dropout.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dropout"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will see the effect of dropout. To do so, we will quickly build a model for image classification using the dataset provided by the Kaggle competition '[Dogs vs. Cats]'().\n",
    "\n",
    "Since the purpose of this example is to see how to use dropout and what happens when we use it, we will not detail the implementation. Nonetheless, we can mention that we will build our model on top of a pretrained convolutional network. This sounds high profile, but using Keras it's quite simple. Also, we created a sub-sample of the data with 200 training pictures and 100 validation pictures (50 dogs pictures + 50 cats pictures). The model doesn't train so well with such a small dataset, but the computational cost is highly reduced.\n",
    "\n",
    "Our approach will be as follows:\n",
    "1. Instantiate convolutional base.\n",
    "1. Extract features using the convolutional base.\n",
    "1. Use the features to train a dense connected classifier (without dropout).\n",
    "1. Train a new dense connected classifier (with dropout).\n",
    "\n",
    "Learning curves will be plotted for both models. Comparing the learning curves it will be possible to evaluate dropout effect on overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Instantiate convolutional base"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Instantiate convolutional base\n",
    "from keras.applications import VGG16\n",
    "\n",
    "img_width, img_height = 150, 150\n",
    "\n",
    "conv_base = VGG16(weights='imagenet', \n",
    "                  include_top=False,\n",
    "                  input_shape=(img_width, img_height, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "input_2 (InputLayer)         (None, 150, 150, 3)       0         \n",
      "_________________________________________________________________\n",
      "block1_conv1 (Conv2D)        (None, 150, 150, 64)      1792      \n",
      "_________________________________________________________________\n",
      "block1_conv2 (Conv2D)        (None, 150, 150, 64)      36928     \n",
      "_________________________________________________________________\n",
      "block1_pool (MaxPooling2D)   (None, 75, 75, 64)        0         \n",
      "_________________________________________________________________\n",
      "block2_conv1 (Conv2D)        (None, 75, 75, 128)       73856     \n",
      "_________________________________________________________________\n",
      "block2_conv2 (Conv2D)        (None, 75, 75, 128)       147584    \n",
      "_________________________________________________________________\n",
      "block2_pool (MaxPooling2D)   (None, 37, 37, 128)       0         \n",
      "_________________________________________________________________\n",
      "block3_conv1 (Conv2D)        (None, 37, 37, 256)       295168    \n",
      "_________________________________________________________________\n",
      "block3_conv2 (Conv2D)        (None, 37, 37, 256)       590080    \n",
      "_________________________________________________________________\n",
      "block3_conv3 (Conv2D)        (None, 37, 37, 256)       590080    \n",
      "_________________________________________________________________\n",
      "block3_pool (MaxPooling2D)   (None, 18, 18, 256)       0         \n",
      "_________________________________________________________________\n",
      "block4_conv1 (Conv2D)        (None, 18, 18, 512)       1180160   \n",
      "_________________________________________________________________\n",
      "block4_conv2 (Conv2D)        (None, 18, 18, 512)       2359808   \n",
      "_________________________________________________________________\n",
      "block4_conv3 (Conv2D)        (None, 18, 18, 512)       2359808   \n",
