_X = feature_norm(X_train_ori)\n",
    "train_Y = convert_to_one_hot(Y_train_ori, 10)\n",
    "layer_dims = set_layers(2, m, last_layer = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 2.348200\n",
      "Cost after epoch 10: 0.822556\n",
      "Cost after epoch 20: 0.477744\n",
      "Cost after epoch 30: 0.361737\n",
      "Cost after epoch 40: 0.298332\n",
      "Cost after epoch 50: 0.254607\n",
      "Cost after epoch 60: 0.225023\n",
      "Cost after epoch 70: 0.203717\n",
      "Cost after epoch 80: 0.187659\n",
      "Cost after epoch 90: 0.175101\n"
     ]
    },
    {
     "data": {
      "image/png": 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Baz9EWY8crrh9Bv96b33UJYmIHDSFVRronZ/NfddM4cjSAr5wz2xueH6xbuAo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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x103095a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.780195107912\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.005,\n",
    "                   mini_batch_size = train_X.shape[1], learning_decay = 0.01,\n",
    "                   num_epochs = 100)\n",
    "#0.94271"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 2.348200\n",
      "Cost after epoch 10: 0.646024\n",
      "Cost after epoch 20: 0.383583\n",
      "Cost after epoch 30: 0.287502\n",
      "Cost after epoch 40: 0.228577\n",
      "Cost after epoch 50: 0.192511\n",
      "Cost after epoch 60: 0.167832\n",
      "Cost after epoch 70: 0.150270\n",
      "Cost after epoch 80: 0.137101\n",
      "Cost after epoch 90: 0.126756\n",
      "Cost after epoch 100: 0.118390\n",
      "Cost after epoch 110: 0.111369\n",
      "Cost after epoch 120: 0.105445\n",
      "Cost after epoch 130: 0.100358\n",
      "Cost after epoch 140: 0.095934\n"
     ]
    },
    {
     "data": {
      "image/png": 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j1/OKyPhB+GbRJnzz10873kf8Ucu26PQJNd9O2M7D/Y8QOX8K1AFtCa8xek7rroTXEN1+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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1026657f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0342743311\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.0167,\n",
    "                   mini_batch_size = train_X.shape[1], learning_decay = 0.01,\n",
    "                   num_epochs = 150)\n",
    "#0.95585"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: -1.195061\n",
      "Cost after epoch 5: -1.110771\n",
      "Cost after epoch 10: -2.094027\n",
      "Cost after epoch 15: -2.233369\n",
      "Cost after epoch 20: -1.202261\n",
      "Cost after epoch 25: -3.314280\n",
      "Cost after epoch 30: -3.660486\n",
      "Cost after epoch 35: -2.968145\n",
      "Cost after epoch 40: -5.140485\n",
      "Cost after epoch 45: -4.577657\n",
      "Cost after epoch 50: -4.795420\n",
      "Cost after epoch 55: -4.582444\n",
      "Cost after epoch 60: -4.677801\n",
      "Cost after epoch 65: -6.242573\n",
      "Cost after epoch 70: -5.461031\n",
      "Cost after epoch 75: -4.759324\n",
      "Cost after epoch 80: -5.567504\n",
      "Cost after epoch 85: -3.220391\n",
      "Cost after epoch 90: -4.275762\n",
      "Cost after epoch 95: -4.931747\n"
     ]
    },
    {
     "data": {
      "image/png": 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68BBwrogMisgtSqkM8F7gbuAZ4FtKqQN1OFZDav0tlVZL9eecozo6pksyvXRn\nH3c+dcpRVh1PZhiennfMjb14Ry/HovEFZerjVXhUQZ+X1qBvEWKKlGPuy/TQTown2Dc4xSt2r8Hn\nkYaE/uKpQo/KDf25uDQHy6H6u0kptU4p5VdKbVBK3WYsv0sptVMptU0p9bE6HWtVelRhvxeR8qG/\nI2MxOsN+bnnRFmbnM44qviNj2uva1ldqqPYO6M9b3DOrmIl4iqDPQyRQudljlyEpL0csmSkxpuOx\nZMWK7D/Zf4qcgqu29dAVCTQk9JdIZhCBkN9DyO91xRQuLk3CGVGZolpWq0flMbr8zpQxVEfHYmzt\njfDC7b30tQX53m9Lw3+HRrShcvKodg90IAL7BitPpI0ak33L1fkz6QpXrs/39i/8hg/dUegAj5fx\nqEB7cMfHEwR8Hi7Z1EVPZPGFbysRT2WNhwIh5HPl6S4uzUJTGarV6lGBFlSUm/B7dCzO1r5WvB7h\nhgvXc+/B0ZIc0eGxGD6PcI5Ds8bWoI8tvZGC5o5OLDTZ16QrHKjoUR0di7F/uPBY0TIeFeRb0l+6\nqYuQ37ugIVwsiVSGsCFcaQl43Am/Li5NQlMZqtXqUUH5wrSz82lGZ5NWSO/1lwyQzip+tO9UwXaH\nR2Ns7o3gL1MI94KBjgVDf+OxynX+TLoj5Q1VJptjMpHmxHjCaiSZzSkmEil6y0wkNpWAV23r0ftv\nbYyhiiezVlgz5POSzSnSi+jZ5eLisrpoKkO1qj2qkJ9ZBzGFKaTYanTF3bVOV7+4q8hQHRmNsd0h\nP2WyZ6CD0zPzFQUVEwtUTjfpCpcvJGsamNn5jCW4mEykUKp0DpVJd5Gh6mlQ649EKkM4oD0qU33o\n1vtzcTnzaSpDtZppDTp7VEejpkhCGyoR4aU7+3j0xKR1k01mspyYSLBjTXlDtZCgQilFNJYsqcXn\nRHfETyyZcRQjRG0iiOPjcWOZlr2Xm0h8TneYrrCfCzd0AtoQTs+l6+7tJFJZIkHDozI8Kzf85+Jy\n5tNUhmq1h/6cKlMcGY3j9QibuvO1A6/e3kMqk+PxE5MAHI8myOZUxbJNCwkqEqksyUyuKo+qM2wW\npi31quy9pZ4fT+hlC7S3v/WlW7nnL15KwOcp2M5p/0shnsrmPSrjWElXUOHicsbTVIZqNYf+2kM+\nxwm/R6MxNnWHrZs4wBVbevB6hAeNSg6HR8tL001agz62VhBU5MsnVZejAudJuab3BKUeVTlvLejz\nFqxbbPXNNGskAAAgAElEQVSLhUgkM3mPyg39ubg0DU1lqFYzZUN/Y3G2FlVibw36uHBDB786EgW0\noRKpbKhAh//2DU05rosanlA1YoqucPl6f6bBawv5LI8qarX4qK4YcE8FQ7gUEjaPqsXvhv5cXJoF\n11AtE61BP3PpLBlbXiabUxyNxtnmENJ74fZenhqcZnY+zeGxGAOdLbQsMFF3z0AHIzNJR0HF0OQc\nAP1tCxfTtQrTOggqorEUAa+H3evbLY9qPJbE5xE6WvwL7hvylTHqbajiqUxe9Wd5VG7oz8XlTKep\nDNVqzlE5NU8cntLFaIs9KtAKuWxO8ZtjExwejVXVVuQCQ6zgJKh47MQkIb+Hc4tqBTrRZdT7c5qU\nqytQBNjcE+H5iXyOqqd14YnEJt1W6C+5wJa1kUhmabFUf/rSdkN/Li5nPk1lqFZzjspq9WEL/5ll\nkbY6hPQu2dRF0OfhgUNRjozFrIaNldi9vr2soOLx5ye5cENn2XlYdkwxhVNh2qhhqM7piRCNpYgl\nM0bFi4XVhCZdVuivfmKKVCZHKptz8KhcQ+XicqbTVIZqNWO1+kjaDZUOnZnSdDshv5fLNnfxgyeG\nSGVyVXlUEUtQUZinSqQyHBie4bLNXVWNNeDz0Bb0OYbmxuMpeiJBq0LGifE40Xiq7BwqJ/xeD+0h\nX109KrMArVmZIuTmqFxcmoZVb6hE5HwR+TcR+Y6IvGelx7NYnFp9HB2L0dHiLysZv3pbrzWpttqO\nwlpQURj6e/LkNNmc4rJzuqseb1ckwFQZMUVvq91QJYjOJstWpShHdyTARB3l6XGjxUfeo3Ll6S4u\nzUJDDZWIfEFERkVkf9Hya0XkoIgcFpH3V9qHUuoZpdS7gd8HLmvkeBuJU6sPXeMvUja3c7VRyQFg\ne9/CuSWACzd2MjKT5Fg0bi177IRuxnjxps6qx9sV9pcYEqUUY7EkvUboD7REfTyerEpNaKc7Eqir\nR5XvRVWo+nObJ7q4nPk02qO6HbjWvkBEvMBngeuAXcBNIrJLRPaKyJ1Ff/3Ge14L/BL4eYPH2zBa\ng845qkqS870DHbQFffS2BukIV6eou3bPWkQoqMD+2IlJdvS3WrmnauiKBEpyVLFkhlQmR09rgNag\nj97WAM+cmmU+nauq4oWd7kjAkrovhkw2x5v/98P8/JkRwN7dtzBH5fakcnE582mooVJK3Q8U91a/\nAjislDqqlEoB3wBuUErtU0q9puhv1NjPHUqpq4G3NHK8jaS9SExhFqPd6pCfMvF5PbzmwvW8dGdf\n1cdZ19HCi7b38t3HB8nlFLmc4rETk1x6TnX5KZNuhwrn49Z8KW2UNnWHreoZ1VRlL9h/hcK31XBg\neIYHj4xz177TgJ5DBTjU+nNDfy4uZzq+FTjmAHDS9noQuLLcxiJyDfAGIAjcVWG7W4FbATZt2lSP\ncdaV1iJ5ulmMtlKhWYBPvGFvzcd6wyUD/OdvPskjxyfojgSYmc/UbKicclRWTT/DKG3uifD481q4\nUe1kX5PuSJCJeAqlVNWydju/PqardphSfDP0Z1am8HqEgNfjhv5cXJqAlTBUTnclVW5jpdR9wH0L\n7VQp9XkROQVcHwgELl306BpEi9+L1yNWdQqrY2+VIolaeOXutYQD+/nu40NcZOSlavaoIgHiqSzz\n6azlnUSLyjBtsvXGqj305yedVcSSGUtoUgu/OaYd9UOjs8ylslYbetOjAgj6PW7oz8WlCVgJ1d8g\nsNH2egMwvALjWFZEdJff2XktUDhiNELc1F3aCHGphAM+rtuzjh/tO8WvDkfpjgTY4jCpuBKdRk7M\nXjjWLEjba/OoTGoXU+h9LKY6hTkRur8tSE7Bs6dnSCQLPSrgrGtHn8q4YU6X5mQlDNUjwA4R2SIi\nAeBNwB0rMI5lpzWYr6B+ZDTOOT3hqibgLoYbLxkglszwo32nuGRTV83htW6HwrFmjqrbwaOqZcKv\n3oc2hOOLMFTPnp5hZj7D2646B9DhPyePqsV/9rSjv/vAaS788E+ZnqtvRXoX3HO6Cmi0PP3rwEPA\nuSIyKCK3KKUywHuBu4FngG8ppQ7U43iruTIF6DJK9tDfQkVml8ILtvawviOEUlQ90deOWT3CLniI\nxpJ0tPitSu+mR9Ue8hVUf68G06Nyqn6xEGbY7/WXbKAr7Gf/UN6jCgfsHtXZE/r76YER5tLZhjSk\nPJt57MQEl3z0Hg6Pzq70UM5qGq36u0kptU4p5VdKbVBK3WYsv0sptVMptU0p9bF6HW811/oDbahm\n5zNksjmOj8cdSyfVC49HeN3FA0Dt+SmwFaZNFHpU9hBfV9hvyedrxcxzLcaj+vXRCTZ0tTDQ2cKe\ngQ72D2uPKuD1FHioIb/3rBFTPHxUi0vOplDnUnl6eIb/88DRitscHo2RzSkePT65TKNycWLVV6Zo\nJlqDPmLJDCcn50hnlWPppHpy60u28v+9ZheXbqrdUJk5KrvHU9whWETY0hehr4bySSaWx1ajoVJK\n8ZvjE1y5RU+G3jPQwXMjs0wlUoSDhdXlQz7vWVHr7+REgqEpXR3frcRRPd9+7CR//aNnyOXKarks\nAdH+4dX58Hu20FSGarWH/lpDusX7kdHGKf7sdIYD/NGLtuDx1C7/NntSjcWKDVWhaOLjr9/LB6/f\nXfP+IwEvAZ+n5lDVodEYE/EUV27R5aD2rO8gnVX89vkpIoFCEWso4GXuDLpxj8zMO5atWoiHDG8K\nIOkKKqrGvPYSFR5mzCkZB4adO2e7LA9NZahWOzr0l85L03sba6iWgt/rYXt/K0+ezBe4NQvS2tkz\n0MGu9e01719E6A4Hag79/drIT125VRuqvQP6oeTgyGxBfgp0O/rkKvGo3vT5h/jBE0Mly7M5xb3P\njnLL7Y9w1Sd+zp9/84ma9/3wEbuhWh2f90zAFAfFk6UNTU1Mj+qZUzNkK3heLo2lqQzVqs9RBXWO\n6shYrKaySCvF1dt6eOT4BOlsjnQ2x1Qivah8VDm6Hco0LcSvj46ztj1kyfo3drdYVT/MOn8mIX91\nob+Z+XRBbcR6M5fK8vDRCR4+WlykBf78m0/wjtsf4cnBaTZ1hzk0Eqtp30opHj46zsbuFsAN/dWC\n+ZA069B52yQ6qz2q+XSOo2O1fTcu9aOpDNWqD/0FfSQzOZ49Pdvw/FQ9uGprD4lUlqcGpyyDUut8\nqUr0tNbmUSml+PWxCa7c2m3J7UWEPYZXFSnyqFr83qrafPzzzw9x0+cfrmHktWEKUsZmS4vwPnQk\nyit3r+HB9/8ur71wPaem50hnqzc2JyfmGJ6e55qd/YAb+qsFsyhyJY9qPJ605iC6eaqVo6kM1ar3\nqIwn/2dOzTQ8P1UPrtyqBQsPHRlnLGZO9q2foeoK11bv77mRGGOzSUtIYWIaqnBxjsrvKZhH9eDh\nKPceHC3Z7/DUPGOxJEo1JrSTN1TzBcvT2Rzj8RTnrm0n4POwoStMTsGpqXmn3Tjy0NEogFUPspbQ\n3/6h6bM2VKiUsnJUC4X+rtzSTdDn4cCQm6daKZrKUK16j8ooFaQVf6vfUHVHApy3to2Hjo6XFKSt\n1/4naqigfveB04jAy87vL1i+28iRRYpVf0Whv0/efZC/+8nBkv2Ox5Nkc6phk4MnjU7Go0UeVTSW\nRClY067P6YYuHb4bnExUve+Hj07Q2xpg94A+B9V6VNFYktd+5pd89/HSvNnZwMx8hnRWP5jEyhiq\nTDbHZCLFmvYQ561rdz2qFaSpDNVqp9WWQzkTQn+gmzc+enySU9Na/lxrlfRKdEcCzCYzVT/V333g\nNBdv7KS/PVSwfG9Zj8pLMpMjl1MopTg6FrPKQNkxn6zL3bCWyoQt9GeXQo/O6LGsadOfZ6ORdztZ\npaFSSvHQkXGu3Npj9d+qVjxyYjxBTsHQ5Fx1H6LJsKtNy33vE4kUSukowp717RwYnmmY1+1SGddQ\nLSNm0h84IzwqgKu29ZDM5LjnaR0yq3eOCqiqL9XJiQQHhme4ds/aknWbeyL0twVZ11FowMxiuslM\njslEmpn5DOOxVMnNptGGypScZ3KqINQ5MqNDfP2GR7W2I4RHYLBK43FiPMHpmXlesLWHoC//WavB\nnHdlyq/PNsZtn7tc6C86m48i7F7fwex8hpMTZ6dhX2maylCt9hyV2eoj6PMw0NmywqOpjiu2dOMR\n+I/nRgn4PLQF61dw31TuHR8vVNzlcop7D46SsYkK7j6g+069cnepofJ4hLv//CW866VbC5ab7ejn\n01mORbViK5NTzMzlb0y5nGLSKLwbq6D+Wgr2p3d7+G/E+P8aw0P0ez2s62jh5ER1HpXZ6uSqrT1W\nCauqDdXkWW6oCjwqZy/UPDe9bUH2GKFVN/y3MjSVoVr1OSrjJr+1r3VRk3BXgo4WP3sG9KTa3khg\nUb2jymGWkCqWhj90dJx3fPERPnvvEWvZTw+McN7aNs7pcQ6ZdkUClldhYobD5tJZq/8XUBD+m5lP\nW/NjGuVR2SX4duXf2Mw8HsmXkwKdp6rWo3rmlJ47tq0vgtcj+L1SdRh1aEobw+gSuiyfydgfHsp5\nVOZ10hMJsHNNG16PcMA1VCtCUxmq1Y7Zd+lMyU+ZXGWo/+qZnwJY1x4i5PcUGBHQqkiAz9x7iGdP\nzzA2m+SRExOO3lQl8l1+swXG0P40PV5FrmKpTCbS+L3awBd4VDNJelqD+Gz1CTd2h6vOUZmFjc2H\nh6DPW/U8qrPeozI+d8jvKfu9W6G/tiAhv5cd/a3sXyHl3+PPT/Lfv7fvrM2RuYZqGWkL+fB7hXPX\ntK30UGriBdu0oaqnNB10yG5zT6RkIuWhkRjtIR/tIT/v+85T3H3gNErhmJ+qRD70l+NYNI7X8GLt\n+YnCpHpj2jlMJlJWTnLUJlEfmZ23FH8mG7paGJlJVuUZHR2LFzz0BH2eReWoim9+n733sFWhvlkZ\nj6doDfroCgfKG6pYsiDcvXt9BweGp1fEWPzoqVN89dfPM9Og8PRq54wwVCISEZHHROQ1Kz2WpRDy\ne/n2u6/mj160ZaWHUhOXb+7G65G6e1SgRSVHi0J/h0Zn2bW+nQ/fsJunBqf5xF3PsKk7zHlrazPw\nIVvo71g0zq51Os9gD3dNVJGrWCoT8RQDnS20Bn2W0g+06s9U/Jls7NJ5u+EF5lLNpbIMTc0ViHKC\nPk9VlTiUUgxNzuH1CPPpnNXLC3RJp7+/5zl++OTy9DKdS2X5x589t+zFg81OAJGgr7yYIpYqCHfv\nGWgnGkuVTDNYDkwP+Gxt49LoflRfEJFREdlftPxaETkoIodF5P1V7OqvgG81ZpTLy0UbO4nUUZCw\nHLQGffztjRdw89Wb677vrX0RTk4kLA9CKcWh0Rg7+tt49d51vHL3GuKpLNfuWVtzfswyVCltqMx2\nJ/Yfe4GhatDT6lQiTWc4QH9bsCBHNTo7byn+TMy5VAsJKo4a4hB7q5igIcdfiOm5NPFU1vLso7Yx\nRWN6Tllimfp4/eb4BP/4s0M8cCi6LMczmYin6I4ErI4GTkRjSXptnQHOW6sfdGotc1UPhqdNQ3V2\nhmob7VHdDlxrXyAiXuCzwHXALuAmEdklIntF5M6iv34ReRnwNDDS4LG6VOCNl26wKkDUk619EXIq\nf2MemUkyO59hxxqde/no6/bwe+f18weXb6x536ahOhaNkczk2LmmjY4Wv2PoT6RxoT99U/TT1xa0\nQn9mVYr+Io9qg6GEXEhQccTI623rLw79FRqYqUSKd3zxN5YU3r7vCzfq79MuLjk1rbebSy9PiMmc\n93Vkmevo6QLL2lCV96gK29qYlWXiqeUPv+U9qrOz23CjGyfeDxQHu68ADiuljiqlUsA3gBuUUvuU\nUq8p+hsFfgd4AfBm4I9FxHHMInKriDwqIo+OjY018FO51JOtRgV588Z7yOikuqNfP+33t4W47ebL\nFzXvzFT9PW2IM7b0RuhpDRC1iyliKSIBL+0hP/EGhP7m01nm0lm6IgH620OWR5WvSlFoqNa2h/B5\nZEFBxZHRGCL5LsvgnKN6eniGew+Oce+z+dJRZn7qwg2dAIzN5s/HKWPdcnlU5njN1jfLxXgsSU8k\nSCToLetRjcdSBYpMuzhnOZlLZS3Rz9nqUa1EDGoAOGl7PQhcWW5jpdR/BxCRm4GoUsoxtqGU+ryI\nnAKuDwQCl9ZvuC6NZIshBjCVf88ZYZUda5Y+IdoUUzx9Shu/rX0ReiKBAo9qMpGiKxJAqcpVtKvl\n5ESCgc4Wa/qBOcG3KxygrzVo5TdGjFxVf1HTSa9HWN+5sET9yFiMjV1h6+YJzqo/s8Oxff7PkOVR\naUNlV/6ZHtVyG6rDy+hRKaUnXne3Bkjnco4PKEopxuOFoT/zelruCvVm2A8W1xG7GVgJMYVTomFB\nGY1S6nal1J0LbLOq51G5lNIe8tPbGrSUf4dHZ+mOBOpSU9C8iR88PUMk4KW/LUhPJFiQl7KHgJYa\n+hudneeaT93Hj/eftpaZx+oKB+hvD5JIZYklM4waobhijwp065KFclRHihR/AEF/aehvLqVvqvbG\nf0NTc7T4vZaXajdUp41xzS2boTJCf6OxZVPTmXX+eiIB2srkqKbn0nruoO06ND30+WUu5Gsvc1VL\nbcxmYiUM1SBgTzhsAOoiMVrtlSlcnNnaF7GUf4dGYmyvU2X5fKgmx5a+CCKiW4sUqP6SOqke8i05\n9DcyrYUIB0dmrWVmQdqusN/ynkZn5q2qFMViCoANneGKHlUupzgWjZWEQ51Cf2abk2dOzViVPoYm\n5xjoaiHg89AZ9hecj7xHtVw5Kj2mmfmMVaG/0ZgetV31V2wko1YR5tLQ33IZcRMzVBvweqy6kWcb\nK2GoHgF2iMgWEQkAbwLuWIFxuKwStvVFOBaNo5TiuZFZdtTNUOUv7y1GLqynNchEImVVo5iIpeiO\nBIkEfcwuccLv9Jw2Svbq52borzsSsIQTo7NJRh2qUphs7G4hGkuWzYUMT88xn84VKP7ACP2VMVTz\n6Zz1MDA0NWeV8OqJBAo9KiPMtNDNOJbMMJ1YemLfPt4jo41rXmnH9HLN7z2TUyXnzSqf1GoP/eUf\nfJYTcyrB9v5WV57eCETk68BDwLkiMigityilMsB7gbuBZ4BvKaUONHIcLqubLb0RJuIpDo3GmJnP\nsLNOE6IDXg+mot1sftdj5KNMAzKR0Iq8tqCP2PzSbryWobIVLrVyVJGA5T1pQ6UVZfaqFCYbukzl\nn3P4z1L8FYf+HFR/8zaDY5b/GZrSHhXoG7FjjmoBwcD7//0p3vqFX1fcphpSNgOxXHkqM89jhnyh\ntCqJk6Eyy1TVEvrLGpX7l8Lw1Bxr20P0tQVdQ9UIlFI3KaXWKaX8SqkNSqnbjOV3KaV2KqW2KaU+\nVsfjuTmqMxBT+Xe3kdupl0clIlZeYatpqIxQzkQ8RSKVYT6dozsSrDifplqm5vRNxG5gzBtLZ0s+\n9Dc2m2TEYQ6ViTWXqkz4z1TIFTffDPo9JYl+06MK+jzsH5ohkcpYE5BBlwcyw1y5nLJk7AuJKQYn\n53hqcLqkTmOtJDNZfB4hHPAum/LPDHWaoT8orfdn38ZOcY+zhXj1px/g3/7j6FKGy+DUHOs7Q4YQ\nyDVUZzxujurMZKvhGfzEqJC+o44lpsxwTd6j0sYhGkvmb0YRM1extNyD6VGdnpm3PIWpRJr2kA+f\n10NHi5+A18Po7LxjVQoTsy/VYBlBxZGxGB0t/pKwYbnQX8Dr4fx17RwYnmbYyHeYxrCvNWhN+I3G\nk5aAIJXJWeHRSp/1x/tPlT8hVZDM5AgZwo7lmktlSry7F/CoPKJFMHZqNVTHonGer7IafjmGJnWo\ntjtSW0fsZqKpDJXrUZ2ZbOwO4/MIB4Zn6Az761pTMGS0v9hc5FGNx1K2XIUWU8SSmYLGhrVi3rxz\nCqvRpFkBAbSH19cWZGwmaVSlcDZUfa1BAj5PWUGFLkYbKanU4RT6m0tlCfk97F7fzoGhGctLszyq\nVt28cj6d5bQR9jMfHCoJKixDte902W2qIZnJEvR52NYXWT6PyqjzF/R584ZqvtRQdUeCVn1Ik5Df\nU3WOKmfkvlJV1l90IptTnJ6ZZ6Crha5IgEQqu+zzuFYDTWWoXI/qzMTv9bCpR3sRO/pb69pKJOT3\n0tsaoKNFV643vZDxWNJSUHUZMmVYWtWBmbl8jss0MpOJFJ22p/K+tiBDU3NEY6mSOVQmHo+wocJc\nKi1NLw2Pmqo/e05kPp2lJeBlz0AHs8kMDx/VPazMHJVZv3E8nrLyU2buq5ygQinF9FyatpCPfUPT\nVffPciKZzhH0edje38rw9HzZKhH1xKzzBxAJao+7+HuPxlKOD0whX/UelZnLSmUXb6hGZubJ5hTr\nO1vy1+5ZmKdqKkPlelRnLmYOqZ5hP4CWgNcK+wF0hgN4RHs6E0WhP6Bs+E8pZXlJ5ZieSxMO6Buf\nmaeaTOQ9KtATfM02Jk5zqEwGulocq1PMzKcZm02W5KdA1/pTCtLZvKGaS2dp8XvZs17/Jn56YASf\nRywFoikWiM4mLY/KNILl8lTxVJZsTnHDReuBpYX/UtkcQducruKWL43A7uXmQ3+Fn7W4fJJJS6B6\nQ2Ua+tQS5l2Z0nQz9Adn51yqpjJULmcuptS6XkIKk//6ynN537XnWa+9HqE7ossoWaG/1oDVfbnc\npN97nh7hqk/8gvd+7fGyPZymEml2GA32zJblk/F0QZ6jvz1otWoobvFhZ2O381wq80a+tbe0p1nQ\n6vKbvzHq0J+XnWtb8XmEY9E46zpDVkjL9BqisSTD03MEvPnu0+UMlRn227O+gz0D7dy1hPBfMp0j\n4PVYc+cOj80u8I6lY07yhnzX7WJPThsqZ49qrlpDlTYN1eI9KnOy74aulrwQ6CzMU1VlqETk/6lm\n2Urjhv7OXMwbb72k6SbXnNvP5Zu7C5Z1G2WUxuMp/F6hLeizQn/lyig9cXIKj2iP5GV//x9877eD\nJdtMz6XpiQRY1xEq8Ki6wn5rG3sR2uKCtHY2dLUwEU+V3EDLKf5Ae1RQODdpzgj9BX1ey1s1DRHk\nParxWIrT0/Os7QgRNs5FucK05vypzrCf6/as44mTU5ZIo1aSmSxBv4dzenSX4uWYS2XW+QMqqv6c\n2toEa8hRWR7VEkJ/pke1vrPFeuA5G+v9VetRfaDKZSuKG/o7c3nl7rW86yVbuWxzV8OP1RMJMh5L\nMRlP0RXW/YYWCv09N6IrQdz1Zy9ia2+E//zNJ60Qnsn0XJqOFr/VTn4+nSWR0gVpTex5qYoeVZdz\nFfUjYzF8HmGToQy0k/eo8jfG+XSWkE8bsN3rdZuKgc78e01DNRZLcso0VEb4ciGPqr3Fz3VGM8uf\n7F+cV5XM6BxVwOfhnO4whxssqLDX+QOIBEofUBKpDIlU1jH0V4vqry4e1dQcXWE/4YDPMq5no0S9\noqESketE5J+BARH5tO3vduDsbDXp0hC6IgE+8KrzCfq8C2+8RHpaA0zEU4w75iqcQ3+HR2fZuaaN\n7f1tfOSGPQCcGC/MIeUNlQ7b2QvSmvQZhsojVGxEWa4v1fHxOBu7w/gdJgqbhsp+I51P52gxDM8e\n01B15T2qloCXSMBLNKZzVOs6Qtbcs4UMVUeLn619rZy3to0f7VtcnkobKmOuW5FEPbMET6Qc9jp/\noEPBLX5vgUdltqAvnkMFut5ftV2U8zmqpYX+zO+rvcWHzyNn5aTfhTyqYeBRYB54zPZ3B/DKxg7N\nxaUxmNUYJuJJ62Zk9hpyCv3Np7OcmEhYeRQrXGYLwWRzitn5DB0tfjZ2hRmZnbcqpHdHSkN/va2l\n0mc75apTHIsm2NxT6k0B1g3fPunXFFMAVj+xDTZDBXrS75ghprB7VOVUf9PGxGZTSXnDRQM8dmKS\nQyO155dShkcFsL2/lePjcWLJDH//04Ps+uDdFXOCi8Fe58+kNeQrUP1Fje+1z9Gj8jieF6epDaZH\nVa1hc2LYVu5KROg6S+dSVTRUSqknlVJfArYrpb5k/P8OdD+pyWUZYQ24OSqXauiOBJiZzzAyo+fK\nQPlcBcDh0RhK5fNn5k0uauvjNGPzMjZ0taAU7B/S12GxmAIqK/5AixxC/sK5VEopTozHrTlhxQT9\n5cUUAJds6uLDr93Nq/auKzpWkEMjMVLZHOvaQ4SNcFg1HhXA71+2gYDXw1cePlHxMzmRzGQJGIZq\nW1+EdFbxu5+6j0//4jCXb+6ycoLfeWzQsRRRLJkhXYPnZa/zZ6KrkuQ/qzkBumzor0jFF09meMHH\nf85dRepH07NdbI5KKcXQ1BzrbTnF7vDZWZ2i2hzVPSLSLiLdwJPAF0Xk7xs4rkXh5qhcqsE0NENT\nc3QbQgdzPo1TGSUzb2L2yPJ7ddVx+5P+dJGhAtg3aBgqW46qJxJApLQPVTEiwoaucIFEfWw2SSKV\nLZDb2ymXo2oJ6OUej/D2qzdbYU77mMyGles6W6xQYbkJv9NzabwesfbT0xrkVXvX8t3Hh2qeB5W0\neVS7jNBka8jH1955JV995wu4689exPa+Vv7Lt5/ki786XvDeVCbHK//hfj72o2eqPp69zp9JJOgt\nqPNo9gzrbXNQ/TnkqCYTKWLJjKX0NFlqjmoqkSaRyhaIX7ojATf0V4EOpdQM8Abgi0qpS4GXNW5Y\nLi6No8f2NG0+WQd9XgI+j2MF9edGZvF5pKCbbnEx1wJDZQgdnnLwqHxeD1t6Io6qvWI2dhVO+jXr\n6p3TU85QlVH9+Svn/XrbgphRq3VVhf50WSj7xOy3XnUOs8kMP3iito49esKvKfbo4M4/eRE//rMX\nc/X2XgC297fxrXddxRVburntl8cKyjr9eP8phqbmuOfpkaoLvzrV8IsECstnnZqeK5hrZkcbqsJJ\n1abnOVdk2BNLzFENFZW7Aj2VwjVU5fGJyDrg94GKzQtdXFY79ptUtz1XYfQmKubQaIzNvRErRAWU\nFP8DvykAACAASURBVAg1DVVn2G+1k3/OyNl02uTpAN95z9X8xct3LjjODV3hAjHF8XFtqLaUNVRm\nB1p9g1RKVWeobCGutR0h/F4Pfq+UraA+PZcpqLYBOqx4/rp2vvLwiZqqhZvydJM9Ax0lghqPR/ij\nF25maGqOnz0zYi3/0oPHAX1DP1plcVx7nT+TtlBhQeLhqXnWtIccc4hWl1+b8TENUrzIsC9Vnp6f\n7JvPSfZEAu48qgp8BN2W44hS6hER2Qocatyw8ojINSLygIj8m4hcsxzHdGlueopCcSatQV9JzTeA\nQyOz7FxT6AHpquPOHpXZTj6bU7SFfCUKve5IoKCFfDk2drcwM5+x9n0smsDvFdZ3Oue3im+iupwS\nhAKVj9VnGGufR+g1PMyQ31vZo2opNL4iwltfcA5Pn5rh8eenFvxsJvbQXyVedv4aBjpbuN0I/+0b\nnObx56e4+erNAPzyULSq40Vj+Tp/JpFgoZjC3q+rGFPqbw//JQwjVxwqnV9i6M+c7Gv/vrvCAaYS\n6YYoIlczVRkqpdS3lVIXKKXeY7w+qpS6caH3icgXRGRURPYXLb9WRA6KyGERef9ChwdiQAjdHdjF\nZUnYZeH2sJxTq4/5dJbnJxJs7y+ciNzXGizoSDtVJDAwwzX2J/daKVb+nTCk6U49rKA09GfeKKv1\nqNa0h/AYXkQ44K2Yo+ooMlQAN1y0ntagj6/WIKpIZXIFnmo5fF4Pb73qHB46Os7B07Pc/uBxwgEv\nf/GKnWzuCfPAobGqjndkLFYyBy1S9IAybLTVcMKpeaLpSRWLT5aaoxqemiPk9xRcQ2Y0YLIOTSvP\nJKqtTLFBRL5nGJ0REfl3EdlQxVtvB64t2pcX+CxwHbALuElEdonIXhG5s+ivH3hAKXUd8FfAh2v5\ncC4uTrSHfPi9+obc01rZUB0Zi5FTlHhUPZEAs/MZS2E3Y5sEC/kJu8VtImqheNLvsWi8IE9WTHEJ\npbkqDZVpuO0353DAV171l0g5GqpI0Mer967jnqdHHN5VSiabI5NTVc+d+4PLNhL0efiHe57jh08N\n84ZLBmgP+Xnxjj4eOjK+oEFQSvHU4DQXbiwUW9m/92xOcXp6vkBpZ8cUphR4VIZBL54sPpfS48nk\n1KKq8o/FkvS3hQpygabROtsk6tWG/r6IlqWvBwaAHxrLKqKUuh+YKFp8BVreflQplQK+AdyglNqn\nlHpN0d+oUsq8+iaBslIpEblVRB4VkUfHxqp7unI5OxER6wdvf1ptDZUaKkvxV+RR9bYVVgmYnksT\n8nusJ27To+oKl97Qq8Xcx+DknCFNTyxgqArnUZmhu5YFQn9mTbu1HbaJwAuE/jpafI7rNna3MJvM\nlLQbccLM3VQT+gOtnnz9xQP85MBpUpkcb79qMwAv2tFLPJXlt89XnjFzcmKO6bk0ewc6C5a3Bn0k\nMzky2Rxjs0kyRrVyJ8zQ31yBoTI9qsJrx16CajF5qrHZpDVB3MS8Xs82iXq1hqpPKfVFpVTG+Lsd\n6FvkMQeAk7bXg8YyR0TkDSLyOeDLwGfKbaeU+jza43o8EKhfPyOX5qQnEkREd941ccpRmYq/Ykm4\nVXXcCP9NJwrDYRu6DUO1hNBfZ9hPa9DHyYkEIzNJ5tJZtvQ6T/YF+zwqw1AZN9OF8mGm0V3XYfeo\nvI4elVKKGWNisxPm552qIjRlGtRqDRXA242c1NXbeqzahVdt68HrER5YIE/11JDOnV2wodCjspfP\nGp4u7NdVTD70lz83cStH5SymgMVN+h2bTZZMOrYqqJ9lyr9qr5CoiPyhiHiNvz8Exhd5TKfp+GX9\nYqXUd5VS71JK/YFS6r5FHtPFpYAeo0eVPd8TKZr4CXBopFTxZ74fCj0q+83bDNt1LyH0p+dSaYm6\nqfgrN9kXIOAtDP3NV2mo2oI+/tM123jtheutZS0B5yrhsWSGbE6VN1Th6kNT5s07WIWwxOT8de18\n/PV7+eD1u61l7SE/F2/sXDBPtW9wmoDXU1L4uNWYQzebTFvFdct5VObDgD1HVd6jyp+/xeSpxmLl\nPaqzrTBttYbqj9DS9NPAKeCNwDsWecxBYKPt9QZ0qaYl4074damWXevbOX9te8EyLVMu9AQOjcYc\nW4/02Yq5AkzNFeZtTCHEUjwqvZ8WBicTHDfk15VCfx6PEPB68h6VkSNZKEclIrzv2vOsEkugPSqn\n0J8lw29x/lz5Ct8LGyrz5h0oIw4px5uv3MS5awuNzYt39PHU0DRTFQzkU4PTnL+ureSho8CjmipV\n2tkxz6W9OkW8XI7KZsxqDf2lMjmmEumS6hj58+uKKZz4KPB2pVSfUqofbbg+tMhjPgLsEJEtIhIA\n3oTOfy0Zt4SSS7V84Lrz+fqtLyhY1hr0MZ/OWSV55tNZTozHHZs59tj6OIGeW9Rhu3mvaQ/ywet3\n8bqLy0a1q8IscHtsPE7A6yn7pG8S9HnyOaoqxRROhAM+Eg5tPqaLRCPFWMn+Km6kpudnn0e1WF68\nsxel4FeHnQM9uZxi/9A0F2zoLFkXsQoSZxiemqct5KMt5Pz5rNCfzYibBr3YA7VvU6tHZdaRLPao\n/F4PHS1+16MqwwX22n5KqQng4oXeJCJfBx4CzhWRQRG5RSmVAd6Lnpf1DPAtpdSB2ofu4lJfiuv9\nHR2Lk1POzRzDAR/hgNeq9zdTFPoTEd7xwi1lcx3VsqGrhVgywxPPT7Gxu6ViIVvQN/3i0J+pVKuF\nlgU8qvKhP728ptBfHSrmXzDQQXvIxy8PO4f/jo/HmU1m2LuhNNrSZvveK82hApuhsntUhidVPFl8\nKaG/sVlnQwVGPzU3R+W8nYhYjYKMmn/Osh8bSqmblFLrlFJ+pdQGpdRtxvK7lFI7lVLblFIfW9zQ\nHY/nhv5cFk2b7ckasOrflWvm2NsatJ58y80tWiobjTk/jz8/WbbGn52gz1uzmMKJsN9ZTDGzgKEy\nK1ZMVnEjtTyqGsQU5fAZXYKfL2qLYrLPKGdVLKSAwgeU4aIisMWEHHNU+npJZnIFJZ4SqYwVZqy3\noXLFFM78L+BBEfmoiHwEeBD4ZOOGtTjc0J/LUsi3o9c3nmdOzeL3lir+THpbA0RjSdLZHLFkeSXc\nUjAl6umsqpifMgn6PDVP+HUibIgpisshmWq+jjKy+4DPQ1vQV1WZn8Wo/iqhb+DOIcenBqcJ+T1s\n7yv1js3iurOWoSpf2b7FSfVnM+h2QcV8OmddE6lsdc0WTVxDVUi1lSn+L3AjMAKMAW9QSn25kQNb\nDK5H5bIUrFyFIVE/MDzNzjWlyXeT3tYg0dmUzctYMMhQM6YoA+CcKjyqgM9j3USrnUflREvAh1KU\ntF1fKPQH0BnxV+dRGbnAaipTVENXOFD2uPsGp9m9vsOxqof5vUdjSSYT6QU8qtJ5VPZitHYvdC6d\ntc5TrfJ0M/fZ4yDG6XENVXmUUk8rpT6jlPpnpdTTjRzUYnE9Kpel0GoL/SmlODA8Y7Vvd6LHCP3l\nC9LWf/5eR4ufdsPTK1eM1k7I7xD6W0QOKFym1YfZ4iNSwfh1hwMlJX6UUgVhMbB7VPXp6mxWFi/2\nArM5xf7hafYOOD/Ami1eDo3oyd2VclT5Lsq2EkpJe74qf77mUllrnt5iQn/tIZ9j2NZsnlhL8d8z\nnfo8yqwSXI/KZSm02UJ/p2fmmYin2L2+/LXUZ9wYTeFAI0J/kM9Tba4w2ddEq/7yKrSgz2PV76uF\nfE+qwpDV9FyazhZ/QVmfYpy60P706REu+shPCwxfPVV/oA1kKpsrqWJ+dCxGIpV1zE+B0eLF67Gq\n3VfyqESEkD9/jkEbczMkaJ4vs3J9x2INlcMcKpOeSIB0VvGPPzvE4dHauyqfiTSVoXJxWQr20N+B\noRkA9gyU96jMPk7HozqBX06yvVQ2dLUQ8HlY37GwgjBo86jmU9lFhf0g71EVS66rEY10h0tDU/uH\nppmdzxSU/smr/uoU+os4CzmeHCwvpDCJBL1WuayFpgAUN0+Mp7KWUTENlfnZ8jmq2j2qcobqd8/r\n5/LNXXz6F4d42d/fz3X/9AAz8809r6qpDJUb+nNZCvbQ3/7haUTgvLUVQn9GS4wjY/oG1yiP6o2X\nbuTdL9lalWdkF1NU04uqHOEKHtVCBrnTaEVh59T0fMn+6ilPh3w+p1i6vW9wikjAy5be8s0qI0a9\nP4/AmgW6L4d83qIcVdaql2hO/jU/pyk6WUzor8+hcSPA1r5Wvv3uq3n4A7/HLS/awjOnZqwJ4c1K\nUxkqN/TnshTshurA8AxbeiOWl+WEeXMyDVVxg8R68fJda/iLV5xb1bbaUJmhv9yiDVWLX3/u4hxV\n8XwxJ7ojfmJFhWlHZrShsvd9MsNn9Qr9lfOojo0n2NbfWnEOmvndr2kPlW2jYhLye6wclVKKeCpj\nVZAonvy72NBfNJayrq9yrGkP8fJdawAc+6g1E01lqFxcloLXI4QDXmLzGZ4enqmYn4J8MdcjY/pp\ntlEeVS0Efd6C6um11NGzU64dfTWhP6fCtJZHZRMemOGwWksolaO7TPmm0Zl5x7bydkxDtVDYDwpD\nf7otfV5GboopzPO2mNBfIpUhlsyUDf05jXvWoTN1M+EaKhcXG5Ggj8HJOYam5thTQfEHWN1wT4zH\nCQe8JZ18VwJdmSI/j6plkd5KudDfVDWGyqEw7YhhqOxtVOo+j6rV2VCNzSbpb69804/UaqiMc2x6\niKZHZZ6v+SV4VGa1k+LK6U60G6WeZl2P6szBzVG5LJW2oI9HjusWagt5VO0tPgJeD+ls+Wriy01h\n6G/xYooWB48ql1NVhf6KC9PGkhnrib9Q9ae7+1ZSENZCW9CHzyMFk43T2Rzj8RT9C3gneY+qsucF\nRujv/2/v3IMkK8/7/Py6e7pnpmf2BuK2ywoQd8myEBgrRrYoESnIAaEkUgksyyqBTewSsmzH5WA5\nDlEqNk4sx3YMkUQhBDgKmBBsL5gysYlLyC4kLwI5ASHiNZJhDKtd2MvszuxOT/e8+eOcr/t079z6\ncra7T79PFbV7vu0+/Z0+w/nNew8d02MLsTWZotX1104d1d7DR5vOueq+Q6aqJ1MMDx6jcrplarxQ\nD8avVkMFUapyaE47OEKVqKOqdJNMcWyM6nClypKtfa2tjWl3x9YUNHdxWKjWemZNQXQ/Npebi35D\n4ex6XX/r6c0YWVSxUMWNe7eUi+TU+L6CwG/owKJarSvFSvt2i8pxRohy/IA+beP4ukZ0DJ5Q5ahU\nlzAzjlZrHfX5g4TrL5HddnCN9kmB0Jg2WDZJoZpfaLaoepXxFzihpWHrntkgVOt0/a2jBGAiEaMK\nxb6TxTyTxUL9OFhWkUtYbcWo9h5ev+uvWMhRKuSOmUydNVyoHCdBcKW8eYUuBq2E2MTACFViyu/R\nLiyqUiGH1Oz6W0/7JGh06DgQC8bu2eUtqkp1qacWFRzbRmlPbJ2sFaMKwxPXn0wRCU+woMqlQtwf\nMToOQjZZjNzD7VpUUsMyXYvp8TFmM25R9b45WY+RlCOah7UBeMrM7unzlpwMEzqor+X2CwycUMUW\nykJ1qasYlaRjOqiv1Tk90NqYdnc83n0sr2Usqt4K1ZZyked3z9aP9xyKRHIt19+J0yUKObF183qE\nKlePQSUtqnKpYVElZ4EVC+0L1Qnl4ppp8oFo4Ge2hSpVi0rSXZL2SHq2Zf1KSS9I2iXp5jVOcw2w\nFVgkmg7sOKlRrgvVkFpUhcY4+m4KfiFqTDvfgUUFzY1pd88eZdPkGBsnis0xqsVazxrSBra0xKj2\nzEbWyVo1SR+6+HT+6BOXrevaSoWG6y9YUOVigYmx/DExqk6FqnWy72pMlQocyngyRdoW1d3AbcC9\nYUFSHrgdeA+R8OyUtAPIA7e2vP964DzgSTP7gqQHgcdT3rMzwtRdf+u2qKIHYFrFvu1Sb5paWeLo\n4lLHMSoI4+gbv6kfaEOoko1pdx9c4JQN4xxZrB2T9ddpnddKbC4XOXBkkdqSkc+JPeu0TiaKed6y\nTnfvRLFRq9ZsUeWPyfobL+YioWorRrVy+6TlmB4vZL7gN1WhMrMnJJ3RsnwpsMvMXgSQdD9wjZnd\nClzVeg5JM0D4FWnFoS6SbgRuBNi+fXvXe3dGk/deeDKV6hKnblw7TRkG0KKKH/yh91unrj+IHr6d\nWlSbE6Mods8e4ZSN43xvdqGp03ivs/4AtkyOYQYH5iucMFVi76GjK7Yi6pTxQp5KLRqSGIR3slRg\nslioi/mRSo2comLmdmNUrx1a4E3rGOkSmCoVeGlu+YGRWaEfyRRbgZcTxzPx2ko8BPwTSb8HPLHS\ni8zsDuAzwNPFYu/HLTijwUXbN/OrV1247tqeIFRpNaRtl/DgD10hunP9Nfe0O3hkkULcvWMtNica\n0+4+uMCpG8cpF/NNFlUayRRb4vsRio33rNLctVMaU35rdeGdGMtHwh46U8RuV0kUEyUDa2FmHVhU\nY5lPT+9HMsVyT4AVB6uY2TxwQ3rbcZzOOf/Uac45aWrFWUfHm/DgDw/qboRqOYtq0+TqIz4Cm+PG\ntJXqEq8dXuDkDeP8w4GjdasMItfflnKvLaq4Me3hCmefFMWozj15uqefMZ6Y8hsEKWq/VWhy/U3E\npQ7tuP5mj1apVJfadv15jKr3zACnJ463Aa/0YR+O0zUnTpX4s194V7+3USdk/QUX1HgXrr+JsQL7\n5o7Uj9fTOT0QGtPO7I9cUsGievVA43xp1FFtLkf72z9fYWnJeO3wwpo1VO1SH0dfXWJuoVq3MKMY\nVZyeXqkxUYxEuJTPUamuGLVoop1i30DI+jOznnX5GDT64frbCZwj6UxJReBaYEcvTuydKZxRJ9RR\nHYwtqvEuXGutyRTraZ8UCLVUz78aDfY7ecN4k8UB6cSowuiVfXOL7JuvUF2yngtVKeH6m6/UmIxr\nsCaK+XpWYzLjsp2sv7pQtZn1t2TH9mXMEmmnp98HPAmcJ2lG0g1mVgVuAh4DngceMLPnevR53uvP\nGWmOiVH1MJli76GFeh+/tQjFqs+/GtU0nbJxnHIp3zLmY6lnIz4CIfty39xCoyvFhh4nU4w1+iDO\nLVTr3UzKxQKV6hLV2tKxQrVO119o+XRiG+IaMlWzHKdKO+vvuhXWHwUeTeHzHgYevuSSS36q1+d2\nnGEgPESD66/rZIpYqKq1JV7cO8e7zn3Dut67ebJZqE7dMBG3GGppStvjjvPjY3nKxTz75hYTxb69\nTqYIRdVRjCq4/pJtp+YrjfZV7WT9dWJRTccd1A8vLAK9FeVBIVMtlNyickadVouq6zqqOOvvO6/N\nUaktcd4p60tMSFpU42M5NkwUKBfzLNas/tCupFBHBdG4j/3zlUb7pB6np9djVIshRhX9vl9v5LtQ\ni0asFDtw/R1eYCyvtsodpkegMW2mhMpjVM6oE5ITQruj7lx/BapLkbB8e3cUa1qvUIXGtK8cPMqp\nGyeQVO/6MV+JAv9pxKggyvx7fa5St07W6vPXLuOtMapEMgVE13cksd6OUL12aIETyiVyq0wjbmV6\nBFx/mRIqt6icUSfEfA4c6T49fSIRi/n27lnyOXH2SVPreu+mRCzr5FgowoN8rlKjumQsWe+GJiYJ\noz72zB5lerzQlVW5HPUY1WKNuUq1LsCN0SiRS3C8gxjVgbgEoB3qM6ky3O8vU0LlFpUz6vSy4LcR\nc6nywu5DnHVied3p5KExLcApcTJDwzVWrRfA9jo9HSK34765CntTSE2HqDMFRK6/pOUU/pxbqMbT\nlRsxqvUW/LZTAhCYrk/5zW4tVaaEynFGnZCc0Iusv/De+UqNb+8+tG63X2BTXNN0SjzjKWlRLcSx\nr143pYXQZ7DCntmFnsenIOrfB43OFMslUySHVpbacP21UwIQGIXhiZkSKnf9OaOOpOjBWAsWSzd1\nVNEDcM/sAjP7j3DBqetr1BsIXSJOiV1/SYuqF/tbic3lIvOVGi/tm+95fAoarr/5SjXO+ovT02PB\nmFuoMt+aTFGLhlmuhQvV8mRKqNz15ziNh3/oNdcpwSL45ssHADivzVZEYUJy3aKKH+iRRRULVY/r\nqKCRcbjnULquv