{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Simple Neural Network\n",
    "A simple 3 layer classifier in python - with no bias or regularization.\n",
    "Created on a [vnode](https://github.com/thomaswilley/vnode) :)\n",
    "\n",
    "@thomaswilley"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c020d780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.datasets import load_digits\n",
    "%matplotlib inline\n",
    "\n",
    "src_X, src_y = load_digits(return_X_y=True)\n",
    "m, dim_input = src_X.shape\n",
    "dim_hidden = 100\n",
    "dim_output = 10\n",
    "m_train = 1000\n",
    "\n",
    "X_train = src_X[0:m_train, :] / 255\n",
    "X_test = src_X[m_train+1::, :]/ 255\n",
    "\n",
    "y = np.zeros((m, 10))\n",
    "y[np.arange(m), src_y]=1\n",
    "y_train = y[0:m_train, :]\n",
    "y_test = y[m_train+1::, :]\n",
    "\n",
    "img_dim = int(np.sqrt(src_X.shape[1]))\n",
    "images_and_labels = list(zip(src_X.reshape(m, img_dim, img_dim), src_y))\n",
    "for index, (image, label) in enumerate(images_and_labels[:10]):\n",
    "    plt.subplot(1, 10, index + 1)\n",
    "    plt.axis('off')\n",
    "    plt.imshow(image, cmap=plt.cm.gray_r)\n",
    "    plt.title('{}'.format(label))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "def nonlin_sigmoid(x, deriv=False):\n",
    "    if deriv:\n",
    "        return x * (1. - x)\n",
    "    return 1. / (1 + np.exp(-x))\n",
    "\n",
    "def nonlin_relu(x, deriv=False):\n",
    "    if deriv:\n",
    "        return 1. * (x > 0)\n",
    "    return np.maximum(x, 0)\n",
    "\n",
    "def forward(model, x):\n",
    "    z1 = np.dot(model['w1'].T, x)\n",
    "    a1 = model['nonlin'](z1)\n",
    "    z2 = np.dot(model['w2'].T, a1)\n",
    "    a2 = model['nonlin'](z2)\n",
    "    return (z1, a1, z2, a2)\n",
    "\n",
    "def backward(model, x, z1, a1, z2, a2, y):\n",
    "    loss = a2 - y\n",
    "    grad_w2 = np.dot(a1, loss.T)\n",
    "    grad_a1 = np.dot(model['w2'], loss) * model['nonlin'](a1, deriv=True)\n",
    "    grad_w1 = np.dot(x, grad_a1.T)\n",
    "    return (loss, grad_w1, grad_w2)\n",
    "\n",
    "def predict(model, x):\n",
    "    return np.argmax(forward(model, x)[3])\n",
    "\n",
    "def accuracy(model, X, y):\n",
    "    correct = []\n",
    "    m = X.shape[0]\n",
    "    for i in range(m):\n",
    "        y_hat = predict(model, X[i,:].reshape(-1, 1))\n",
    "        _y = np.argmax(y[i,:].reshape(-1, 1))\n",
    "        correct.append(y_hat == _y)\n",
    "    return np.sum(1.*np.array(correct)) / m\n",
    "\n",
    "def create_model(dim_input, dim_hidden, dim_output, nonlin=nonlin_sigmoid, epochs=30, learning_rate=0.9):    \n",
    "    model = {}\n",
    "    model['dims'] = (dim_input, dim_hidden, dim_output)\n",
    "    model['nonlin'] = nonlin # which non linearity fn we use for the activations of hidden & output\n",
    "    model['w1'] = np.random.random((dim_input, dim_hidden))\n",
    "    model['w2'] = np.random.random((dim_hidden, dim_output))\n",
    "    model['epochs'] = epochs\n",
    "    model['learning_rate'] = learning_rate\n",
    "    return model\n",
    "\n",
    "def train_model(model):\n",
    "    all_examples_err = []\n",
    "    for e in range(model['epochs']):\n",
    "        single_example_err = []\n",
    "        for i in range(m_train):\n",
    "            _x = X_train[i,:].reshape(-1, 1)\n",
    "            _y = y_train[i,:].reshape(-1, 1)\n",
    "\n",
    "            z1, a1, z2, a2 = forward(model, _x)\n",
    "            loss, grad_w1, grad_w2 = backward(model, _x, z1, a1, z2, a2, _y)\n",
    "\n",
    "            model['w2'] -= model['learning_rate'] * grad_w2\n",
    "            model['w1'] -= model['learning_rate'] * grad_w1\n",
    "\n",
    "            single_example_err.append(np.square(loss).sum())\n",
    "\n",
    "        all_examples_err.append(np.sum(single_example_err) / m_train)\n",
    "    model['error'] = all_examples_err\n",
    "    return model\n",
    "\n",
    "def plot_model_error(model, label=\"Model\"):\n",
    "    f, ax = plt.subplots()\n",
    "    ax.plot(model['error'])\n",
    "    ax.set_title(\"Model-{} Train accuracy: {:.02f}%\\nTest accuracy: {:.02f}%\".format(\n",
    "        label,\n",
    "        accuracy(model, X_train, y_train),\n",
    "        accuracy(model, X_test, y_test)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kBBsy3N29C7gZeIQQ2A+4+1ozu8nMboqWWQf8N/As8CRwl7s/P3xlx+esqeMY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\nm38vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c019a860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SLo1bD/yKtDP4WZ43o7j9PG0aaUewjnR0fXp+H88vzP9Q/lzWk+o/Liysf3Le5nMb3ts3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\nOLjNzErGwW1mVjIObjOzkvlPvgiP/qsSSggAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c019aa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model1 = create_model(dim_input, dim_hidden, dim_output, nonlin=nonlin_sigmoid, epochs=10, learning_rate=0.9)\n",
    "model1 = train_model(model1)\n",
    "plot_model_error(model1, \"Sigmoid\")\n",
    "\n",
    "model2 = create_model(dim_input, dim_hidden, dim_output, nonlin=nonlin_relu, epochs=10, learning_rate=0.05)\n",
    "model2 = train_model(model2)\n",
    "plot_model_error(model2, \"ReLU\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model 1 predicts 7\n",
      "model 2 predicts 7\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPgAAAD8CAYAAABaQGkdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f618fea9a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# \"create\" an arbitrary digit and predict its label\n",
    "example = np.array([[  0.,   0.,   2.,  1.,   1.,   1.,   0.,   0.],\n",
    "           [  0.,   24.,  22.,  22.,  22.,  15.,   20.,   0.],\n",
    "           [  0.,   0.,  0.,   0.,   0.,  0.,   22.,   0.],\n",
    "           [  0.,   0.,  0.,   0.,   0.,  22.,   0.,   0.],\n",
    "           [  0.,   0.,   0.,   0.,   22.,   0.,   0.,   0.],\n",
    "           [  0.,   0.,  0.,   20.,   0.,  0.,   0.,   0.],\n",
    "           [  0.,   0.,  0.,   20.,  1.,  0.,   0.,   0.],\n",
    "           [  0.,   0.,   20.,  0.,  0.,   0.,   0.,   0.]])\n",
    "f, ax = plt.subplots(figsize=(4,4))\n",
    "ax.imshow(example, cmap=plt.cm.gray_r)\n",
    "print(\"model 1 predicts {}\\nmodel 2 predicts {}\".format(\n",
    "    predict(model1, example.reshape(-1, 1)),\n",
    "    predict(model2, example.reshape(-1, 1))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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    "editable": true
   },
   "outputs": [],
   "source": []
  }
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