      "_________________________________________________________________\n",
      "block4_pool (MaxPooling2D)   (None, 9, 9, 512)         0         \n",
      "_________________________________________________________________\n",
      "block5_conv1 (Conv2D)        (None, 9, 9, 512)         2359808   \n",
      "_________________________________________________________________\n",
      "block5_conv2 (Conv2D)        (None, 9, 9, 512)         2359808   \n",
      "_________________________________________________________________\n",
      "block5_conv3 (Conv2D)        (None, 9, 9, 512)         2359808   \n",
      "_________________________________________________________________\n",
      "block5_pool (MaxPooling2D)   (None, 4, 4, 512)         0         \n",
      "=================================================================\n",
      "Total params: 14,714,688\n",
      "Trainable params: 14,714,688\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Check architecture\n",
    "conv_base.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Extract features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found 200 images belonging to 2 classes.\n",
      "Found 100 images belonging to 2 classes.\n",
      "Found 100 images belonging to 2 classes.\n"
     ]
    }
   ],
   "source": [
    "# Extract features\n",
    "import numpy as np\n",
    "import os, shutil\n",
    "from keras.preprocessing.image import ImageDataGenerator\n",
    "\n",
    "base_dir = '/Users/macbook/blog/data/dogs_cats'\n",
    "train_dir = os.path.join(base_dir, 'train')\n",
    "validation_dir = os.path.join(base_dir, 'validation')\n",
    "test_dir = os.path.join(base_dir, 'test')\n",
    "\n",
    "datagen = ImageDataGenerator(rescale=1./255)\n",
    "batch_size = 32\n",
    "\n",
    "def extract_features(directory, sample_count):\n",
    "    # Preprocess data\n",
    "    features = np.zeros(shape=(sample_count, 4, 4, 512))  # Must be equal to the output of the convolutional base\n",
    "    labels = np.zeros(shape=(sample_count))\n",
    "    generator = datagen.flow_from_directory(directory,\n",
    "                                            target_size=(img_width,img_height),\n",
    "                                            batch_size = batch_size,\n",
    "                                            class_mode='binary')\n",
    "    # Pass data through convolutional base\n",
    "    i = 0\n",
    "    for inputs_batch, labels_batch in generator:\n",
    "        features_batch = conv_base.predict(inputs_batch)\n",
    "        features[i * batch_size: (i + 1) * batch_size] = features_batch\n",
    "        labels[i * batch_size: (i + 1) * batch_size] = labels_batch\n",
    "        i += 1\n",
    "        if i * batch_size >= sample_count:\n",
    "            break\n",
    "    return features, labels\n",
    "    \n",
    "train_features, train_labels = extract_features(train_dir, 200)\n",
    "validation_features, validation_labels = extract_features(validation_dir, 100)\n",
    "test_features, test_labels = extract_features(test_dir, 100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Train classifier (without classifier)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 200 samples, validate on 100 samples\n",
      "Epoch 1/50\n",
      "200/200 [==============================] - 3s - loss: 1.7227 - acc: 0.5550 - val_loss: 1.0448 - val_acc: 0.5000\n",
      "Epoch 2/50\n",
      "200/200 [==============================] - 1s - loss: 0.5839 - acc: 0.7050 - val_loss: 0.6455 - val_acc: 0.6100\n",
      "Epoch 3/50\n",
      "200/200 [==============================] - 0s - loss: 0.4701 - acc: 0.7500 - val_loss: 0.5370 - val_acc: 0.6800\n",
      "Epoch 4/50\n",
      "200/200 [==============================] - 0s - loss: 0.3368 - acc: 0.8700 - val_loss: 0.4270 - val_acc: 0.8300\n",
      "Epoch 5/50\n",
