One-Shot Image Verification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One-Shot Image Verification using deep learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the Olivetti face database is not large enough to do well training the network and the architecture of this network is really optimized for character recognition, it probably makes more sense to use a pretrained face recognition network for encoding the images. The result of this encoding will then be compared between the two and the final stage will be trained to complete the discrimination. Weights for the final layer can be loaded into the complete model after training that layer alone.\n",
    "\n",
    "The best choice for pretrained face recognition networks is probably the VGG-Face network, as described in this paper - http://www.robots.ox.ac.uk/~vgg/publications/2015/Parkhi15/parkhi15.pdf, which has already been converted to Keras here - https://gist.github.com/EncodeTS/6bbe8cb8bebad7a672f0d872561782d9."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One difficulty may be the differning format between the VGG face dataset and the Olivetti set. To accomodate the different format and grayscale the Olivetti images will be adjusted to match the expected input with a similar placement of the face in the image and the grayscale repeated on all three rbg planes.\n",
    "\n",
    "The VGG-Faces based siamese model will be fine tuned to the first 30 of the Olivetti faces and the remaining 10 will be used to test one-shot accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I was trying to determine the way faces should be framed in the image I found this paper which describes adapting the VGG-Faces model for cross-over learning - http://cs231n.stanford.edu/reports/2016/pdfs/006_Report.pdf\n",
    "\n",
    "It seems that the Olivetti faces are probably reasonably well cropped, so we will only need to change them to RGB format for the input.\n",
    "\n",
    "One thing I did not understand at the outset was that the model does not actually learn anything from the one image. All features need to be encoded in the network to begin with. So it is critically important that a wide range of faces be present in the training data. For this reason the VGG-Face dataset is probably not sufficient for the wider population as it was mostly trained on celebrity faces."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I was looking for how to merge the results from the branches and found this blog post on how someone implemented the model in the paper - https://sorenbouma.github.io/blog/oneshot/ So, some of the following code is adapted from that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%pylab inline\n",
    "from sklearn.datasets import fetch_olivetti_faces\n",
    "from itertools import combinations\n",
    "from keras.models import Model\n",
    "from keras.layers import Input, Conv2D, ZeroPadding2D, MaxPooling2D, Flatten, Dense, Dropout, Lambda\n",
    "from keras.optimizers import SGD, Adam\n",
    "from keras.losses import binary_crossentropy\n",
    "from keras.initializers import TruncatedNormal\n",
    "from keras.utils.data_utils import get_file\n",
    "from PIL import Image\n",
    "from sklearn.metrics import roc_curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### If we use 75% of the Olivetti Faces data set for training, the number of positive and negative pairs we can get is 9X5X30 = 1350 and 150x290 = 43,500.\n",
    "We will draw evenly and randomly from those sets for training batches and run until we are not seeing much additional improvement.\n",
    "For validation we will have 450 positive cases and 4500 negative cases. The validation data will be used to assess the training of the final layers and to construct the one-shot tests."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Seems that for training the final layer it may be faster to precompute the output of the VGG-Face branches for all the images and train the final layer on its own. I will see if I can figure out how to do that once I have things set up.\n",
    "\n",
    "If the performance is not so good with only the final fully connected layer trained we could also make the second to last layer trainable and include it in the discriminator, with initial wieghts starting where they were for VGG-Face.\n",
    "\n",
