Binary Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary classification with neural networks\n",
    "\n",
    "Neural networks are adept at fitting non-linear datasets. To demonstrate, we'll fit a binary classifier to a two-class dataset generated with Scikit's [make_circles](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_circles.html) function. Start by creating the dataset and plotting it. In the plot, purple corresponds to class 0 (the negative class) and red corresponds to class 1 (the positive class)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import make_circles\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "x, y = make_circles(100, factor=0.4, noise=0.15, random_state=1)\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.axes().set_aspect('equal')\n",
    "plt.scatter(x[:, 0], x[:, 1], c=y, s=300, cmap=plt.cm.get_cmap('rainbow', 2), alpha=0.5)\n",
    "plt.colorbar(ticks=range(2))\n",
    "plt.clim(-0.5, 1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a simple neural network (a multilayer perceptron) with a single hidden layer. Since this network is intended to perform binary classification, include an output layer that contains one neuron and uses the [sigmoid](https://keras.io/api/layers/activations/#sigmoid-function) activation function, and specify [binary_crossentropy](https://keras.io/api/losses/probabilistic_losses/#binary_crossentropy-function) as the loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: \"sequential\"\n",
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 128)               384       \n",
      "_________________________________________________________________\n",
      "dense_1 (Dense)              (None, 1)                 129       \n",
      "=================================================================\n",
      "Total params: 513\n",
      "Trainable params: 513\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers import Dense\n",
    " \n",
    "model = Sequential()\n",
    "model.add(Dense(128, activation='relu', input_dim=2))\n",
    "model.add(Dense(1, activation='sigmoid'))\n",
    "model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train the network. Use a small batch size since there are only 100 samples in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/40\n",
      "8/8 [==============================] - 7s 39ms/step - loss: 0.6836 - accuracy: 0.5172 - val_loss: 0.6617 - val_accuracy: 0.6500\n",
      "Epoch 2/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6800 - accuracy: 0.4408 - val_loss: 0.6558 - val_accuracy: 0.6500\n",
      "Epoch 3/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6645 - accuracy: 0.5378 - val_loss: 0.6481 - val_accuracy: 0.7000\n",
      "Epoch 4/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6629 - accuracy: 0.5166 - val_loss: 0.6420 - val_accuracy: 0.7000\n",
      "Epoch 5/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6675 - accuracy: 0.5281 - val_loss: 0.6368 - val_accuracy: 0.7000\n",
      "Epoch 6/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6545 - accuracy: 0.5892 - val_loss: 0.6293 - val_accuracy: 0.7000\n",
      "Epoch 7/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6582 - accuracy: 0.5648 - val_loss: 0.6249 - val_accuracy: 0.7000\n",
      "Epoch 8/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6460 - accuracy: 0.6156 - val_loss: 0.6182 - val_accuracy: 0.7000\n",
      "Epoch 9/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6382 - accuracy: 0.6522 - val_loss: 0.6126 - val_accuracy: 0.7000\n",
      "Epoch 10/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6353 - accuracy: 0.6184 - val_loss: 0.6051 - val_accuracy: 0.7000\n",
      "Epoch 11/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6294 - accuracy: 0.6446 - val_loss: 0.6003 - val_accuracy: 0.7500\n",
      "Epoch 12/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6201 - accuracy: 0.7218 - val_loss: 0.5956 - val_accuracy: 0.7500\n",
      "Epoch 13/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6251 - accuracy: 0.6744 - val_loss: 0.5900 - val_accuracy: 0.8000\n",
      "Epoch 14/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6236 - accuracy: 0.7241 - val_loss: 0.5849 - val_accuracy: 0.8500\n",
      "Epoch 15/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.6107 - accuracy: 0.7183 - val_loss: 0.5809 - val_accuracy: 0.9000\n",
      "Epoch 16/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5998 - accuracy: 0.7419 - val_loss: 0.5734 - val_accuracy: 0.9000\n",
      "Epoch 17/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5806 - accuracy: 0.8035 - val_loss: 0.5671 - val_accuracy: 0.9000\n",
      "Epoch 18/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5683 - accuracy: 0.8380 - val_loss: 0.5611 - val_accuracy: 0.9000\n",
