15. Parametrised Neural Network Implementation with Matrices (Algorithm).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = 'retina'\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "np.set_printoptions(precision=3)\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Neural Network implementation with Matrices #5: Parametrised Algorhytm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will implement an algorithm that can train a neural network of a flexible size in terms of the number of layers and neurons therein."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this first example, the data and the labels will remain the same as in the previous examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = np.array([[ 1.2, 0.7],\n",
    "                 [-0.3,-0.5],\n",
    "                 [ 3.0, 0.1],\n",
    "                 [-0.1,-1.0],\n",
    "                 [-0.0, 1.1],\n",
    "                 [ 2.1,-1.3],\n",
    "                 [ 3.1,-1.8],\n",
    "                 [ 1.1,-0.1],\n",
    "                 [ 1.5,-2.2],\n",
    "                 [ 4.0,-1.0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = np.array([  1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                     1,\n",
    "                    -1,\n",
    "                    -1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transformation of the data in the matrix format"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From now on, we will expect our data to be already transformed in the proper style, so we will do it right from the beginning, and update the plotting functions to accomodate for this,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 1.2],\n",
       "        [ 0.7]],\n",
       "\n",
       "       [[-0.3],\n",
       "        [-0.5]],\n",
       "\n",
       "       [[ 3. ],\n",
       "        [ 0.1]],\n",
       "\n",
       "       [[-0.1],\n",
       "        [-1. ]],\n",
       "\n",
       "       [[-0. ],\n",
       "        [ 1.1]],\n",
       "\n",
       "       [[ 2.1],\n",
       "        [-1.3]],\n",
       "\n",
       "       [[ 3.1],\n",
       "        [-1.8]],\n",
       "\n",
       "       [[ 1.1],\n",
       "        [-0.1]],\n",
       "\n",
       "       [[ 1.5],\n",
       "        [-2.2]],\n",
       "\n",
       "       [[ 4. ],\n",
       "        [-1. ]]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.array([d.reshape(1,2).T for d in data])\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0],\n",
       "        [1]],\n",
       "\n",
       "       [[1],\n",
       "        [0]],\n",
       "\n",
       "       [[0],\n",
       "        [1]],\n",
       "\n",
       "       [[1],\n",
       "        [0]],\n",
       "\n",
       "       [[1],\n",
       "        [0]],\n",
       "\n",
       "       [[0],\n",
       "        [1]],\n",
       "\n",
       "       [[1],\n",
       "        [0]],\n",
       "\n",
       "       [[0],\n",
       "        [1]],\n",
       "\n",
       "       [[1],\n",
       "        [0]],\n",
       "\n",
       "       [[1],\n",
       "        [0]]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels = np.array([np.array([1,0]).reshape(1,2).T if l==-1 \n",
    "          else np.array([0,1]).reshape(1,2).T if l==1 \n",
    "          else None \n",
    "          for l in labels])\n",
    "labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "code_folding": [
     0,
     11
    ]
   },
   "outputs": [],
   "source": [
    "def plot_data(data, labels):\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    labels = [np.argmax(l) for l in labels]\n",
    "    ax.scatter(data[:,0].T[0], data[:,1].T[0], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    nudge = 0.08\n",
    "    for i, (X,Y) in enumerate(data):\n",
    "        ax.annotate(f'{i}',(X+nudge,Y+nudge))\n",
    "    ax.set_aspect('equal', 'datalim')\n",
    "    plt.show()\n",
    "\n",
    "def create_meshgrid(data):\n",
    "    h = 0.02\n",
    "    x_min, x_max = data[:, 0].min() - 1, data[:, 0].max() + 1\n",
    "    y_min, y_max = data[:, 1].min() - 1, data[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "    return (xx,yy,np.ones(xx.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 304,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(data, labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The flexible neural network algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "code_folding": [
     0,
     9,
     41
    ]
   },
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1.0/(1.0+np.exp(-z))\n",
    "\n",
    "def plot_neural_simple(grid, weights, biases, data, labels, iteration, accuracy):\n",
    "    nudge = 0.06\n",
    "    xx,yy,Z = grid\n",
    "    \n",
    "    for i in range(xx.shape[0]): # row\n",
    "        for j in range(yy.shape[1]): #column\n",
    "                a = np.array([xx[i][j], yy[i][j]]).reshape(1,2).T # current activation\n",
    "                # calculate all the weighted sums and activations\n",
    "                for b, w in zip(biases, weights):\n",
    "                    w_sum = np.dot(w, a)+b #current weighted sum\n",
    "                    a = sigmoid(w_sum) # current activation is updated and then the loop goes to the next layer\n",
    "                    score = 0\n",
    "                    if (np.argmax(a)==0):\n",
    "                        score =  -1\n",
    "                    else:\n",
    "                        score =  1\n",