    "To multiply the amount of data we have we might also just do some transformations on the image vectors for training the final layer rather than on the original images. Perhaps a dropout of 10% of the components. If we were to start from the original images we could add noise or perform affine distortions that approximate changes in the angle of the photo or lighting without creating abnormal facial shapes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Improved source for VGG-Face\n",
    "After mucking around with VGG-Face trying to get it to work I think I found a better source for a Keras-based VGG-Face model ready for fine tuning here - https://github.com/rcmalli/keras-vggface. It has the weights in TensorFlow format."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AWS\n",
    "Although it was not really necessary due to the small amount of data and single training layer, training was performed on an AWS p2 instance. If we had progressed to training more of the fully connected layers it may have been a help to have the GPU machine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "WEIGHTS_PATH = 'https://github.com/rcmalli/keras-vggface/releases/download/v2.0/rcmalli_vggface_tf_v2.h5'\n",
    "\n",
    "class Siamese_Face_Tester(object):\n",
    "    \"\"\"Loads Olivetti Face data and generates sets for training and testing one-shot learning on Siamese Network.\"\"\"\n",
    "    def __init__(self):\n",
    "        self.train, self.test = self.new_train_test_split()\n",
    "        # Pairs of indices for images of the same subject.\n",
    "        self.test_pairs_pos, self.train_pairs_pos = self.get_pos_pairs()\n",
    "        # Train and test sets for training the discriminator.\n",
    "        self.train_pairs = []\n",
    "        self.train_target = []\n",
    "        self.test_pairs = []\n",
    "        self.test_target = []\n",
    "        self.refresh_train_sets()\n",
    "        # Fetch and convert Olivetti Face data.\n",
    "        self.data = fetch_olivetti_faces()\n",
    "        self.images = np.zeros((400, 224, 224, 3))\n",
    "        for i in range(400):\n",
    "            self.images[i, :, :, :] = self.convert_image(self.data.images[i])\n",
    "        self.image_vectors = None\n",
    "        self.branch_encoder = None\n",
    "        self.weights_path = None\n",
    "        self.discriminator = self.get_discriminator()\n",
    "\n",
    "\n",
    "    def convert_image(self, img):\n",
    "        \"\"\"Convert gray scale image to color in [h, w, channels] format.\"\"\"\n",
    "        new_image = Image.fromarray(img).resize((224, 224))\n",
    "        img = np.asarray(new_image)\n",
    "        color_image = np.array([img, img, img])\n",
    "        return transpose(color_image, (1, 2, 0))\n",
    "\n",
    "\n",
    "    def new_train_test_split(self):\n",
    "        \"\"\"Olivetti Faces includes 40 sets of 10 images. This returns a 75/25 random split of 40 indices.\"\"\"\n",
    "        # Randomly choose 75% of the indices for the Olivetti subjects for the training set.\n",
    "        train = np.random.choice(range(40), 30, replace=False)\n",
    "        # Take the remaining 25% for the test set.\n",
    "        test = np.array([idx for idx in range(40) if idx not in train])\n",
    "        return train, test\n",
    "\n",
    "\n",
    "    def get_pos_pairs(self):\n",
    "        \"\"\"Returns all possible positive pairs for the current train-test split.\"\"\"\n",
    "        test_pairs_pos = np.concatenate([np.array(list(combinations(range(10), 2)))+idx*10 for idx in self.test])\n",
    "        train_pairs_pos = np.concatenate([np.array(list(combinations(range(10), 2)))+idx*10 for idx in self.train])\n",
    "        return test_pairs_pos, train_pairs_pos\n",
    "\n",
    "\n",
    "    def refresh_train_sets(self, batch_size=32):\n",
    "        \"\"\"Refreshes the train and test sets of index pairs and targets with a new random draw of negative pairs.\"\"\"\n",
    "        # Make the train set an integer multiple of the batch size (not sure if this matters...)\n",
    "        drop = len(self.train_pairs_pos)%batch_size\n",
    "        train_pairs = np.concatenate((self.train_pairs_pos[:-drop], self.draw_random_neg_pairs(self.train, len(self.train_pairs_pos)-drop)))\n",
    "        train_targets = np.concatenate((np.ones(len(train_pairs)/2), np.zeros(len(train_pairs)/2)))\n",