      "Epoch 19/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5848 - accuracy: 0.7853 - val_loss: 0.5564 - val_accuracy: 0.9500\n",
      "Epoch 20/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5537 - accuracy: 0.8739 - val_loss: 0.5511 - val_accuracy: 0.9500\n",
      "Epoch 21/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5684 - accuracy: 0.8803 - val_loss: 0.5458 - val_accuracy: 0.9500\n",
      "Epoch 22/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5748 - accuracy: 0.8840 - val_loss: 0.5375 - val_accuracy: 0.9500\n",
      "Epoch 23/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5604 - accuracy: 0.9202 - val_loss: 0.5358 - val_accuracy: 0.9500\n",
      "Epoch 24/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5436 - accuracy: 0.9213 - val_loss: 0.5264 - val_accuracy: 0.9500\n",
      "Epoch 25/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5389 - accuracy: 0.9297 - val_loss: 0.5221 - val_accuracy: 0.9500\n",
      "Epoch 26/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5209 - accuracy: 0.9184 - val_loss: 0.5187 - val_accuracy: 0.9500\n",
      "Epoch 27/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5259 - accuracy: 0.9193 - val_loss: 0.5145 - val_accuracy: 1.0000\n",
      "Epoch 28/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5099 - accuracy: 0.9189 - val_loss: 0.5043 - val_accuracy: 0.9500\n",
      "Epoch 29/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5032 - accuracy: 0.9515 - val_loss: 0.4994 - val_accuracy: 1.0000\n",
      "Epoch 30/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4858 - accuracy: 0.9770 - val_loss: 0.4904 - val_accuracy: 1.0000\n",
      "Epoch 31/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.5026 - accuracy: 0.9026 - val_loss: 0.4823 - val_accuracy: 1.0000\n",
      "Epoch 32/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4699 - accuracy: 0.9489 - val_loss: 0.4719 - val_accuracy: 1.0000\n",
      "Epoch 33/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4539 - accuracy: 0.9696 - val_loss: 0.4640 - val_accuracy: 1.0000\n",
      "Epoch 34/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4625 - accuracy: 0.9820 - val_loss: 0.4553 - val_accuracy: 1.0000\n",
      "Epoch 35/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4645 - accuracy: 0.9501 - val_loss: 0.4530 - val_accuracy: 1.0000\n",
      "Epoch 36/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4453 - accuracy: 0.9388 - val_loss: 0.4431 - val_accuracy: 1.0000\n",
      "Epoch 37/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4247 - accuracy: 0.9733 - val_loss: 0.4360 - val_accuracy: 1.0000\n",
      "Epoch 38/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4250 - accuracy: 0.9752 - val_loss: 0.4244 - val_accuracy: 1.0000\n",
      "Epoch 39/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4415 - accuracy: 0.9473 - val_loss: 0.4158 - val_accuracy: 1.0000\n",
      "Epoch 40/40\n",
      "8/8 [==============================] - 0s 2ms/step - loss: 0.4209 - accuracy: 0.9803 - val_loss: 0.4058 - val_accuracy: 1.0000\n"
     ]
    }
   ],
   "source": [
    "hist = model.fit(x, y, validation_split=0.2, epochs=40, batch_size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the training and validation accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 4,
     "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": [
    "err = hist.history['accuracy']\n",
    "val_err = hist.history['val_accuracy']\n",
    "epochs = range(1, len(err) + 1)\n",
    " \n",
    "plt.plot(epochs, err, '-', label='Training Accuracy')\n",
    "plt.plot(epochs, val_err, ':', label='Validation Accuracy')\n",
    "plt.title('Training and Validation Accuracy')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Accuracy')\n",
    "plt.legend(loc='lower right')\n",
    "plt.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict the probability that a point that lies at (-0.5, 0.0) belongs to the positive class (red)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5906321"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(np.array([[-0.5, 0.0]]))[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict which class a point that lies at (-0.5, 0.0) belongs to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(model.predict(np.array([[-0.5, 0.0]])) > 0.5).astype('int32')[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict the probability that a point that lies at (0.6, 0.6) belongs to the positive class (red)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4519902"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(np.array([[0.6, 0.6]]))[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict which class a point that lies at (0.6, 0.6) belongs to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(model.predict(np.array([[0.6, 0.6]])) > 0.5).astype('int32')[0][0]"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}