shallow_neural_net.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Shallow Neural Network\n",
    "\n",
    "Creating a shallow neural network from memory as a learning exercise.\n",
    "\n",
    "The network will be 1 hidden layer with 4 neurons, and the output layer will be a single neuron."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "## import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_circles, make_moons, make_classification\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "m = 600\n",
    "# data = make_circles(n_samples=m, factor=.5, noise=.03)\n",
    "data = make_moons(n_samples=m, noise=.2)\n",
    "# data = make_classification(n_features=2, n_redundant=0, n_informative=2,\n",
    "#                            n_clusters_per_class=2, n_samples=m)\n",
    "\n",
    "X, y = data[0].T, data[1].reshape(1, -1)\n",
    "\n",
    "idx = np.arange(X.shape[1])\n",
    "np.random.shuffle(idx)\n",
    "\n",
    "X_train = X[:, idx[0:400]]\n",
    "X_test = X[:, idx[400:]]\n",
    "y_train = y[:, idx[0:400]]\n",
    "y_test = y[:, idx[400:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 4 neurons in hidden layer\n",
    "n_h = 4\n",
    "\n",
    "def sigmoid(X):\n",
    "    z = 1 / (1 + np.exp(-X))\n",
    "    return z\n",
    "\n",
    "def initialise_weights(X, y, n_h):\n",
    "    n_x = X.shape[0]\n",
    "    n_y = y.shape[0]\n",
    "    # make this small so that sigmoid has an actual slope at the output\n",
    "    W1 = np.random.randn(n_h, n_x) * .01\n",
    "    b1 = np.zeros([n_h, 1])\n",
    "    W2 = np.random.randn(n_y, n_h) * .01\n",
    "    b2 = np.zeros([n_y, 1])\n",
    "    \n",
    "    init_params = dict()\n",
    "    init_params['W1'] = W1\n",
    "    init_params['b1'] = b1\n",
    "    init_params['W2'] = W2\n",
    "    init_params['b2'] = b2    \n",
    "    \n",
    "    return init_params\n",
    "\n",
    "def forward_prop(X, params):\n",
    "    m = X.shape[1]\n",
    "    \n",
    "    W1 = params['W1']\n",
    "    b1 = params['b1']\n",
    "    W2 = params['W2']\n",
    "    b2 = params['b2']\n",
    "\n",
    "    Z1 = np.dot(W1, X) + b1\n",
    "    A1 = np.tanh(Z1)\n",
    "    Z2 = np.dot(W2, A1) + b2\n",
    "    A2 = sigmoid(Z2)\n",
    "    \n",
    "    preds = dict()\n",
    "    preds['Z1'] = Z1\n",
    "    preds['A1'] = A1\n",
    "    preds['Z2'] = Z2\n",
    "    preds['A2'] = A2\n",
    "    \n",
    "    return preds\n",
    "    \n",
    "def compute_cost(A2, y):\n",
    "    m = y.shape[1]\n",
    "    J = - np.sum(\n",
    "        np.multiply(y, np.log(A2)) + np.multiply(1 - y, np.log(1 - A2))) / m\n",
    "    return J\n",
    "\n",
    "def backward_prop(X, y, params, preds):\n",
    "    m = X.shape[1]\n",
    "\n",
    "    Z1 = preds['Z1']\n",
    "    A1 = preds['A1']\n",
    "    Z2 = preds['Z2']\n",
    "    A2 = preds['A2']\n",
    "    \n",
    "    W2 = params['W2']\n",
    "    \n",
    "    # dL/dZ2 = A - y and g'(Z1) = 1 - np.power(A1, 2)\n",
    "    dZ2 = A2 - y\n",
    "    dW2 = np.dot(dZ2, A1.T) / m\n",
    "    db2 = np.sum(dZ2, axis=1, keepdims=True) / m\n",
    "    dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))\n",
    "    dW1 = np.dot(dZ1, X.T) / m\n",
    "    db1 = np.sum(dZ1, axis=1, keepdims=True) / m\n",
    "    \n",
    "    grads = dict()\n",
    "    grads['dW2'] = dW2\n",
    "    grads['db2'] = db2\n",
    "    grads['dW1'] = dW1\n",
    "    grads['db1'] = db1\n",
    "    \n",
    "    return grads\n",
    "    \n",
    "def update(grads, params, alpha):\n",