      "200/200 [==============================] - 0s - loss: 0.2302 - acc: 0.9450 - val_loss: 0.3926 - val_acc: 0.8300\n",
      "Epoch 6/50\n",
      "200/200 [==============================] - 0s - loss: 0.1552 - acc: 0.9550 - val_loss: 0.3689 - val_acc: 0.8400\n",
      "Epoch 7/50\n",
      "200/200 [==============================] - 0s - loss: 0.1115 - acc: 0.9800 - val_loss: 0.3477 - val_acc: 0.8600\n",
      "Epoch 8/50\n",
      "200/200 [==============================] - 0s - loss: 0.0962 - acc: 0.9900 - val_loss: 0.3437 - val_acc: 0.8600\n",
      "Epoch 9/50\n",
      "200/200 [==============================] - 0s - loss: 0.0674 - acc: 1.0000 - val_loss: 0.3360 - val_acc: 0.8700\n",
      "Epoch 10/50\n",
      "200/200 [==============================] - 0s - loss: 0.0531 - acc: 1.0000 - val_loss: 0.3558 - val_acc: 0.8600\n",
      "Epoch 11/50\n",
      "200/200 [==============================] - 0s - loss: 0.0410 - acc: 1.0000 - val_loss: 0.3409 - val_acc: 0.8600\n",
      "Epoch 12/50\n",
      "200/200 [==============================] - 0s - loss: 0.0305 - acc: 1.0000 - val_loss: 0.3523 - val_acc: 0.8700\n",
      "Epoch 13/50\n",
      "200/200 [==============================] - 0s - loss: 0.0255 - acc: 1.0000 - val_loss: 0.3505 - val_acc: 0.8500\n",
      "Epoch 14/50\n",
      "200/200 [==============================] - 0s - loss: 0.0196 - acc: 1.0000 - val_loss: 0.3822 - val_acc: 0.8400\n",
      "Epoch 15/50\n",
      "200/200 [==============================] - 0s - loss: 0.0167 - acc: 1.0000 - val_loss: 0.3618 - val_acc: 0.8500\n",
      "Epoch 16/50\n",
      "200/200 [==============================] - 0s - loss: 0.0138 - acc: 1.0000 - val_loss: 0.3647 - val_acc: 0.8700\n",
      "Epoch 17/50\n",
      "200/200 [==============================] - 0s - loss: 0.0115 - acc: 1.0000 - val_loss: 0.3795 - val_acc: 0.8600\n",
      "Epoch 18/50\n",
      "200/200 [==============================] - 0s - loss: 0.0098 - acc: 1.0000 - val_loss: 0.3779 - val_acc: 0.8500\n",
      "Epoch 19/50\n",
      "200/200 [==============================] - 0s - loss: 0.0085 - acc: 1.0000 - val_loss: 0.3825 - val_acc: 0.85001\n",
      "Epoch 20/50\n",
      "200/200 [==============================] - 0s - loss: 0.0080 - acc: 1.0000 - val_loss: 0.3789 - val_acc: 0.8600\n",
      "Epoch 21/50\n",
      "200/200 [==============================] - 0s - loss: 0.0066 - acc: 1.0000 - val_loss: 0.4030 - val_acc: 0.8600\n",
      "Epoch 22/50\n",
      "200/200 [==============================] - 0s - loss: 0.0059 - acc: 1.0000 - val_loss: 0.4039 - val_acc: 0.8600\n",
      "Epoch 23/50\n",
      "200/200 [==============================] - 0s - loss: 0.0052 - acc: 1.0000 - val_loss: 0.3966 - val_acc: 0.8300\n",
      "Epoch 24/50\n",
      "200/200 [==============================] - 0s - loss: 0.0047 - acc: 1.0000 - val_loss: 0.3997 - val_acc: 0.8300\n",
      "Epoch 25/50\n",
      "200/200 [==============================] - 0s - loss: 0.0042 - acc: 1.0000 - val_loss: 0.4133 - val_acc: 0.8600\n",
      "Epoch 26/50\n",
      "200/200 [==============================] - 0s - loss: 0.0039 - acc: 1.0000 - val_loss: 0.4116 - val_acc: 0.8300\n",
      "Epoch 27/50\n",
      "200/200 [==============================] - 0s - loss: 0.0036 - acc: 1.0000 - val_loss: 0.4018 - val_acc: 0.8600\n",
      "Epoch 28/50\n",
      "200/200 [==============================] - 0s - loss: 0.0033 - acc: 1.0000 - val_loss: 0.4170 - val_acc: 0.8300\n",
      "Epoch 29/50\n",
      "200/200 [==============================] - 0s - loss: 0.0029 - acc: 1.0000 - val_loss: 0.4332 - val_acc: 0.8500\n",
      "Epoch 30/50\n",
      "200/200 [==============================] - 0s - loss: 0.0028 - acc: 1.0000 - val_loss: 0.4268 - val_acc: 0.8400\n",
      "Epoch 31/50\n",
      "200/200 [==============================] - 0s - loss: 0.0025 - acc: 1.0000 - val_loss: 0.4185 - val_acc: 0.8400\n",