    "        train_labeled = np.hstack([train_pairs, np.array([train_targets]).T])\n",
    "        np.random.shuffle(train_labeled)\n",
    "        self.train_pairs = train_labeled[:, :2]\n",
    "        self.train_target = train_labeled[:, 2]\n",
    "        # Repeat same procedure for the test set. Clearly could be refactored in some way, but no time now.\n",
    "        drop = len(self.test_pairs_pos)%batch_size\n",
    "        test_pairs = np.concatenate((self.test_pairs_pos[:-drop], self.draw_random_neg_pairs(self.test, len(self.test_pairs_pos)-drop)))\n",
    "        test_targets = np.concatenate((np.ones(len(test_pairs)/2), np.zeros(len(test_pairs)/2)))\n",
    "        test_labeled = np.hstack([test_pairs, np.array([test_targets]).T])\n",
    "        np.random.shuffle(test_labeled)\n",
    "        self.test_pairs = test_labeled[:, :2]\n",
    "        self.test_target = test_labeled[:, 2]\n",
    "        \n",
    "\n",
    "    def random_neg_pair(self, subject_indices):\n",
    "        \"\"\"Takes an array of subject indices and returns a pair of indices to non-matching image vectors.\"\"\"\n",
    "        subject = random.choice(subject_indices)\n",
    "        ind1 = 10*subject + random.choice(range(10))\n",
    "        others = subject_indices.tolist()\n",
    "        others.remove(subject)\n",
    "        ind2 = 10*random.choice(others) + random.choice(range(10))\n",
    "        return [ind1, ind2]\n",
    "\n",
    "\n",
    "    def draw_random_neg_pairs(self, subject_indices, number):\n",
    "        \"\"\"Returns a set of number unique negative pairs\"\"\"\n",
    "        pairs = []\n",
    "        while (len(pairs) < number):\n",
    "            pair = set(self.random_neg_pair(subject_indices))\n",
    "            if pair not in pairs:\n",
    "                pairs.append(pair)\n",
    "        return np.array([list(s) for s in pairs])\n",
    "\n",
    "\n",
    "    def vgg_face(self, weights_path=None):\n",
    "        \"\"\"The VGGFace network.\"\"\"\n",
    "        img = Input(shape=(224, 224, 3))\n",
    "\n",
    "        conv1_1 = Conv2D(64, (3, 3), activation='relu', padding='same', name='conv1_1', trainable=False)(img)\n",
    "        conv1_2 = Conv2D(64, (3, 3), activation='relu', padding='same', name='conv1_2', trainable=False)(conv1_1)\n",
    "        pool1 = MaxPooling2D((2, 2), strides=(2, 2), name='pool1', trainable=False)(conv1_2)\n",
    "\n",
    "        conv2_1 = Conv2D(128, (3, 3), activation='relu', padding='same', name='conv2_1', trainable=False)(pool1)\n",
    "        conv2_2 = Conv2D(128, (3, 3), activation='relu', padding='same', name='conv2_2', trainable=False)(conv2_1)\n",
    "        pool2 = MaxPooling2D((2, 2), strides=(2, 2), name='pool2', trainable=False)(conv2_2)\n",
    "\n",
    "        conv3_1 = Conv2D(256, (3, 3), activation='relu', padding='same', name='conv3_1', trainable=False)(pool2)\n",
    "        conv3_2 = Conv2D(256, (3, 3), activation='relu', padding='same', name='conv3_2', trainable=False)(conv3_1)\n",
    "        conv3_3 = Conv2D(256, (3, 3), activation='relu', padding='same', name='conv3_3', trainable=False)(conv3_2)\n",
    "        pool3 = MaxPooling2D((2, 2), strides=(2, 2), name='pool3', trainable=False)(conv3_3)\n",
    "\n",
    "        conv4_1 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv4_1', trainable=False)(pool3)\n",
    "        conv4_2 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv4_2', trainable=False)(conv4_1)\n",
    "        conv4_3 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv4_3', trainable=False)(conv4_2)\n",
    "        pool4 = MaxPooling2D((2, 2), strides=(2, 2), name='pool4', trainable=False)(conv4_3)\n",
    "\n",
    "        conv5_1 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv5_1', trainable=False)(pool4)\n",
    "        conv5_2 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv5_2', trainable=False)(conv5_1)\n",
    "        conv5_3 = Conv2D(512, (3, 3), activation='relu', padding='same', name='conv5_3', trainable=False)(conv5_2)\n",
    "        pool5 = MaxPooling2D((2, 2), strides=(2, 2), name='pool5', trainable=False)(conv5_3)\n",
    "\n",
    "        flat = Flatten()(pool5)\n",
    "        fc6 = Dense(4096, activation='relu', name='fc6', trainable=False)(flat)\n",
