{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Networks\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Activation functions\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the common activation functions:\n",
    "\n",
    "def logistic(x):\n",
    "    return 1/(1 + np.exp(-x))\n",
    "\n",
    "def tanh(x):\n",
    "    return np.tanh(x)\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(x, 0)\n",
    "\n",
    "# and their derivatives:\n",
    "\n",
    "def tanh_deriv(x):\n",
    "    return 1.0 - np.tanh(x)**2\n",
    "\n",
    "def logistic_deriv(x):\n",
    "    return logistic(x)*(1-logistic(x))\n",
    "\n",
    "def relu_deriv(x) :\n",
    "    deriv = x.copy()\n",
    "    deriv[deriv < 0] = 0\n",
    "    return deriv\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 900x400 with 0 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x106a0be48>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x106a0bda0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a61128>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a61588>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a619e8>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112a71278>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Activation functions')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[-5, 5, -1.2, 1.2]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x106a34b00>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a714e0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a9c400>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112a9c860>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x112aa0198>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Derivatives')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[-5, 5, -0.2, 1.2]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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63ntr5yUKC4P77zfbL73k3jiOgn9SUycwEeVE8C4eUE6yP8lm1593UbCu+gyD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\nrkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-5, 5, 200)\n",
    "plt.figure(figsize=(9,4))\n",
    "plt.subplot(121)\n",
    "plt.plot(x, np.sign(x), \"r-\", linewidth=2, label=\"sign\")\n",
    "plt.plot(x, logistic(x), \"g--\", linewidth=2, label=\"logistic\");\n",
    "plt.plot(x, np.tanh(x), \"b-\", linewidth=2, label=\"tanh\");\n",
    "plt.plot(x, relu(x), \"m-.\", linewidth=2, label=\"ReLU\");\n",
    "plt.grid(True);\n",
    "plt.legend(fontsize=12);\n",
    "plt.title(\"Activation functions\", fontsize=14);\n",
    "plt.axis([-5, 5, -1.2, 1.2]);\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(x, logistic_deriv(x), \"g--\", linewidth=2, label=\"logistic\")\n",
    "plt.plot(x, tanh_deriv(x), \"b-\", linewidth=2, label=\"tanh\")\n",
    "plt.plot(x, relu_deriv(x), \"m-.\", linewidth=2, label=\"ReLU\")\n",
    "plt.grid(True)\n",
    "plt.legend(fontsize=14)\n",
    "plt.title(\"Derivatives\", fontsize=14)\n",
    "plt.axis([-5, 5, -0.2, 1.2])\n",
    "plt.savefig('activation_functions.png')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "## The XOR learning problem\n",
    "\n",
    "The XOR problem is an example of data that is not linearly separable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x112c8a390>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PRDwUEd+JiMu70We7tJrvmLobIiIjYkbfXVFlvhFxY+M53h0RX57uHtupwuv5sojYGhG7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\nyHCXpAIZ7pJUoP8DB5Pp1pzNGvgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.array( [[0,0], [0,1], [1,0], [1,1]])\n",
    "y = np.array([0,1,1,0])\n",
    "colors = np.array(['#377eb8', '#ff7f00'])\n",
    "plt.scatter(X[:, 0], X[:, 1], color=colors[y])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's demonstrate that this problem can be solved with a very simple neural network:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mlp_xor(x1, x2, activation=tanh):\n",
    "    return activation(-activation(x1 + x2 - 1.5) + activation(x1 + x2 - 0.5) - 0.5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x112debf98>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1047bddd8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'XOR network with tanh activation')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ni332yKrYZ9nK6XKxr8VmYF7Z6yOBp2NcOxjaPqPA94BXNFKY3Ah9iU7z7fOE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\n",
      "text/plain": [
       "<Figure size 600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1_values = np.linspace(-0.2, 1.2, 100)\n",