      "Epoch 32/50\n",
      "200/200 [==============================] - 0s - loss: 0.0024 - acc: 1.0000 - val_loss: 0.4229 - val_acc: 0.8300\n",
      "Epoch 33/50\n",
      "200/200 [==============================] - ETA: 0s - loss: 0.0021 - acc: 1.000 - 0s - loss: 0.0022 - acc: 1.0000 - val_loss: 0.4385 - val_acc: 0.8600\n",
      "Epoch 34/50\n",
      "200/200 [==============================] - 0s - loss: 0.0021 - acc: 1.0000 - val_loss: 0.4374 - val_acc: 0.8400\n",
      "Epoch 35/50\n",
      "200/200 [==============================] - 0s - loss: 0.0019 - acc: 1.0000 - val_loss: 0.4347 - val_acc: 0.8300\n",
      "Epoch 36/50\n",
      "200/200 [==============================] - 0s - loss: 0.0018 - acc: 1.0000 - val_loss: 0.4400 - val_acc: 0.8400\n",
      "Epoch 37/50\n",
      "200/200 [==============================] - 0s - loss: 0.0017 - acc: 1.0000 - val_loss: 0.4400 - val_acc: 0.8300\n",
      "Epoch 38/50\n",
      "200/200 [==============================] - 0s - loss: 0.0016 - acc: 1.0000 - val_loss: 0.4401 - val_acc: 0.8300\n",
      "Epoch 39/50\n",
      "200/200 [==============================] - 0s - loss: 0.0015 - acc: 1.0000 - val_loss: 0.4441 - val_acc: 0.8300\n",
      "Epoch 40/50\n",
      "200/200 [==============================] - 0s - loss: 0.0014 - acc: 1.0000 - val_loss: 0.4494 - val_acc: 0.8400\n",
      "Epoch 41/50\n",
      "200/200 [==============================] - 0s - loss: 0.0014 - acc: 1.0000 - val_loss: 0.4566 - val_acc: 0.8500\n",
      "Epoch 42/50\n",
      "200/200 [==============================] - 0s - loss: 0.0013 - acc: 1.0000 - val_loss: 0.4507 - val_acc: 0.8400\n",
      "Epoch 43/50\n",
      "200/200 [==============================] - 0s - loss: 0.0012 - acc: 1.0000 - val_loss: 0.4514 - val_acc: 0.8300\n",
      "Epoch 44/50\n",
      "200/200 [==============================] - 0s - loss: 0.0012 - acc: 1.0000 - val_loss: 0.4598 - val_acc: 0.8400\n",
      "Epoch 45/50\n",
      "200/200 [==============================] - 0s - loss: 0.0011 - acc: 1.0000 - val_loss: 0.4554 - val_acc: 0.8400\n",
      "Epoch 46/50\n",
      "200/200 [==============================] - 0s - loss: 0.0011 - acc: 1.0000 - val_loss: 0.4562 - val_acc: 0.8300\n",
      "Epoch 47/50\n",
      "200/200 [==============================] - 0s - loss: 0.0010 - acc: 1.0000 - val_loss: 0.4622 - val_acc: 0.8400\n",
      "Epoch 48/50\n",
      "200/200 [==============================] - 0s - loss: 9.5319e-04 - acc: 1.0000 - val_loss: 0.4675 - val_acc: 0.8500\n",
      "Epoch 49/50\n",
      "200/200 [==============================] - 0s - loss: 9.1632e-04 - acc: 1.0000 - val_loss: 0.4702 - val_acc: 0.8500\n",
      "Epoch 50/50\n",
      "200/200 [==============================] - 0s - loss: 8.8087e-04 - acc: 1.0000 - val_loss: 0.4724 - val_acc: 0.8500\n"
     ]
    }
   ],
   "source": [
    "# Train classifier\n",
    "from keras import models\n",
    "from keras import layers\n",
    "from keras import optimizers\n",
    "\n",
    "epochs = 50\n",
    "\n",
    "model = models.Sequential()\n",
    "model.add(layers.Flatten(input_shape=train_features.shape[1:]))  # Check original shape to understand\n",
    "model.add(layers.Dense(256, activation='relu'))\n",
    "#model.add(layers.Dropout(0.9))\n",
    "model.add(layers.Dense(1, activation='sigmoid'))\n",
    "\n",
    "model.compile(optimizer=optimizers.Adam(),\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['acc'])\n",
    "\n",
    "history = model.fit(train_features,\n",
    "                    train_labels,\n",
    "                    epochs=epochs, \n",
    "                    batch_size=batch_size,\n",