31zkdUaLMXwfe2fX8SMpvR0M6gurS1UB48ssmG8PaHK50S5mPcYleM4w0NI+e7G\n7Zd8/zMv7QfWn/EXCLVUp8Sd6CcTWXFpx6gCabj+xvIiJ+pzr1otqn2Hw3rDogLWdP8t1paYq9Q6\n6sQ/lfF+fy5UjpMxkhZVN4QH7dMvHWCqVGDbOqbfJqkLVZxMUbeoFmosxL3vUklPTwpVCq4/SUyM\n5Xl9rlmQwp+vz0Vp8cnOFNAsVJ95+Dk++9gLTecNrruNE+33YZgeH3OLaljwGJXjNB7+3brVwoP3\ntcMLnHfKdNtuxAtP28DWTRP14ZLHy6JKtnnq9YiPwPhYnn2xIAWLqlTIkVPUuR1oilEBTSnqT/7d\n6/zV373WdM7QWb6TkTHRlF8XqqHAY1SO03j4d2tRJV2H7br9AD548Tb+6uZ316frTo6F9O1a3bpI\nI+vvhJRdfxAJVbCoQoxKEuViod6vLxmjgmaL6tDRaj0zMzDbxmDKVqJRHy5UjuMMCcGS6t7113BB\nXdCBULVSyOcoFXKxRZWe62/DxBihsUMarj+IvuN9LTEqiKzGIGCtrr9kLdXhhWr9/YF2Jii3EkZ9\nZJV+zKNqC0k/DHyEaK8XmtkP9XlLjjPQ1GNU3SZTjCUtqvZS01eiXCowV6mmmvWXz4lNk0XmK9V6\n0XGvmRjL1y2Y5MTjyWKB12OLKnz/pZYYlZkxt1ClZka1tlS3OLt3/XkyRUdIukvSHknPtqxfKekF\nSbsk3bzaOczsq2b208AjwD1p7tdxskBw/XXbOiifU/0h225q+kpE49prqcaoIEqoOGl6PLVBgsnv\ntpy0qIr5YzrXt8aoFqpLVJcMM5omHs8e7caiGuNwhl1/aVtUdwO3AfeGBUl54HbgPUTTfndK2gHk\ngVtb3n+9me2J//5jwE+mvF/HGXp6lfUH0YP3hHKRjW32n1uJqVLkokrT9QfRROHaOuqWOmU8YQmG\nJBGIRCvU9daTKfLRn8GiSsaS9s9XOCEe6VG3qNqso4Loe52r1KgtGfk2GtoOC2nPo3pC0hkty5cC\nu8zsRQBJ9wPXmNmtwFXLnUfSduCgmc2muF3HyQT1OqoeCFW5VOCcdTaiXQ9hGONCiskUAL/xL96a\nynkD44XlLaqku3Wl9PRkLGl/IqHi4JFFivlckwiul+lEY9pOLLJBpx8xqq3Ay4njGeAH13jPDcCX\nVnuBpBuBGwG2b9/ezf4cZ6jpVYwK4DPvfzMn93BCbjm2qCrV9FooAWzd1F7NV7uMF0OmX7N1VS6t\nIlS1yIpMDo9MJlTMHqmyYWKsI3dlY9RH+y2YhoF+CNVyd2FVG93MblnrpGZ2h6RXgauLxeLFnW7O\ncYad8PDvxXiLKy44uetzJJks5tkzu5B6jCptgkU12dKmanIZ66o1PT3p+jswnxSqRTZ0UOwLMFUK\nU36zGafqR3r6DHB64ngb8Eof9uE4maRXdVRpUC6GrL8aUtSOaBgJVtRkS1bhZMLSCr8wtKanH26y\nqJqTKTq1huquv4wmVPRDqHYC50g6U1IRuBbY0Yd9OE4mqddRFQevTHKy1IhRlQq51LLy0iZYq+UW\n92qwqJINgVvT0w8vNMQpaVEd7KBzemAq41N+005Pvw94EjhP0oykG8ysCtwEPAY8DzxgZs/14vO8\nM4XjNNxSA2tRxYMTg0tsGAnfbdLVBw3hSn73renpweop5nNNMapOOqcHNgShyqjrL+2sv+tWWH8U\neLTXnyfpauDqs88+u9endpyhIVhUpQEUqsligYXqEvOV6kDub73UXX8tFlWISyXjg60xqsMLUVLF\nts0T7G+JUXVsUZWyPeV3eH+lWQa3qBynt3VUvSZkxe2fX0wt4+94EISoNUYVRn0kMy6PTU9fJJ8T\np2wcr6enmxmzR6sdJ1N4jGqI8O7pjjPYyRTBVbZ/rjLUQlVaMUa1iuuv2nD9TZUKbC4X6zOtDi9U\nqS1ZxxbVZDGP5DGqocAtKsfpbR1VrwkW1b75ytCmpsPKMapkMkWgkBNSI0Z1aCESqi2Txbrrb7Y+\ni6ozoZJU7/qRRTIlVG5ROU4jRtWLOqpek7So0upKcTxYKUZVT6ZIrEuimM/VLaq5hSrT4wU2T45x\n4MgitSXj4Hzn7ZMCG8bH3KIaBtyichw468QpNk6McXqbE3mPB+FBfuDIkMeoQsFvqcX1VzrWooLI\n/ZesoyrHrj+zKImim4a0gSx3UB/4MR+O47THhadt4G9ueW+/t7EsIdnAbDCzEtdLo45q+YLfVrdr\nqZBrSk/fNFlkSzzgcd98pasRH4Esz6Qa3l9plsFdf44z2CR74Q2zRRWKqVtdf5PLpKcDTa6/QwtV\npsYLbJqMhGr/XKWroYmBqQxP+R3en5RlcNef4ww2yeSDYRaqkAhybMHvyq6/ZNbfdJxMAVGq/mxP\nLKoxt6gcx3G6JekqG+Zkis2x2+7EqWLT+kTd9dd8bUmhmouz/jbFM772z1WYPbKIRFcTiT1G5TiO\n0wOSsZthTk/fummCRz75Ti44dUPTeqmQ47pLt3P5eSc1rRfjGFVtyZir1CiXCvUY1f44RjVdKpDr\nYujhdIZdf5kSKm+h5DiDTbGQi+I1taWhdv0BvGXrsSEGSdz6z7/vmPUQo5qrREIyPV5gspiP+v3N\nV5g9Wu16ivJ0KWpPVakuDbW1uhyZuhqPUTnO4BNSuksdTLIdVoLrL7Q4mioVkMTm8hgH5ha7akgb\nmEpM+c0ao/OT4jjOQBDiVMPs+muXYiHPQm2pPt03iMrmyWJkUXXRkDYwHQtdFvv9DbxQSdouaYek\nuyTd3O/9OI7THSGFe9hdf+0QXH9hDMdUqSFUB+IYVbdCFc45m8GEirTnUd0laY+kZ1vWr5T0UtQn\nbwAADGtJREFUgqRd6xCfc4E/MbPrgQtT26zjOMeF0L1hlISqVMhRqdaaXH8Am8tj7IvrqLp1/W3I\nsOsv7WSKu4HbgHvDgqQ8cDvwHqKx9Dsl7QDywK0t778eeAb4FUkfBn4/5f06jpMy5VG0qOKsv8PL\nuP72zy8yX+k+meL7tm3kkU++kzNPLHe930Ej7cGJT0g6o2X5UmCXmb0IIOl+4BozuxW4qvUckn4R\nuCU+14PAl9Lcs+M46TI5ijGq/LHJFABbylEHdbPuulJAFKNaLhMxC/TjV5qtwMuJ45l4bSX+FPhZ\nSZ8HvrvSiyTdKOkpSU/t3bu3Jxt1HKf3lEcw6680FgtVbFFNxxN5N01GjWmh4bpzjqUf38xyFW22\n0ovN7Fngg2ud1MzukPQqcHWxWLy4i/05jpMi5RGMUdUtqlioglhvKTesqG7aJ2WdfvykzACnJ463\nAa/0YR+O4/SBEKPKWlHqaiRjVONjOQr56NpDY1pwoVqNfvyk7ATOkXSmpCJwLbCjD/twHKcPjGSM\nqpBjsWbMHllkqtQQpC0Joeo2RpVl0k5Pvw94EjhP0oykG8ysCtwEPAY8DzxgZs/14vO8M4XjDD71\nGNWIWVQA++YqTCdiUZtdqNZF2ll/162w/ijwaK8/z3v9Oc7gM5IWVb4hVFOJDumbkzGqLuuosszo\n/ErjOM5AEB7UI5X1l7CoksMjp0oFCnHHdLeoViZTPynu+nOcwefdF5zEp3/0fM5+w1S/t3LcCK6/\n1+cqTTGqqDFtkYmx/Egll7SLJ+47jnNc2TA+xo0/8qZ+b+O4EkTo4JHFphgVRAkVXYyhGgkyJeGS\nrpZ0x8GDB/u9FcdxnDrFfLO7L8mmyTF3+61BpoTKXX+O4wwiSbfeVItFdd2l2/noO954vLc0VGTK\n9edZf47jDCJNQtViUX3gotU6yDngFpXjOE7qhPR0OFaonLXJlFA5juMMIqtZVM7auFA5juOkTGmV\nGJWzNpkSKs/6cxxnEHGLqjsyJVQeo3IcZxDxGFV3ZEqoHMdxBpHV0tOdtXGhchzHSZmkUE27RdU2\nAy9Uki6U9ICkz0lac9Kv4zjOoOEWVXekPY/qLkl7JD3bsn6lpBck7ZJ08xqneR/we2b2M8BPpLZZ\nx3GclAgxqpxgYmx0xpv0irSl/W7gNuDesCApD9wOvIdoLP1OSTuAPHBry/uvB34fuEXS+4ETUt6v\n4zhOzwlCVS4VkLwDbbukPTjxCUlntCxfCuwysxcBJN0PXGNmtwJXrXCqT8QC99BKnyXpRuBGgO3b\nt3e5c8dxnN6Ry4mxvDw+1SH9+Na2Ai8njmeAH1zpxbHQfRooA7+50uvM7A5JrwJXF4vFi3uyU8dx\nnB5RzOc8PtUh/UimWM7utZVebGbfNbMbzewjZvaXq53Y66gcxxlUioWc11B1SD+EagY4PXG8DXil\nFyf2zhSO4wwqxUKOsgtVR/RDqHYC50g6U1IRuBbY0Yd9OI7jHDdKhbxbVB2S6rcm6T7gcuBESTPA\nLWb2RUk3AY8RZfrdZWbPpbkPx3GcfvOpK87htE0T/d7GUCKzFcNDQ8sll1xiTz31VL+34TiOM1RI\n+oaZXdLvfbQy8J0p2sFjVI7jONkjU0LlWX+O4zjZI1NC5RaV4zhO9siUULlF5TiOkz0yJVSO4zhO\n9siUULnrz3EcJ3tkSqjc9ec4jpM9MiVUjuM4TvbIZMGvpL3A33f49hOB13q4nWFhFK97FK8ZRvO6\nR/Gaof3rfqOZvSGtzXRKJoWqGyQ9NYiV2Wkzitc9itcMo3ndo3jNkJ3rdtef4ziOM9C4UDmO4zgD\njQvVsdzR7w30iVG87lG8ZhjN6x7Fa4aMXLfHqBzHcZyBxi0qx3EcZ6BxoXIcx3EGGheqBJKulPSC\npF2Sbu73ftJA0umS/kLS85Kek/SpeH2LpD+T9Lfxn5v7vddeIykv6RlJj8THZ0r6enzNfyCp2O89\n9hpJmyQ9KOnb8T3/R1m/15J+Pv7ZflbSfZLGs3ivJd0laY+kZxNry95bRfyX+Nn2fyS9vX87bx8X\nqhhJeeB24H3AhcB1ki7s765SoQr8KzO7AHgH8In4Om8GHjezc4DH4+Os8Sng+cTxfwR+O77m/cAN\nfdlVuvwu8Kdmdj7w/UTXn9l7LWkr8LPAJWb2FiAPXEs27/XdwJUtayvd2/cB58T/3Qh87jjtsSe4\nUDW4FNhlZi+aWQW4H7imz3vqOWb2qpk9Hf/9ENGDayvRtd4Tv+we4AP92WE6SNoG/FPgzvhYwLuB\nB+OXZPGaNwA/AnwRwMwqZnaAjN9roABMSCoAk8CrZPBem9kTwL6W5ZXu7TXAvRbxNWCTpFOPz067\nx4WqwVbg5cTxTLyWWSSdAVwEfB042cxehUjMgJP6t7NU+B3gl4Cl+PgE4ICZVePjLN7vs4C9wJdi\nl+edkspk+F6b2T8AnwVeIhKog8A3yP69Dqx0b4f6+eZC1UDLrGU2d1/SFPA/gZ8zs9l+7ydNJF0F\n7DGzbySXl3lp1u53AXg78DkzuwiYI0NuvuWIYzLXAGcCpwFlIrdXK1m712sx1D/vLlQNZoDTE8fb\ngFf6tJdUkTRGJFJfNrOH4uXvBVdA/Oeefu0vBS4D3i/pu0Qu3XcTWVibYvcQZPN+zwAzZvb1+PhB\nIuHK8r3+x8B3zGyvmS0CDwE/RPbvdWClezvUzzcXqgY7gXPi7KAiUQB2R5/31HPi2MwXgefN7D8n\n/mkH8LH47x8D/vh47y0tzOyXzWybmZ1BdF//t5l9BPgL4IPxyzJ1zQBmtht4WdJ58dIVwLfI8L0m\ncvm9Q9Jk/LMerjnT9zrBSvd2B/ATcfbfO4CDwUU4DHhnigSSfpToN+08cJeZ/Vqft9RzJL0T+Crw\nf2nEaz5NFKd6ANhO9D/7h8ysNVA79Ei6HPhFM7tK0llEFtYW4Bngx81soZ/76zWS3kaUQFIEXgQ+\nTvQLambvtaTPAB8mynB9BvhJonhMpu61pPuAy4lGeXwPuAX4I5a5t7Fo30aUJTgPfNzMnurHvjvB\nhcpxHMcZaNz15ziO4ww0LlSO4zjOQONC5TiO4ww0LlSO4zjOQONC5TiO4ww0LlSO0wWSLg/d2Dt8\n/wck/dte7ilx7l+T9LKkwy3rN0n6eBqf6Thp4ELlOP3ll4D/2u1J4u7/rTxM1Gy5lbuIOow7zlDg\nQuVkHkk/LumvJX1T0hfCQ13SYUm/JelpSY9LekO8/jZJX4vn9vxhYqbP2ZL+XNLfxO95U/wRU4mZ\nT1+OiyuR9BuSvhWf57PL7OtcYMHMXouP75b0eUlflfT/4h6FYY7Wb0raGZ/rX8brlyuaLfbfiQq4\nmzCzry3XfcDM5oHvSlpOxBxn4HChcjKNpAuIuhRcZmZvA2rAR+J/LgNPm9nbga8QVfYD3Av8azN7\nK5EAhPUvA7eb2fcT9Y8LInAR8HNEc8zOAi6TtAX4Z8Cb4/P8h2W2dxnwdMvaGcC7iEaSfF7SONHs\npINm9gPADwA/JenM+PWXAr9iZu3OTnsK+OE23+M4faGw9kscZ6i5ArgY2BkbOhM0GnUuAX8Q//2/\nAQ9J2ghsMrOvxOv3AP9D0jSw1cz+EMDMjgLE5/xrM5uJj79JJDZfA44Cd0r6E2C5ONapRGM4kjxg\nZkvA30p6ETgfeC/wVkmhV91GogF4lfizv9PulxJ/B+d38D7HOe64UDlZR8A9ZvbL63jtav3ElhuT\nEEj2jKsBBTOrxq61K4ga4d5E1LU9yREi0VltDxZ/9ifN7LGmDUV9C+dW2ddqjMef7zgDj7v+nKzz\nOPBBSScBSNoi6Y3xv+VodNT+MeAvzewgsF9ScIt9FPhKPLNrRtIH4vOUJE2u9KHxvK+NZvYokVvw\nbcu87Hng7Ja1D0nKxfGvs4AXgMeAn4nHsyDp3HgAYjecCzzb5Tkc57jgFpWTaczsW5L+DfC/JOWA\nReATwN8TWSNvlvQNokmwH47f9jGi+NAkjY7jEInWFyT9+/g8H1rlo6eBP45jTAJ+fpnXPAH8liRZ\nozv0C0TxspOBnzazo5LuJHInPh0nauxlHaPUJf0nIgGelDQD3Glm/y7+58uAz6x1DscZBLx7ujOy\nSDpsZlN93sPvAg+b2Z9Luht4xMweTPkzLwJ+wcw+mubnOE6vcNef4/SXXwdWdCGmxInArx7nz3Sc\njnGLynEcxxlo3KJyHMdxBhoXKsdxHGegcaFyHMdxBhoXKsdxHGegcaFyHMdxBpr/D+R98eBhpz90\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cba5128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-7.90973020004\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, layer_dims, optimizer = 'adam', learning_rate = 0.00250, \n",
    "                   learning_decay = 0.00942,\n",
    "                   mini_batch_size = 128, beta = 0.9, beta1 = 0.9, beta2 = 0.999,  \n",
    "                   epsilon = 1e-8, num_epochs = 100, print_cost = True)\n",
    "\n",
    "#0.97057"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.891992\n",
      "Cost after epoch 10: 0.144779\n",
      "Cost after epoch 20: 0.083543\n",
      "Cost after epoch 30: 0.054696\n",
      "Cost after epoch 40: 0.039167\n",