    "x2_values = np.linspace(-0.2, 1.2, 100)\n",
    "x1, x2 = np.meshgrid(x1_values, x2_values)\n",
    "\n",
    "z = mlp_xor(x1, x2, activation=tanh)\n",
    "\n",
    "plot=plt.contourf(x1, x2, z, 20, cmap=plt.cm.bone)\n",
    "plt.colorbar(plot)\n",
    "\n",
    "plt.scatter(X[:, 0], X[:, 1], color=colors[y])\n",
    "plt.title(\"XOR network with tanh activation\", fontsize=12)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also solve this problem with the ReLu activation fuction:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x112e41e48>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PRDwUEd+JiMu70We7tJrvmLobIiIjYkbfXVFlvhFxY+M53h0RX57uHtupwuv5sojYGhG7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\nyHCXpAIZ7pJUoP8DB5Pp1pzNGvgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "def relu(x):\n",
    "    return np.maximum(x, 0)\n",
    "\n",
    "w1 = np.ones((2,2))\n",
    "b1 = np.array([0, -1])\n",
    "w2 = np.array([1, -2])\n",
    "b2 = 0\n",
    "\n",
    "y_pred = relu(X.dot(w1) + b1).dot(w2) + b2\n",
    "\n",
    "# plot the output generated by the network:\n",
    "y_pred = np.array(y_pred, dtype='int')\n",
    "plt.scatter(X[:, 0], X[:, 1], color=colors[y_pred])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the representation that was used to classify the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x112afc7f0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nktQgw12SGmS4S1KDDHdJapDhLkkN+v/VWXcoiaDChgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = relu(X.dot(w1) + b1)\n",
    "plt.scatter(h[:, 0], h[:, 1], color=colors[y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "class NeuralNetwork :\n",
    "    def __init__(self, architecture, activation='logistic') :\n",
    "        self.architecture = architecture\n",
    "        if activation == 'logistic':\n",
    "            self.activation = logistic\n",
    "            self.activation_deriv = logistic_deriv\n",
    "        elif activation == 'tanh':\n",
    "            self.activation = tanh\n",
    "            self.activation_deriv = tanh_deriv\n",
    "        else :\n",
    "            raise ValueError('Activation does not match options')\n",
    "        self.initialize_weights()\n",
    "        \n",
    "    def initialize_weights(self) :\n",
    "        W = {}\n",
    "        b = {}\n",
    "        for l in range(1, len(self.architecture)):\n",
    "            W[l] = np.random.random((self.architecture[l], self.architecture[l-1]))\n",
    "            b[l] = np.random.random((self.architecture[l],))\n",
    "            #W[l] = np.random.randn(self.architecture[l], self.architecture[l-1])\n",
    "            #b[l] = np.random.randn(self.architecture[l])\n",
    "        self.W, self.b = W, b\n",
    "\n",
    "    def forward(self, x):\n",
    "        h = {1: x}\n",
    "        s = {}\n",
    "        for l in range(1, len(self.W) + 1):\n",
    "            s[l+1] = self.W[l].dot(h[l]) + self.b[l]\n",
    "            h[l+1] = self.activation(s[l+1])\n",
    "        return h, s\n",
    "        \n",
    "    def init_delta_values(self):\n",
    "        delta_W = {}\n",
    "        delta_b = {}\n",
    "        for l in range(1, len(self.architecture)):\n",
    "            delta_W[l] = np.zeros((self.architecture[l], self.architecture[l-1]))\n",
    "            delta_b[l] = np.zeros((self.architecture[l],))\n",
    "        return delta_W, delta_b\n",
    "\n",
    "    def calculate_output_layer_delta(self, y, h_out, s_out):\n",
    "        return -(y-h_out) * self.activation_deriv(s_out)\n",
    "\n",
    "    def calculate_hidden_delta(self, delta_plus_1, w_l, s_l):\n",
    "        # delta^(l) = (transpose(W^(l)) * delta^(l+1)) * f'(s^(l))\n",
    "        return np.dot(np.transpose(w_l), delta_plus_1) * self.activation_deriv(s_l)\n",
    "\n",
    "    def fit(self, X, y, num_iterations=3000, alpha=0.25):\n",
    "        iterations = 0\n",
    "        N = len(y)\n",
    "        avg_cost_func = []\n",
    "        print('Starting gradient descent for {} iterations'.format(num_iterations))\n",
    "        while iterations < num_iterations :\n",
    "            if iterations%100 == 0:\n",
    "                print('Iteration {} of {}'.format(iterations, num_iterations))\n",
    "                if len(avg_cost_func) > 0 :\n",
    "                    print('cost: ', avg_cost_func[-1])\n",
    "            delta_W, delta_b = self.init_delta_values()\n",
    "            avg_cost = 0\n",
    "            for i in range(len(y)):\n",
    "                delta = {}\n",