    "                    validation_data=(validation_features, validation_labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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77jluuOGGsPmVVkTdMiIyTES+EZGNIjI5yPZBIrJfRNb4Hr+Lekl9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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x125231390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/TLHvPXpAdfWR04EDoXWgoiLcD6yoqJu2b4cdO0LwT6Rr1zBGWGzq0QN69Qo9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\nJM8o8IuI5Jn/D2MmHNB8PWmxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1251566d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot results\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "acc = history.history['acc']\n",
    "val_acc = history.history['val_acc']\n",
    "loss = history.history['loss']\n",
    "val_loss = history.history['val_loss']\n",
    "\n",
    "epochs = range(1, len(acc)+1)\n",
    "\n",
    "plt.plot(epochs, acc, 'bo', label='Training accuracy')\n",
    "plt.plot(epochs, val_acc, 'b', label='Validation accuracy')\n",
    "plt.title('Training and validation accuracy')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "plt.plot(epochs, loss, 'bo', label='Training loss')\n",
    "plt.plot(epochs, val_loss, 'b', label='Validation loss')\n",
    "plt.title('Training and validation loss')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The gap between training accuracy and validation accuracy shows that the model is overfitting.\n",
    "* Training accuracy approaches 1 and training loss approaches 0. Thus, the model perfectly fits the training set, which is a sign of overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Train classifier (with dropout)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 200 samples, validate on 100 samples\n",
      "Epoch 1/50\n",
      "200/200 [==============================] - 1s - loss: 1.9910 - acc: 0.5450 - val_loss: 0.6032 - val_acc: 0.6100\n",
      "Epoch 2/50\n",
      "200/200 [==============================] - 0s - loss: 1.3816 - acc: 0.5850 - val_loss: 0.6119 - val_acc: 0.6800\n",
      "Epoch 3/50\n",
      "200/200 [==============================] - 0s - loss: 0.8552 - acc: 0.6450 - val_loss: 0.4574 - val_acc: 0.7900\n",
      "Epoch 4/50\n",
      "200/200 [==============================] - 0s - loss: 0.8235 - acc: 0.6150 - val_loss: 0.4385 - val_acc: 0.8400\n",
      "Epoch 5/50\n",
      "200/200 [==============================] - 0s - loss: 0.6635 - acc: 0.6650 - val_loss: 0.4436 - val_acc: 0.8500\n",
      "Epoch 6/50\n",
      "200/200 [==============================] - 0s - loss: 0.5849 - acc: 0.7100 - val_loss: 0.4547 - val_acc: 0.8500\n",
      "Epoch 7/50\n",
      "200/200 [==============================] - 0s - loss: 0.5022 - acc: 0.7300 - val_loss: 0.4655 - val_acc: 0.7600\n",
      "Epoch 8/50\n",
      "200/200 [==============================] - 0s - loss: 0.4317 - acc: 0.7850 - val_loss: 0.4196 - val_acc: 0.8500\n",
      "Epoch 9/50\n",
      "200/200 [==============================] - 0s - loss: 0.4326 - acc: 0.7700 - val_loss: 0.4062 - val_acc: 0.8400\n",
      "Epoch 10/50\n",
      "200/200 [==============================] - 0s - loss: 0.4476 - acc: 0.7600 - val_loss: 0.4118 - val_acc: 0.8000\n",
      "Epoch 11/50\n",
      "200/200 [==============================] - 0s - loss: 0.3924 - acc: 0.8000 - val_loss: 0.3874 - val_acc: 0.8300\n",
      "Epoch 12/50\n",
      "200/200 [==============================] - 0s - loss: 0.3261 - acc: 0.8350 - val_loss: 0.3702 - val_acc: 0.8400\n",
      "Epoch 13/50\n",
      "200/200 [==============================] - 0s - loss: 0.3611 - acc: 0.8450 - val_loss: 0.3588 - val_acc: 0.8500\n",
      "Epoch 14/50\n",
      "200/200 [==============================] - 0s - loss: 0.3750 - acc: 0.8300 - val_loss: 0.3606 - val_acc: 0.8300\n",
      "Epoch 15/50\n",
      "200/200 [==============================] - 0s - loss: 0.3716 - acc: 0.8300 - val_loss: 0.3568 - val_acc: 0.8600\n",
      "Epoch 16/50\n",
      "200/200 [==============================] - 0s - loss: 0.3459 - acc: 0.8150 - val_loss: 0.3559 - val_acc: 0.8500\n",