    "                    Z[i][j] = score\n",
    "    \n",
    "    labels = [np.argmax(l) for l in labels]\n",
    "    fig = plt.figure(figsize=(5,5))\n",
    "    ax = fig.add_subplot(111)\n",
    "    plt.title(f'accuracy at the iteration {iteration}: {accuracy}')\n",
    "    ax.contourf(xx, yy, Z, cmap=plt.cm.binary, alpha=0.1, zorder=15)\n",
    "    ax.scatter(data[:, 0].T[0], data[:, 1].T[0], c=labels, s=50,  cmap=plt.cm.bwr,zorder=50)\n",
    "    ax.set_aspect('equal')\n",
    "    for i in range(data.shape[0]):\n",
    "        d = data[i]\n",
    "        ax.annotate(f'{i}',(d[0]+nudge,d[1]+nudge))\n",
    "    plt.xlim(xx.min(), xx.max())\n",
    "    plt.ylim(yy.min(), yy.max())\n",
    "    plt.show()\n",
    "    \n",
    "def eval_accuracy_neural(weights, biases, data, labels):\n",
    "    num_correct = 0;\n",
    "    for dpoint, label in zip(data, labels):\n",
    "        a = dpoint\n",
    "        for b, w in zip(biases, weights):\n",
    "            w_sum = np.dot(w, a)+b #current weighted sum\n",
    "            a = sigmoid(w_sum) # current activation is updated and then the loop goes to the next layer\n",
    "        sc = np.array((int(a[0]>0.5),int(a[1]>0.5)))\n",
    "        if (sc[0]==label[0] and sc[1]==label[1]):\n",
    "            num_correct += 1\n",
    "    return round(num_correct / len(data), 4)\n",
    "\n",
    "def backprop(x, y, weights, biases, num_layers):\n",
    "    # storing derivatives for the current data point\n",
    "    d_biases =  [np.zeros(b.shape) for b in biases]\n",
    "    d_weights = [np.zeros(w.shape) for w in weights]\n",
    "    \n",
    "    a = x # current activation\n",
    "    activations = [x] # here we store all the activations, layer by layer\n",
    "    weighted_sums = [] # here we store all the weighted sums, layer by layer\n",
    "    \n",
    "    # calculate all the weighted sums and activations\n",
    "    for b, w in zip(biases, weights):\n",
    "        w_sum = np.dot(w, a)+b #current weighted sum\n",
    "        weighted_sums.append(w_sum) \n",
    "        a = sigmoid(w_sum) # current activation is updated and then the loop goes to the next layer\n",
    "        activations.append(a)\n",
    "    \n",
    "    # computing the cost for a single example\n",
    "    cost = 0.5*sum((y - a)**2)[0]\n",
    "        \n",
    "    #backward pass\n",
    "    # output layer\n",
    "    d_w_sum = (activations[-1] - y) * (activations[-1] * (1 - activations[-1]))\n",
    "    d_biases[-1] = d_w_sum\n",
    "    d_weights[-1] = np.dot(d_w_sum, activations[-2].T)\n",
    "        \n",
    "    # other layers\n",
    "    for i in range(2, num_layers):\n",
    "        act = activations[-i]\n",
    "        d_w_sum = np.dot(weights[-i+1].T, d_w_sum) * (act * (1 - act))\n",
    "        d_biases[-i] = d_w_sum\n",
    "        d_weights[-i] = np.dot(d_w_sum, activations[-i-1].T)\n",
    "    return (d_biases, d_weights, cost)\n",
    "\n",
    "\n",
    "def train_neural_network(sizes, data, labels, step_size, no_epochs, iter_info):\n",
    "    \n",
    "    grid = create_meshgrid(data) # used for visualisation\n",
    "    num_layers = len(sizes)  # number of layers\n",
    "    data_len = len(data) # number of data points\n",
    "    \n",
    "    # initialising random weights and biases \n",
    "    biases  = [np.random.randn(y, 1) for y in sizes[1:]]\n",
    "    weights = [np.random.randn(x, y) for x, y in zip(sizes[1:], sizes[:-1])]\n",
    "    \n",
    "    for epoch in range(no_epochs):\n",
    "        total_cost = 0 # total cost for all training examples\n",
    "        # in avg_d_biases/weights we store the averaged partial derivatives\n",
    "        avg_d_biases =  [np.zeros(b.shape) for b in biases]\n",
    "        avg_d_weights = [np.zeros(w.shape) for w in weights]\n",
    "\n",
    "        for x, y in zip(data, labels):\n",
    "            d_biases, d_weights, cost = backprop(x, y, weights, biases, num_layers)\n",
    "            # averaging the derivatives of weights and biases\n",
    "            avg_d_biases  = [nb+dnb for nb, dnb in zip(avg_d_biases, d_biases)]\n",
    "            avg_d_weights = [nw+dnw for nw, dnw in zip(avg_d_weights, d_weights)]\n",
    "            total_cost += cost\n",
    "            \n",
    "        # updating the weights and biases\n",
    "        weights = [w - (step_size/data_len * dw) \n",
    "               for w, dw in zip(weights, avg_d_weights)]\n",
    "        biases =  [b - (step_size/data_len * db)\n",
    "              for b, db in zip(biases, avg_d_biases)]\n",
    "        \n",
    "        if (epoch%iter_info==0):\n",
    "            accuracy = eval_accuracy_neural(weights, biases, data, labels)\n",
    "            plot_neural_simple(grid, weights, biases, data, labels, epoch, accuracy)\n",
    "            print (f'total cost: {round(total_cost,4)}')\n",
    "    return (weights, biases)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 2.7253\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.8337\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.3916\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.228\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 281,
       "width": 316
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total cost: 0.1168\n"
     ]
    }
   ],
   "source": [
    "weights, biases = train_neural_network([2,3,2], data, labels, step_size=6, no_epochs=401, iter_info=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}