    "    dW2 = grads['dW2']\n",
    "    db2 = grads['db2']\n",
    "    dW1 = grads['dW1']\n",
    "    db1 = grads['db1']\n",
    "    \n",
    "    W1 = params['W1']\n",
    "    b1 = params['b1']\n",
    "    W2 = params['W2']\n",
    "    b2 = params['b2']\n",
    "    \n",
    "    W1 = W1 - (alpha * dW1)\n",
    "    W2 = W2 - (alpha * dW2)\n",
    "    b1 = b1 - (alpha * b1)\n",
    "    b2 = b2 - (alpha * b2)\n",
    "    \n",
    "    params['W1'] = W1\n",
    "    params['W2'] = W2\n",
    "    params['b1'] = b1\n",
    "    params['b2'] = b2\n",
    "    \n",
    "    return params\n",
    "    \n",
    "def fit(X, y, n_h, num_iterations, alpha):\n",
    "    params = initialise_weights(X, y, n_h)\n",
    "    for i in range(num_iterations):\n",
    "        preds = forward_prop(X, params)\n",
    "        J = compute_cost(preds['A2'], y)\n",
    "        if i % 1000 == 0:\n",
    "            print(f'cost after iter {i}: {J}')\n",
    "        grads = backward_prop(X, y, params, preds)\n",
    "        params = update(grads, params, alpha)\n",
    "    return params, preds\n",
    "\n",
    "def predict(X, params):\n",
    "    preds = forward_prop(X, params)\n",
    "    y_pred = preds['A2']\n",
    "    y_pred[y_pred > 0.5] = 1\n",
    "    y_pred[y_pred <= 0.5] = 0\n",
    "    return y_pred\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit, Predict, Score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cost after iter 0: 0.6932163379597316\n",
      "cost after iter 1000: 0.3203272712246846\n",
      "cost after iter 2000: 0.32203576191988303\n",
      "cost after iter 3000: 0.322010823057061\n",
      "cost after iter 4000: 0.3219953392079351\n",
      "cost after iter 5000: 0.32198563252270546\n",
      "cost after iter 6000: 0.32197951429350735\n",
      "cost after iter 7000: 0.3219756443675277\n",
      "cost after iter 8000: 0.321973190945891\n",
      "cost after iter 9000: 0.32197163320355926\n",
      "accuracy:  0.88\n"
     ]
    }
   ],
   "source": [
    "params, preds = fit(X_train, y_train, n_h, 10000, 1.2)\n",
    "y_pred = predict(X_test, params)\n",
    "\n",
    "print('accuracy: ',accuracy_score(y_test[0], y_pred[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualise Performance\n",
    "\n",
    "Plotting a visualisation here showing the test points against what the model calculates for different regions on the graph.\n",
    "\n",
    "Note the regions here use `forward_prop`, so the regions take on values between 0 and 1 rather than being in the set (0, 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x235f10d9148>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set min and max values for meshgrid\n",
    "x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1\n",
    "y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1\n",
    "\n",
    "# Generate a grid of points with distance h between them\n",
    "h = 0.01\n",
    "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
    "# Predict the function value for the whole grid using previous params\n",
    "X_mesh = np.c_[xx.ravel(), yy.ravel()].T\n",
    "Z = forward_prop(X_mesh, params)['A2']\n",
    "Z = Z.reshape(xx.shape)\n",
    "\n",
    "# Plot the contour and training examples\n",
    "plt.contourf(xx, yy, Z, cmap=plt.cm.coolwarm)\n",
    "plt.ylabel('x2')\n",
    "plt.xlabel('x1')\n",
    "plt.scatter(X_test[0, :], X_test[1, :], c=np.squeeze(y_test), cmap=plt.cm.coolwarm)"
   ]
  }
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