      "Epoch 17/50\n",
      "200/200 [==============================] - 0s - loss: 0.3528 - acc: 0.8100 - val_loss: 0.3552 - val_acc: 0.8400\n",
      "Epoch 18/50\n",
      "200/200 [==============================] - 0s - loss: 0.3313 - acc: 0.8500 - val_loss: 0.3491 - val_acc: 0.8300\n",
      "Epoch 19/50\n",
      "200/200 [==============================] - 0s - loss: 0.3534 - acc: 0.8500 - val_loss: 0.3525 - val_acc: 0.8600\n",
      "Epoch 20/50\n",
      "200/200 [==============================] - 0s - loss: 0.3707 - acc: 0.7900 - val_loss: 0.3540 - val_acc: 0.8400\n",
      "Epoch 21/50\n",
      "200/200 [==============================] - 0s - loss: 0.3773 - acc: 0.8050 - val_loss: 0.3600 - val_acc: 0.8400\n",
      "Epoch 22/50\n",
      "200/200 [==============================] - 0s - loss: 0.4296 - acc: 0.7750 - val_loss: 0.3763 - val_acc: 0.8400\n",
      "Epoch 23/50\n",
      "200/200 [==============================] - 0s - loss: 0.3124 - acc: 0.8650 - val_loss: 0.3608 - val_acc: 0.8200\n",
      "Epoch 24/50\n",
      "200/200 [==============================] - 0s - loss: 0.3534 - acc: 0.8100 - val_loss: 0.3559 - val_acc: 0.8600\n",
      "Epoch 25/50\n",
      "200/200 [==============================] - 0s - loss: 0.3249 - acc: 0.8600 - val_loss: 0.3514 - val_acc: 0.8400\n",
      "Epoch 26/50\n",
      "200/200 [==============================] - 0s - loss: 0.2801 - acc: 0.8400 - val_loss: 0.3481 - val_acc: 0.8200\n",
      "Epoch 27/50\n",
      "200/200 [==============================] - 0s - loss: 0.2515 - acc: 0.9050 - val_loss: 0.3483 - val_acc: 0.8700\n",
      "Epoch 28/50\n",
      "200/200 [==============================] - 0s - loss: 0.2776 - acc: 0.8800 - val_loss: 0.3469 - val_acc: 0.8600\n",
      "Epoch 29/50\n",
      "200/200 [==============================] - 0s - loss: 0.2968 - acc: 0.8600 - val_loss: 0.3474 - val_acc: 0.8600\n",
      "Epoch 30/50\n",
      "200/200 [==============================] - 0s - loss: 0.2658 - acc: 0.8500 - val_loss: 0.3447 - val_acc: 0.8600\n",
      "Epoch 31/50\n",
      "200/200 [==============================] - 0s - loss: 0.2856 - acc: 0.8900 - val_loss: 0.3476 - val_acc: 0.8300\n",
      "Epoch 32/50\n",
      "200/200 [==============================] - 0s - loss: 0.2078 - acc: 0.9150 - val_loss: 0.3441 - val_acc: 0.8400\n",
      "Epoch 33/50\n",
      "200/200 [==============================] - 0s - loss: 0.2297 - acc: 0.8750 - val_loss: 0.3448 - val_acc: 0.8500\n",
      "Epoch 34/50\n",
      "200/200 [==============================] - 0s - loss: 0.2250 - acc: 0.8950 - val_loss: 0.3435 - val_acc: 0.8700\n",
      "Epoch 35/50\n",
      "200/200 [==============================] - 0s - loss: 0.2988 - acc: 0.8500 - val_loss: 0.3333 - val_acc: 0.87000.83\n",
      "Epoch 36/50\n",
      "200/200 [==============================] - 0s - loss: 0.2295 - acc: 0.8750 - val_loss: 0.3283 - val_acc: 0.8400\n",
      "Epoch 37/50\n",
      "200/200 [==============================] - 0s - loss: 0.2523 - acc: 0.8750 - val_loss: 0.3328 - val_acc: 0.8200\n",
      "Epoch 38/50\n",
      "200/200 [==============================] - 0s - loss: 0.2565 - acc: 0.8700 - val_loss: 0.3385 - val_acc: 0.8600\n",
      "Epoch 39/50\n",
      "200/200 [==============================] - 0s - loss: 0.2183 - acc: 0.8950 - val_loss: 0.3411 - val_acc: 0.8500\n",
      "Epoch 40/50\n",
      "200/200 [==============================] - 0s - loss: 0.2256 - acc: 0.8850 - val_loss: 0.3380 - val_acc: 0.8500\n",
      "Epoch 41/50\n",
      "200/200 [==============================] - 0s - loss: 0.2041 - acc: 0.8950 - val_loss: 0.3354 - val_acc: 0.8600\n",
      "Epoch 42/50\n",
      "200/200 [==============================] - 0s - loss: 0.2314 - acc: 0.9050 - val_loss: 0.3426 - val_acc: 0.8300\n",
      "Epoch 43/50\n",