      "Cost after epoch 50: 0.025854\n",
      "Cost after epoch 60: 0.018329\n",
      "Cost after epoch 70: 0.012115\n",
      "Cost after epoch 80: 0.008740\n",
      "Cost after epoch 90: 0.006350\n",
      "Cost after epoch 100: 0.003516\n",
      "Cost after epoch 110: 0.003598\n",
      "Cost after epoch 120: 0.002651\n",
      "Cost after epoch 130: 0.001902\n",
      "Cost after epoch 140: 0.001665\n",
      "Cost after epoch 150: 0.001601\n",
      "Cost after epoch 160: 0.001219\n",
      "Cost after epoch 170: 0.001108\n",
      "Cost after epoch 180: 0.001079\n",
      "Cost after epoch 190: 0.000878\n"
     ]
    },
    {
     "data": {
      "image/png": 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KdTRHKlHtBhYDFcASt9d04Ny2DU21l5NSohnQNYpJg7sANuH866qhnJKZwAPv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\ncsYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10266bb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.03303926697\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.00513,\n",
    "                   mini_batch_size = int(train_X.shape[1]/10), learning_decay = 0.005,\n",
    "                   num_epochs = 200)\n",
    "#0.96542"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.478312\n",
      "Cost after epoch 10: 0.067373\n",
      "Cost after epoch 20: 0.035165\n",
      "Cost after epoch 30: 0.014133\n",
      "Cost after epoch 40: 0.006181\n",
      "Cost after epoch 50: 0.004290\n",
      "Cost after epoch 60: 0.002054\n",
      "Cost after epoch 70: 0.001105\n",
      "Cost after epoch 80: 0.001337\n",
      "Cost after epoch 90: 0.000612\n",
      "Cost after epoch 100: 0.000509\n",
      "Cost after epoch 110: 0.000690\n",
      "Cost after epoch 120: 0.000508\n",
      "Cost after epoch 130: 0.000272\n",
      "Cost after epoch 140: 0.000257\n",
      "Cost after epoch 150: 0.000269\n",
      "Cost after epoch 160: 0.000247\n",
      "Cost after epoch 170: 0.000256\n",
      "Cost after epoch 180: 0.000267\n",
      "Cost after epoch 190: 0.000219\n"
     ]
    },
    {
     "data": {
      "image/png": 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yxmw3xnzK61Uhlt8ArxpjNvW3LhG5QUQ2iMiGysrKIX4s/zItOZJUVwg/e3EX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\nCkU4riAIgqBQ/AvBEyQ3tWTjogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1067fd0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.66037066953\n"
     ]
    }
   ],
   "source": [
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.007,\n",
    "                   mini_batch_size = 2048, learning_decay = 0.01,\n",
    "                   num_epochs = 200)\n",
    "#0.96300"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[784, 68, 37, 10]\n",
      "Cost after epoch 0: 0.486092\n",
      "Cost after epoch 10: 0.070487\n",
      "Cost after epoch 20: 0.027688\n",
      "Cost after epoch 30: 0.010519\n",
      "Cost after epoch 40: 0.002995\n",
      "Cost after epoch 50: 0.001996\n",
      "Cost after epoch 60: 0.001829\n",
      "Cost after epoch 70: 0.000761\n",
      "Cost after epoch 80: 0.001390\n",
      "Cost after epoch 90: 0.000676\n",
      "Cost after epoch 100: 0.000720\n",
      "Cost after epoch 110: 0.001072\n",
      "Cost after epoch 120: 0.000832\n",
      "Cost after epoch 130: 0.000530\n",
      "Cost after epoch 140: 0.000539\n",
      "Cost after epoch 150: 0.000572\n",
      "Cost after epoch 160: 0.000522\n",
      "Cost after epoch 170: 0.000443\n",
      "Cost after epoch 180: 0.000785\n",
      "Cost after epoch 190: 0.000629\n"
     ]
    },
    {
     "data": {
      "image/png": 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P7W8FoK5tJHOwq9+GAzUsqChKOjDZkOCd2LFXs4AK4EFnnjLN5MQlXRyJ9FGW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\nZqXghGVmZqXghGVmZqXghGVmZqXwP6YjbFRRSHDBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1064a7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.19997343033\n"
     ]
    }
   ],
   "source": [
    "layer_dims = set_layers(2, m, last_layer = 10, seed = 150)\n",
    "print(layer_dims)\n",
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.033,\n",
    "                   mini_batch_size = 2048, learning_decay = 0.033,\n",
    "                   num_epochs = 200)\n",
    "#0.95871"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[784, 74, 13, 22, 10]\n",
      "Cost after epoch 0: 0.613082\n",
      "Cost after epoch 10: 0.074964\n",
      "Cost after epoch 20: 0.037727\n",
      "Cost after epoch 30: 0.015720\n",
      "Cost after epoch 40: 0.009467\n",
      "Cost after epoch 50: 0.011934\n",
      "Cost after epoch 60: 0.009671\n",
      "Cost after epoch 70: 0.004354\n",
      "Cost after epoch 80: 0.006117\n",
      "Cost after epoch 90: 0.003878\n"
     ]
    },
    {
     "data": {
      "image/png": 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0MZRSasIQkc3GmKWBLsdIaFOhUkqpCUUDl1JKqQlFA5dSSqkJJagCl4hcIiJ3Njc3B7oo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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e01cb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.42781763417\n"
     ]
    }
   ],
   "source": [
    "layer_dims = set_layers(3, m, last_layer = 10, seed = 41)\n",
    "print(layer_dims)\n",
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.00591,\n",
    "                   mini_batch_size = 2048, learning_decay = 0.037,\n",
    "                   num_epochs = 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the mini-batch process is correct, but when the batch size is too small, the cost would shake dramatically. Also, I suppose the data size limits the accuracy, so no matter how I changed the layers, neurons of each layer, learning rate, and learning decay rate, the cost went unstable when hit 10^(-3). If data augmentation is applied and database is enlarged, we might get better accuracy. Also, validation process should be built to compare which algorithms performs better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Data Augmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_X = X_train_ori\n",
    "train_Y = Y_train_ori"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "9\n",
      "2\n",
      "9\n",
      "2\n",
      "2\n",
      "4\n",
      "1\n",
      "9\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f53a908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from keras.preprocessing.image import ImageDataGenerator # for data augmentation\n",
    "import csv\n",
    "for i in range(0, 9):\n",
    "    plt.subplot(3,3,i+1)\n",
    "    plt.imshow(train_X[i*11].reshape((28, 28)))\n",
    "    print(train_Y[i*11])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_X = train_X.reshape(train_X.shape[0], 1, 28, 28)\n",
    "train_X = train_X.astype('float32')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/KunWuYao/anaconda/lib/python3.5/site-packages/keras/preprocessing/image.py:685: UserWarning: Expected input to be images (as Numpy array) following the data format convention \"channels_last\" (channels on axis 3), i.e. expected either 1, 3 or 4 channels on axis 3. However, it was passed an array with shape (42000, 1, 28, 28) (28 channels).\n",
      "  ' (' + str(x.shape[self.channel_axis]) + ' channels).')\n"
     ]
    }
   ],
   "source": [
    "# more kinds of augmentation can be found at https://keras.io/preprocessing/image/\n",
    "datagen = ImageDataGenerator(zoom_range=0.017,\n",
    "                             width_shift_range=0.07,\n",
    "                             height_shift_range=0.07,\n",
    "                             rotation_range=13)\n",
    "datagen.fit(train_X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filename = \"data/new_image_data.csv\"\n",
    "new_data = [] #store new images\n",
    "new_label = [] #store the lable of new images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#output new images into CSV\n",
    "def write_to_csv(original_data, label, filename):\n",
    "    for i in range(0, len(original_data)):\n",