    "                # perform the feed forward pass and return the stored h and z values, to be used in the\n",
    "                # gradient descent step\n",
    "                h, s = self.forward(X[i, :])\n",
    "                # backpropagate the errors\n",
    "                for l in range(len(self.architecture), 0, -1):\n",
    "                    if l == len(self.architecture):\n",
    "                        delta[l] = self.calculate_output_layer_delta(y[i,:], h[l], s[l])\n",
    "                        avg_cost += (np.linalg.norm((y[i,:]-h[l])) / N)\n",
    "                    else:\n",
    "                        if l > 1:\n",
    "                            delta[l] = self.calculate_hidden_delta(delta[l+1], self.W[l], s[l])\n",
    "                        delta_W[l] += np.dot(delta[l+1][:,np.newaxis], np.transpose(h[l][:,np.newaxis]))\n",
    "                        delta_b[l] += delta[l+1]\n",
    "            # perform the gradient descent step for the weights in each layer\n",
    "            for l in range(len(self.architecture) - 1, 0, -1):\n",
    "                self.W[l] += -alpha * (1.0/N * delta_W[l])\n",
    "                self.b[l] += -alpha * (1.0/N * delta_b[l])\n",
    "            # complete the average cost calculation\n",
    "            avg_cost_func.append(avg_cost)\n",
    "            iterations += 1\n",
    "        return avg_cost_func\n",
    "\n",
    "    def predict(self, X):\n",
    "        N = X.shape[0]\n",
    "        y = np.zeros((N,))\n",
    "        for i in range(N):\n",
    "            h, _ = self.forward(X[i, :])\n",
    "            y[i] = np.argmax(h[len(self.architecture)])\n",
    "        return y\n",
    "\n",
    "    def decision_function(self, X):\n",
    "        N = X.shape[0]\n",
    "        scores = np.zeros((N,self.architecture[-1]))\n",
    "        for i in range(N):\n",
    "            h, _ = self.forward(X[i, :])\n",
    "            scores[i]=h[len(self.architecture)]\n",
    "        return scores\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 2)\n",
      "(10, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.83997171,  0.80862343],\n",
       "       [ 0.77539435,  0.77146198],\n",
       "       [ 0.7585131 ,  0.76352457],\n",
       "       [ 0.77129192,  0.77047476],\n",
       "       [ 0.73082053,  0.72970056],\n",
       "       [ 0.79830232,  0.78025445],\n",
       "       [ 0.80332407,  0.78607616],\n",
       "       [ 0.86150465,  0.82762999],\n",
       "       [ 0.80025889,  0.78521383],\n",
       "       [ 0.78597356,  0.75506333]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "architecture = [2, 3, 2]\n",
    "network = NeuralNetwork(architecture)\n",
    "X = np.random.randn(10, 2)\n",
    "network.decision_function(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's apply the network to a digit recognition problem.  But before we do so, let's see how well we can do with an SVM..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python3.5/site-packages/sklearn/utils/fixes.py:313: FutureWarning: numpy not_equal will not check object identity in the future. The comparison did not return the same result as suggested by the identity (`is`)) and will change.\n",
      "  _nan_object_mask = _nan_object_array != _nan_object_array\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a15a9ba58>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAP4AAAECCAYAAADesWqHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIYIPJPRfwIPOarFTewYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "//anaconda/lib/python3.5/site-packages/sklearn/model_selection/_search.py:841: DeprecationWarning: The default of the `iid` parameter will change from True to False in version 0.22 and will be removed in 0.24. This will change numeric results when test-set sizes are unequal.\n",
      "  DeprecationWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.95331503132520745"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import cross_validate\n",
    "from sklearn import svm\n",
    "from sklearn import metrics\n",
    "\n",
    "digits = load_digits()\n",
    "\n",
    "plt.matshow(digits.images[0], cmap=plt.cm.gray_r)\n",
    "plt.show()\n",
    "\n",
    "digits = load_digits()\n",
    "X_scale = StandardScaler()\n",
    "#X = X_scale.fit_transform(digits.data)\n",
    "X = digits.data / digits.data.max()\n",
    "y = digits.target\n",
    "\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "C_list = np.logspace(-2, 2, 10)\n",
