002-keras.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multilayer networks with Keras \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will use a few functions from [`scikit-learn`](http://scikit-learn.org) to generate data sets:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_blobs, make_circles, make_moons\n",
    "from conv_net_utils import generate_dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll also set up some configuration variables up-front:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The first example is a linearly separable data-set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data, test_data, train_labels, test_labels = generate_dataset(make_blobs, \n",
    "                                                                    n_train=1000, \n",
    "                                                                    n_test=200, \n",
    "                                                                    num_labels=2,\n",
    "                                                                    centers=2, \n",
    "                                                                    center_box=[-4., 4.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data.shape, train_labels.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_labels[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(train_data[:, 0], train_data[:, 1], c=np.where(train_labels)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(32, input_shape=(train_data.shape[-1],), activation='relu'))\n",
    "model.add(Dense(2, activation='softmax'))\n",
    "\n",
    "model.compile(loss='categorical_crossentropy',\n",
    "              optimizer='rmsprop',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An aside about the softmax function \n",
    "\n",
    "The softmax function defined mathemtatically as: \n",
    "\n",
    "$f(y_i) = \\frac{e^{y_i}}{\\sum_i{e^{y_i}}}$\n",
    "\n",
    "assigns each of the possible outputs a probability (a number between 0-1, all sum together to 1). \n",
    "\n",
    "It also has the effect of 'mutual inhibition' between alternative options. \n",
    "\n",
    "Consider our case, with two options:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(x):\n",
    "    return np.exp(x) / np.sum(np.exp(x), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "output = []\n",
    "xs = np.arange(1, 11, 1)\n",
    "for ii in xs:\n",
    "    x = [10-ii, ii]\n",
    "    output.append(softmax(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit(train_data, train_labels, epochs=5, batch_size=100, validation_split=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_and_metrics = model.evaluate(test_data, test_labels, batch_size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for name, metric in zip(model.metrics_names, loss_and_metrics):\n",
    "    print(name, \":\", metric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = np.round(model.predict(test_data)).astype(int).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], c=np.where(prediction)[1])\n",
    "ax.set_aspect('equal')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The next set of data is not linearly separable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data, test_data, train_labels, test_labels = generate_dataset(make_moons, \n",
    "                                                                    n_train=1000, \n",
    "                                                                    n_test=200,\n",
    "                                                                    num_labels=2, \n",
    "                                                                    noise=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(train_data[:, 0], train_data[:, 1], c=np.where(train_labels)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit(train_data, train_labels, nb_epoch=5, batch_size=100, validation_split=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_and_metrics = model.evaluate(test_data, test_labels, batch_size=100)\n",
    "print()\n",
    "for name, metric in zip(model.metrics_names, loss_and_metrics):\n",
    "    print(name, \":\", metric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = np.round(model.predict(test_data)).astype(int).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], c=np.where(prediction)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data, test_data, train_labels, test_labels = generate_dataset(make_circles, \n",
    "                                                                    n_train=1000,\n",
    "                                                                    n_test=200, \n",
    "                                                                    noise=0.2, \n",
    "                                                                    num_labels=2,\n",
    "                                                                    factor=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(train_data[:, 0], train_data[:, 1], c=np.where(train_labels)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit(train_data, train_labels, nb_epoch=5, batch_size=100, validation_split=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss_and_metrics = model.evaluate(test_data, test_labels, batch_size=100)\n",
    "print()\n",
    "for name, metric in zip(model.metrics_names, loss_and_metrics):\n",
    "    print(name, \":\", metric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = np.round(model.predict(test_data)).astype(int).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], c=np.where(prediction)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Sequential()\n",
    "model.add(Dense(32, input_shape=(train_data.shape[-1],), activation='relu'))\n",
    "model.add(Dense(32, activation='relu'))\n",
    "model.add(Dense(2, activation='softmax'))\n",
    "\n",
    "model.compile(loss='categorical_crossentropy',\n",
    "              optimizer='rmsprop',\n",
    "              metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.fit(train_data, train_labels, epochs=5, batch_size=100, validation_split=0.2)\n",
    "print()\n",
    "loss_and_metrics = model.evaluate(test_data, test_labels, batch_size=100)\n",
    "print()\n",
    "for name, metric in zip(model.metrics_names, loss_and_metrics):\n",
    "    print(name, \":\", metric)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = np.round(model.predict(test_data)).astype(int).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(test_data[:, 0], test_data[:, 1], c=np.where(prediction)[1])\n",
    "ax.set_aspect('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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