    "        pre_process = original_data[i].reshape((28*28,1))\n",
    "        single_pic = []\n",
    "        single_pic.append(label[i])\n",
    "        for j in range(0,len(pre_process)):\n",
    "            temp_pix = pre_process[j][0]\n",
    "            single_pic.append(temp_pix)\n",
    "        with open(filename,\"a\") as f:\n",
    "            f_csv = csv.writer(f, delimiter=',',quotechar='|', quoting=csv.QUOTE_MINIMAL)\n",
    "            f_csv.writerow(single_pic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/KunWuYao/anaconda/lib/python3.5/site-packages/keras/preprocessing/image.py:857: UserWarning: NumpyArrayIterator is set to use the data format convention \"channels_last\" (channels on axis 3), i.e. expected either 1, 3 or 4 channels on axis 3. However, it was passed an array with shape (42000, 1, 28, 28) (28 channels).\n",
      "  ' (' + str(self.x.shape[channels_axis]) + ' channels).')\n"
     ]
    }
   ],
   "source": [
    "number_of_batches = 2000\n",
    "batches = 0\n",
    "\n",
    "for X_batch, Y_batch in datagen.flow(train_X, train_Y.T, batch_size=10):\n",
    "    new_data.append(X_batch)\n",
    "    new_label.append(Y_batch) \n",
    "#         loss = model.train(X_batch, Y_batch)\n",
    "    batches += 1\n",
    "    if batches >= number_of_batches:\n",
    "        # we need to break the loop by hand because\n",
    "        # the generator loops indefinitely\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "9\n",
      "9\n",
      "4\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ab8a898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#show the new images\n",
    "for i in range(0, 4):\n",
    "    plt.subplot(2,2,i+1)\n",
    "    plt.imshow(new_data[333][i].reshape((28, 28)))\n",
    "    print(new_label[333][i])\n",
    "    # show the plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2000, 10)"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(new_data), len(new_data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#write new images into CSV\n",
    "for i in range(0,len(new_data)):\n",
    "    write_to_csv(new_data[i], new_label[i], filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.7 Implement NN with data augmentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    <tr>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>15 rows × 785 columns</p>\n",
       "</div>"
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       "\n",
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       "\n",
       "[15 rows x 785 columns]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_train = pd.read_csv('data/new_image_data.csv', index_col = False)\n",
    "new_train.head(15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 785 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  \\\n",
       "0      0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "1      4     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "2      0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "3      8     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "4      3     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   \n",
       "\n",
       "   pixel8    ...     pixel774  pixel775  pixel776  pixel777  pixel778  \\\n",
       "0     0.0    ...          0.0       0.0       0.0       0.0       0.0   \n",
       "1     0.0    ...          0.0       0.0       0.0       0.0       0.0   \n",
       "2     0.0    ...          0.0       0.0       0.0       0.0       0.0   \n",
       "3     0.0    ...          0.0       0.0       0.0       0.0       0.0   \n",
       "4     0.0    ...          0.0       0.0       0.0       0.0       0.0   \n",
       "\n",
       "   pixel779  pixel780  pixel781  pixel782  pixel783  \n",
       "0       0.0       0.0       0.0       0.0       0.0  \n",
       "1       0.0       0.0       0.0       0.0       0.0  \n",
       "2       0.0       0.0       0.0       0.0       0.0  \n",
       "3       0.0       0.0       0.0       0.0       0.0  \n",
       "4       0.0       0.0       0.0       0.0       0.0  \n",
       "\n",
       "[5 rows x 785 columns]"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_train.columns = train.columns\n",
    "new_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#reset training and test datasets\n",
    "del(X_train_ori)\n",
    "del(Y_train_ori)\n",
    "del(X_norm)\n",
    "del(test_norm)\n",
    "del(Y_norm)\n",
    "del(new_data)\n",
    "del(new_label)\n",
    "del(train_X)\n",
    "del(train_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "#Merge 2 diff training sets and implement normalization\n",
    "#Then rerun NN\n",
    "\n",
    "training = train.append(new_train, ignore_index = True)\n",
    "print(np.sum(np.sum(training.isnull(), axis = 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#remove train and new_train to release space\n",
    "del(train)\n",
    "del(new_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>label</th>\n",
       "      <th>pixel0</th>\n",
       "      <th>pixel1</th>\n",
       "      <th>pixel2</th>\n",
       "      <th>pixel3</th>\n",
       "      <th>pixel4</th>\n",
       "      <th>pixel5</th>\n",
       "      <th>pixel6</th>\n",
       "      <th>pixel7</th>\n",
       "      <th>pixel8</th>\n",
       "      <th>...</th>\n",
       "      <th>pixel774</th>\n",
       "      <th>pixel775</th>\n",
       "      <th>pixel776</th>\n",
       "      <th>pixel777</th>\n",
       "      <th>pixel778</th>\n",
       "      <th>pixel779</th>\n",
       "      <th>pixel780</th>\n",
       "      <th>pixel781</th>\n",
       "      <th>pixel782</th>\n",
       "      <th>pixel783</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.0</td>\n",
       "      <td>61999.0</td>\n",
       "      <td>61999.0</td>\n",
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       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.000000</td>\n",
       "      <td>61999.0</td>\n",
       "      <td>61999.0</td>\n",
       "      <td>61999.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>4.459346</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.003548</td>\n",
       "      <td>0.018355</td>\n",
       "      <td>0.021984</td>\n",
       "      <td>...</td>\n",
       "      <td>0.569251</td>\n",
       "      <td>0.341199</td>\n",
       "      <td>0.202568</td>\n",
       "      <td>0.084195</td>\n",
       "      <td>0.043920</td>\n",
       "      <td>0.015274</td>\n",
       "      <td>0.000048</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.887448</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.505226</td>\n",
       "      <td>1.918234</td>\n",
       "      <td>2.160333</td>\n",
       "      <td>...</td>\n",
       "      <td>10.585790</td>\n",
       "      <td>8.112557</td>\n",
       "      <td>6.344911</td>\n",
       "      <td>3.905284</td>\n",
       "      <td>2.749805</td>\n",
       "      <td>1.541707</td>\n",
       "      <td>0.012048</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>9.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>85.000000</td>\n",
       "      <td>254.000000</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>255.000000</td>\n",
       "      <td>254.000000</td>\n",
       "      <td>254.000000</td>\n",
       "      <td>252.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 785 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              label   pixel0   pixel1   pixel2   pixel3   pixel4   pixel5  \\\n",
       "count  61999.000000  61999.0  61999.0  61999.0  61999.0  61999.0  61999.0   \n",
       "mean       4.459346      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "std        2.887448      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "min        0.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "25%        2.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "50%        4.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "75%        7.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "max        9.000000      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "\n",