    "classifier = GridSearchCV(svm.SVC(kernel='linear'), dict(C=C_list), cv=5)\n",
    "cv_results_nested = cross_validate(classifier, X, y, cv=5, scoring='accuracy')\n",
    "np.mean(cv_results_nested['test_score'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_digits\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "def y_to_vect(y):\n",
    "    y_vect = np.zeros((len(y), 10))\n",
    "    for i in range(len(y)):\n",
    "        y_vect[i, y[i]] = 1\n",
    "    return y_vect\n",
    "\n",
    "digits = load_digits()\n",
    "X_scale = StandardScaler()\n",
    "X = X_scale.fit_transform(digits.data)\n",
    "#X = digits.data / digits.data.max()\n",
    "y = digits.target\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.4)\n",
    "# convert labels to vectors\n",
    "y_vec_train = y_to_vect(y_train)\n",
    "y_vec_test = y_to_vect(y_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Starting gradient descent for 4000 iterations\n",
      "Iteration 0 of 4000\n",
      "Iteration 100 of 4000\n",
      "cost:  2.57537345395\n",
      "Iteration 200 of 4000\n",
      "cost:  2.18130487651\n",
      "Iteration 300 of 4000\n",
      "cost:  1.39322466988\n",
      "Iteration 400 of 4000\n",
      "cost:  0.91675175766\n",
      "Iteration 500 of 4000\n",
      "cost:  0.896294919991\n",
      "Iteration 600 of 4000\n",
      "cost:  0.875248649357\n",
      "Iteration 700 of 4000\n",
      "cost:  0.853556450919\n",
      "Iteration 800 of 4000\n",
      "cost:  0.831206649849\n",
      "Iteration 900 of 4000\n",
      "cost:  0.808409560832\n",
      "Iteration 1000 of 4000\n",
      "cost:  0.785314116242\n",
      "Iteration 1100 of 4000\n",
      "cost:  0.762069879728\n",
      "Iteration 1200 of 4000\n",
      "cost:  0.738954628916\n",
      "Iteration 1300 of 4000\n",
      "cost:  0.716239757337\n",
      "Iteration 1400 of 4000\n",
      "cost:  0.694048380588\n",
      "Iteration 1500 of 4000\n",
      "cost:  0.672417383751\n",
      "Iteration 1600 of 4000\n",
      "cost:  0.651396671924\n",
      "Iteration 1700 of 4000\n",
      "cost:  0.631071663657\n",
      "Iteration 1800 of 4000\n",
      "cost:  0.611523173857\n",
      "Iteration 1900 of 4000\n",
      "cost:  0.592791512152\n",
      "Iteration 2000 of 4000\n",
      "cost:  0.574934823047\n",
      "Iteration 2100 of 4000\n",
      "cost:  0.558021500537\n",
      "Iteration 2200 of 4000\n",
      "cost:  0.542031571625\n",
      "Iteration 2300 of 4000\n",
      "cost:  0.526913371074\n",
      "Iteration 2400 of 4000\n",
      "cost:  0.5126048701\n",
      "Iteration 2500 of 4000\n",
      "cost:  0.499040260894\n",
      "Iteration 2600 of 4000\n",
      "cost:  0.486159406177\n",
      "Iteration 2700 of 4000\n",
      "cost:  0.473912157258\n",
      "Iteration 2800 of 4000\n",
      "cost:  0.462255630165\n",
      "Iteration 2900 of 4000\n",
      "cost:  0.451149453357\n",
      "Iteration 3000 of 4000\n",
      "cost:  0.440555103145\n",
      "Iteration 3100 of 4000\n",
      "cost:  0.430439017608\n",
      "Iteration 3200 of 4000\n",
      "cost:  0.420773232112\n",
      "Iteration 3300 of 4000\n",
      "cost:  0.411530756284\n",
      "Iteration 3400 of 4000\n",
      "cost:  0.4026794059\n",
      "Iteration 3500 of 4000\n",
      "cost:  0.394186489876\n",
      "Iteration 3600 of 4000\n",
      "cost:  0.386041608596\n",
      "Iteration 3700 of 4000\n",
      "cost:  0.378280784085\n",
      "Iteration 3800 of 4000\n",
      "cost:  0.37088390664\n",
      "Iteration 3900 of 4000\n",
      "cost:  0.363820171413\n",
      "Prediction accuracy is 88.73435326842836%\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1a15a71630>]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Average loss')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'Iteration number')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k32Nm0FhRzMKaUlprS1lUUxosT32tLdVAiVkimSGxETjHzJYSXL30OuANkRuY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\nTkSuQmCC\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# the NN architecture\n",
    "architecture = [64, 30, 10]\n",
    "# train the NN\n",
    "network = NeuralNetwork(architecture, 'logistic')\n",
    "cost_func = network.fit(X_train, y_vec_train, 4000)\n",
    "y_pred = network.predict(X_test)\n",
    "print('Prediction accuracy is {}%'.format(accuracy_score(y_test, y_pred) * 100))\n",
    "\n",
    "# plot the avg_cost_func\n",
    "plt.plot(cost_func)\n",
    "plt.ylabel('Average loss')\n",
    "plt.xlabel('Iteration number')\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}