      "200/200 [==============================] - 0s - loss: 0.2014 - acc: 0.9150 - val_loss: 0.3602 - val_acc: 0.8300\n",
      "Epoch 44/50\n",
      "200/200 [==============================] - 0s - loss: 0.2088 - acc: 0.8850 - val_loss: 0.3692 - val_acc: 0.8500\n",
      "Epoch 45/50\n",
      "200/200 [==============================] - 0s - loss: 0.1827 - acc: 0.9100 - val_loss: 0.3813 - val_acc: 0.8600\n",
      "Epoch 46/50\n",
      "200/200 [==============================] - 0s - loss: 0.1735 - acc: 0.9200 - val_loss: 0.4058 - val_acc: 0.8500\n",
      "Epoch 47/50\n",
      "200/200 [==============================] - 0s - loss: 0.2224 - acc: 0.9050 - val_loss: 0.3814 - val_acc: 0.8600\n",
      "Epoch 48/50\n",
      "200/200 [==============================] - 0s - loss: 0.1905 - acc: 0.9200 - val_loss: 0.3933 - val_acc: 0.8500\n",
      "Epoch 49/50\n",
      "200/200 [==============================] - 0s - loss: 0.2262 - acc: 0.8800 - val_loss: 0.3682 - val_acc: 0.8700\n",
      "Epoch 50/50\n",
      "200/200 [==============================] - 0s - loss: 0.2171 - acc: 0.8950 - val_loss: 0.3631 - val_acc: 0.8300\n"
     ]
    }
   ],
   "source": [
    "# Train classifier\n",
    "from keras import models\n",
    "from keras import layers\n",
    "from keras import optimizers\n",
    "\n",
    "epochs = 50\n",
    "\n",
    "model = models.Sequential()\n",
    "model.add(layers.Flatten(input_shape=train_features.shape[1:]))  # Check original shape to understand\n",
    "model.add(layers.Dense(256, activation='relu'))\n",
    "model.add(layers.Dropout(0.9))\n",
    "model.add(layers.Dense(1, activation='sigmoid'))\n",
    "\n",
    "model.compile(optimizer=optimizers.Adam(),\n",
    "              loss='binary_crossentropy',\n",
    "              metrics=['acc'])\n",
    "\n",
    "history = model.fit(train_features,\n",
    "                    train_labels,\n",
    "                    epochs=epochs, \n",
    "                    batch_size=batch_size,\n",
    "                    validation_data=(validation_features, validation_labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VN2ig+re/RW9z2jR3sygqci6pBg3cDSIaH3+svgbZ/RK04j8UeD1s/Ubgxog6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dd52160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Lr7m+yNtQ4saujRvDr4vEjV0K/iKSb5nU+CcCG9z9NXf/AFgMTM9w/y3ZtlX0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\n/CIiMaPALyISMwr8IiIxo8AvIhIz/x8I2YbLiFWRngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12dd48400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot results\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "acc = history.history['acc']\n",
    "val_acc = history.history['val_acc']\n",
    "loss = history.history['loss']\n",
    "val_loss = history.history['val_loss']\n",
    "\n",
    "epochs = range(1, len(acc)+1)\n",
    "\n",
    "plt.plot(epochs, acc, 'bo', label='Training accuracy')\n",
    "plt.plot(epochs, val_acc, 'b', label='Validation accuracy')\n",
    "plt.title('Training and validation accuracy')\n",
    "plt.legend()\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "plt.plot(epochs, loss, 'bo', label='Training loss')\n",
    "plt.plot(epochs, val_loss, 'b', label='Validation loss')\n",
    "plt.title('Training and validation loss')\n",
    "plt.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Although the model is not totally stable, we can see that the gap between training and validation accuracy is smaller. Actually, the difference between these two curves is small enough to consider that the model is not overfitting anymore.\n",
    "* Training and validation loss confirm that the model doesn't overfit. Both loss values are similar.\n",
    "* Also, the model does not predict the training set perfectly anymore. This is also a sign that the model is not overfitting and it generalizes better."
   ]
  }
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