       "             pixel6        pixel7        pixel8    ...         pixel774  \\\n",
       "count  61999.000000  61999.000000  61999.000000    ...     61999.000000   \n",
       "mean       0.003548      0.018355      0.021984    ...         0.569251   \n",
       "std        0.505226      1.918234      2.160333    ...        10.585790   \n",
       "min        0.000000      0.000000      0.000000    ...         0.000000   \n",
       "25%        0.000000      0.000000      0.000000    ...         0.000000   \n",
       "50%        0.000000      0.000000      0.000000    ...         0.000000   \n",
       "75%        0.000000      0.000000      0.000000    ...         0.000000   \n",
       "max       85.000000    254.000000    255.000000    ...       255.000000   \n",
       "\n",
       "           pixel775      pixel776      pixel777      pixel778      pixel779  \\\n",
       "count  61999.000000  61999.000000  61999.000000  61999.000000  61999.000000   \n",
       "mean       0.341199      0.202568      0.084195      0.043920      0.015274   \n",
       "std        8.112557      6.344911      3.905284      2.749805      1.541707   \n",
       "min        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
       "25%        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
       "50%        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
       "75%        0.000000      0.000000      0.000000      0.000000      0.000000   \n",
       "max      255.000000    255.000000    254.000000    254.000000    252.000000   \n",
       "\n",
       "           pixel780  pixel781  pixel782  pixel783  \n",
       "count  61999.000000   61999.0   61999.0   61999.0  \n",
       "mean       0.000048       0.0       0.0       0.0  \n",
       "std        0.012048       0.0       0.0       0.0  \n",
       "min        0.000000       0.0       0.0       0.0  \n",
       "25%        0.000000       0.0       0.0       0.0  \n",
       "50%        0.000000       0.0       0.0       0.0  \n",
       "75%        0.000000       0.0       0.0       0.0  \n",
       "max        3.000000       0.0       0.0       0.0  \n",
       "\n",
       "[8 rows x 785 columns]"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 4, 7, 3, 5, 8, 9, 2, 6])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training['label'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((61999, 784), (61999,))"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_ori = training.iloc[:, 1:].values\n",
    "Y_train_ori = training.iloc[:, 0].values\n",
    "X_test_ori = test.values\n",
    "X_train_ori.shape, Y_train_ori.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_norm = feature_norm(X_test_ori)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_X = feature_norm(X_train_ori)\n",
    "train_Y = convert_to_one_hot(Y_train_ori, 10)\n",
    "layer_dims = [784, 90, 33, 10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.265565\n",
      "Cost after epoch 10: 0.018500\n",
      "Cost after epoch 20: 0.003013\n",
      "Cost after epoch 30: 0.000852\n",
      "Cost after epoch 40: 0.000884\n",
      "Cost after epoch 50: 0.000490\n",
      "Cost after epoch 60: 0.000357\n",
      "Cost after epoch 70: 0.000262\n",
      "Cost after epoch 80: 0.000341\n",
      "Cost after epoch 90: 0.000183\n"
     ]
    },
    {
     "data": {
      "image/png": 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VWCWFOqx25PNdpnX7fdnH6Rf291WD1avzy277fC1WtZp7++ZZdr7q3PLW1g7zOF2fndvu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\nIiKi0f4Bk4535cqIUQUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f53ab70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.64255157913\n"
     ]
    }
   ],
   "source": [
    "#try whole batch first\n",
    "parameters = model(train_X, train_Y, layer_dims, optimizer = \"adam\", learning_rate = 0.00531,\n",
    "                   mini_batch_size = 1024, learning_decay = 0.0361,\n",
    "                   num_epochs = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ac2bd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "plt.imshow(np.multiply(train_X.T[57839], 255).reshape(28,28))\n",
    "plt.show()\n",
    "print(np.argmax(train_Y.T[57839]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.8 Introduce Cross-Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((61999, 784), (61999,))"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_ori.shape, Y_train_ori.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "def validation_split(train_X, train_Y, seed = np.random.randint(0, 100)):\n",
    "    train_f, validation_f, train_l, validation_l = train_test_split(train_X, train_Y, \n",
    "                                                                    test_size = 6000,\n",
    "                                                                    random_state = seed)\n",
    "    return train_f, validation_f, train_l, validation_l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((55999, 784), (55999,), (6000, 784), (6000,))"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_X, validation_X, train_Y, validation_Y = validation_split(X_train_ori, Y_train_ori, \n",
    "                                                                seed = np.random.randint(0, 100))\n",
    "train_X.shape, train_Y.shape, validation_X.shape, validation_Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Normalization\n",
    "train_X = feature_norm(train_X)\n",
    "validation_X = feature_norm(validation_X)\n",
    "train_Y = convert_to_one_hot(train_Y, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#compute validation accuracy!\n",
    "def validation_accuracy(validation_X, parameters, validation_Y):\n",
    "    '''\n",
    "    Whenever an iteration is over, check the validation accuracy and see if it is improving.\n",
    "    Arguments:\n",
    "    validation_X -- validation input data\n",
    "    parameters -- forward propagation parameters updated from each iteration\n",
    "    validation_Y -- validation label data\n",
    "    \n",
    "    Returns:\n",
    "    Error_rate -- validation set accuracy\n",
    "    '''\n",
    "    Y_hat, _ = forward_propagation(validation_X, parameters)\n",
    "    prediction = np.argmax(Y_hat.T, axis = 1)\n",
    "    accuracy = np.equal(prediction, validation_Y).sum() / 6000.\n",
    "    error_rate = 1-accuracy\n",
    "    return error_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_validation(X, Y, layers_dims, optimizer = 'adam', learning_rate = 0.005, mini_batch_size = 2048, \n",
    "                     beta = 0.9, learning_decay = 0.001, beta1 = 0.9, beta2 = 0.999,  \n",
    "                     epsilon = 1e-8, num_epochs = 50, seed = 10, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- original data (number of examples, number of pixels)\n",
    "    Y -- number from 0 to 9 (number of examples, 1)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    #seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    error_rates = []                 # to keep track of validation error rates\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        #train validation split\n",
    "        train_X, validation_X, train_Y, validation_Y = validation_split(X, Y, \n",
    "                                                                seed = np.random.randint(0, 100))\n",
    "        #normalization\n",
    "        train_X = feature_norm(train_X)\n",
    "        validation_X = feature_norm(validation_X)\n",
    "        train_Y = convert_to_one_hot(train_Y, 10)\n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 3\n",
    "        minibatches = random_mini_batches(train_X, train_Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            aL, cache = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(aL, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, cache)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        #compute validation error rate\n",
    "        error_rate = validation_accuracy(validation_X, parameters, validation_Y)\n",
    "        \n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 10 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "            print ('Validation error after epoch %i: %f' %(i, error_rate))\n",
    "        if print_cost and i % 1 == 0:\n",
    "            costs.append(cost)\n",
    "            error_rates.append(error_rate)\n",
    "        if np.log10(cost) <= -9 : break\n",
    "        learning_rate = learning_rate / (1+learning_decay)\n",
    "        \n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.plot(error_rates)\n",
    "    plt.ylabel('cost')\n",
    "    plt.yscale('log')\n",
    "    plt.xlabel('epochs (per 1)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate) + ', ' + 'mini_batch_size = ' + str(mini_batch_size))\n",
    "    plt.legend()\n",
    "    plt.show()\n",
    "    print(cost, error_rate)\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.721377\n",
      "Validation error after epoch 0: 0.195500\n",
      "Cost after epoch 10: 0.119697\n",
      "Validation error after epoch 10: 0.036667\n",
      "Cost after epoch 20: 0.064105\n",
      "Validation error after epoch 20: 0.017667\n",
      "Cost after epoch 30: 0.036628\n",
      "Validation error after epoch 30: 0.009333\n",
      "Cost after epoch 40: 0.022311\n",
      "Validation error after epoch 40: 0.004667\n",
      "Cost after epoch 50: 0.014411\n",
      "Validation error after epoch 50: 0.002000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/KunWuYao/anaconda/lib/python3.5/site-packages/matplotlib/axes/_axes.py:545: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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Qu2Hor6FOPbcjqxGOFhYzb+M+Pl+1h6/W7CH7aJHP6epEhPHSxH6c2aF23y+n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11494b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00699247859208 0.000333333333333\n"
     ]
    }
   ],
   "source": [
    "layer_dims = [784, 90, 33, 10]\n",
    "parameters = model_validation(X_train_ori, Y_train_ori, layer_dims, optimizer = 'adam', \n",
    "                 learning_rate = 0.005, mini_batch_size = 55999//10 + 1, \n",
    "                 beta = 0.9, learning_decay = 0.01, beta1 = 0.9, beta2 = 0.999,  \n",
    "                 epsilon = 1e-8, num_epochs = 60, seed = 10, print_cost = True)\n",
    "#0.97100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.276065\n",
      "Validation error after epoch 0: 0.113000\n",
      "Cost after epoch 10: 0.052260\n",
      "Validation error after epoch 10: 0.016000\n",
      "Cost after epoch 20: 0.030112\n",
      "Validation error after epoch 20: 0.002833\n",
      "Cost after epoch 30: 0.003999\n",
      "Validation error after epoch 30: 0.000167\n",
      "Cost after epoch 40: 0.001901\n",
      "Validation error after epoch 40: 0.000000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/KunWuYao/anaconda/lib/python3.5/site-packages/matplotlib/axes/_axes.py:545: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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PlTt3k3Utq0+rhszbfJDcgiKPla2U8h5NWjVRi3Phstdh5y/w5Z1QXOx0RI4a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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ab713c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000769176552177 0.0\n"
     ]
    }
   ],
   "source": [
    "layer_dims = [784, 97, 37, 10]\n",
    "parameters = model_validation(X_train_ori, Y_train_ori, layer_dims, optimizer = 'adam', \n",
    "                 learning_rate = 0.005, mini_batch_size = 2048, \n",
    "                 beta = 0.9, learning_decay = 0.01, beta1 = 0.9, beta2 = 0.999,  \n",
    "                 epsilon = 1e-8, num_epochs = 50, seed = 10, print_cost = True)\n",
    "#0.97500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.281975\n",
      "Validation error after epoch 0: 0.088500\n",
      "Cost after epoch 10: 0.028476\n",
      "Validation error after epoch 10: 0.009833\n",
      "Cost after epoch 20: 0.009898\n",
      "Validation error after epoch 20: 0.002000\n",
      "Cost after epoch 30: 0.001108\n",
      "Validation error after epoch 30: 0.000000\n",
      "Cost after epoch 40: 0.000662\n",
      "Validation error after epoch 40: 0.000000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/KunWuYao/anaconda/lib/python3.5/site-packages/matplotlib/axes/_axes.py:545: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
      "  warnings.warn(\"No labelled objects found. \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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ux+hhmSTHRnFVp1QKi0v4bun2MxS9UiqQaRtXoFvxLXwxDM66Bq56z6pSrEJm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ae0c518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000562359802016 0.0\n"
     ]
    }
   ],
   "source": [
    "layer_dims = [784, 103, 41, 10]\n",
    "parameters = model_validation(X_train_ori, Y_train_ori, layer_dims, optimizer = 'adam', \n",
    "                 learning_rate = 0.0043, mini_batch_size = 1024, \n",
    "                 beta = 0.9, learning_decay = 0.007, beta1 = 0.95, beta2 = 0.999,  \n",
    "                 epsilon = 1e-8, num_epochs = 43, seed = 10, print_cost = True)\n",
    "#0.97514"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.493499\n",
      "Validation error after epoch 0: 0.142667\n",
      "Cost after epoch 10: 0.046184\n",
      "Validation error after epoch 10: 0.013500\n",
      "Cost after epoch 20: 0.031161\n",
      "Validation error after epoch 20: 0.003667\n",
      "Cost after epoch 30: 0.001215\n",
      "Validation error after epoch 30: 0.000000\n",
      "Cost after epoch 40: 0.000503\n",
      "Validation error after epoch 40: 0.000000\n",
      "Cost after epoch 50: 0.000173\n",
      "Validation error after epoch 50: 0.000000\n"
     ]
    },
    {
     "data": {
      "image/png": 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0xQoWbi6k+GiZV+LL2VRIUkwYZ2clsrbgACVlvr2UQCnlW9pUWN91vMgarLHp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\n3FxsPAC2nwF+S7puNyoXnYayjrfpwPskbQd+Sho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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ae28438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000219661454005 0.0\n"
     ]
    }
   ],
   "source": [
    "layer_dims = [784, 103, 41, 19, 10]\n",
    "parameters = model_validation(X_train_ori, Y_train_ori, layer_dims, optimizer = 'adam', \n",
    "                 learning_rate = 0.00331, mini_batch_size = 1024, \n",
    "                 beta = 0.9, learning_decay = 0.00597, beta1 = 0.95, beta2 = 0.999,  \n",
    "                 epsilon = 1e-8, num_epochs = 60, seed = 10, print_cost = True)\n",
    "#0.97585"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mistake on Applying Cross-Validation\n",
    "Here I did something wrong: I should not redo data split in each iteration.\n",
    "From the last three tries we can observe that the validation error kept droping, and hit 0 after around 30 iterations and kept in 0. I think the main reason is that since I did reshuffle in each iteration, the data of validation set were also put into training and tuning, so the tuned parameters would adapt the validation set through iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Make Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 28000)"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_hat, _ = forward_propagation(test_norm, parameters)\n",
    "Y_hat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prediction = np.argmax(Y_hat.T, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#print it out!\n",
    "output = pd.DataFrame(prediction, columns = ['Label']).reset_index()\n",
    "output.rename(columns = {'index': 'ImageId'}, inplace = True)\n",
    "output.iloc[:, 0] += 1\n",
    "output.to_csv('DL_augment.csv', index = False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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