    "        fc7 = Dense(4096, activation='relu', name='fc7', trainable=False)(fc6)\n",
    "        out = Dense(2622, activation='softmax', name='fc8')(fc7)\n",
    "\n",
    "        model = Model(inputs=img, outputs=out)\n",
    "\n",
    "        if weights_path:\n",
    "            model.load_weights(weights_path)\n",
    "\n",
    "        return model\n",
    "\n",
    "\n",
    "    def get_branch_model(self):\n",
    "        \"\"\"Returns a model that can be used to encode images into vectors using the trained VGG-Face model.\"\"\"\n",
    "        if self.branch_encoder == None:\n",
    "            # Set up VGGFace network and load weights.\n",
    "            if self.weights_path == None:\n",
    "                self.get_VGG_weights()\n",
    "            encode_image = self.vgg_face(self.weights_path)\n",
    "\n",
    "            # Strip off the final layer used for prediction, leaving the image feature vector.\n",
    "            # Unfortunately, popping off layers still does not work correctly. After popping\n",
    "            # you still need to reassign the output of the model to the final layer or it will\n",
    "            # still be trying to look at the old final layer. See here - https://github.com/fchollet/keras/issues/2371\n",
    "            encode_image.layers.pop()\n",
    "            encode_image.outputs = [encode_image.layers[-1].output]\n",
    "            encode_image.layers[-1].outbound_nodes = []\n",
    "            self.branch_encoder = encode_image\n",
    "        return self.branch_encoder\n",
    "    \n",
    "    \n",
    "    def encode_image_vectors(self):\n",
    "        \"\"\"Uses the image encoding branch to turn the Olivetti images into vectors.\"\"\"\n",
    "        encoder = self.get_branch_model()\n",
    "        vectors = encoder.predict(self.images[:16], batch_size = 16)\n",
    "        for i in range(24):\n",
    "            vectors = np.concatenate((vectors, encoder.predict(self.images[16*(i+1):16*(i+2)], batch_size = 16)))\n",
    "        return vectors\n",
    "\n",
    "\n",
    "    def get_image_vectors(self):\n",
    "        \"\"\"Returns the image vectors, computing them if necessary.\"\"\"\n",
    "        if self.image_vectors == None:\n",
    "            self.image_vectors = self.encode_image_vectors()\n",
    "        return self.image_vectors\n",
    "    \n",
    "    \n",
    "    def get_VGG_weights(self):\n",
    "        \"\"\"Download VGGFace weights if they are not present.\"\"\"\n",
    "        self.weights_path = get_file('rcmalli_vggface_tf_v2.h5',\n",
    "                                     WEIGHTS_PATH,\n",
    "                                     cache_subdir='models')\n",
    "        \n",
    "        \n",
    "    def get_discriminator(self):\n",
    "        \"\"\"The discriminator is the part of the siamese network that we will train to tell the difference between encoded image vectors.\"\"\"\n",
    "        discrim_input = Input(shape=(2, 4096))\n",
    "        # Merge two encoded inputs with the L1 distance between them.\n",
    "        both = Lambda(lambda x: np.abs(x[:,0]-x[:,1]), output_shape=(4096,))(discrim_input)\n",
    "        # Make the final prediction layer as described in the paper. This is the only layer we will train to begin with.\n",
    "        # We can unfreeze additional fc layers and train them if it seems to be needed.\n",
    "        prediction = Dense(1, activation='sigmoid', bias_initializer=TruncatedNormal(mean=0.5, stddev=0.01))(both)\n",
    "        discriminator = Model(inputs=discrim_input, outputs=prediction)\n",
    "        return discriminator\n",
    "    \n",
    "    \n",
    "    def get_oneshot_set(self, N):\n",
    "        \"\"\"Return a set of N pairs, one of which has two images of the same face.\"\"\"\n",
    "        pairs = [10*np.random.choice(self.test) + np.random.choice(range(10), 2, replace=False)]\n",
    "        pairs.extend(self.draw_random_neg_pairs(self.test, N-1))\n",
    "        targets = np.zeros((N,))\n",
    "        targets[0] = 1\n",
    "        return [[np.array(self.image_vectors[int(pair[0])]),\n",
    "                 np.array(self.image_vectors[int(pair[1])])] for pair in pairs], targets\n",
    "    \n",
    "    \n",
    "    def test_oneshot(self, N, k, model=None, verbose=0):\n",
    "        \"\"\"Test average N way oneshot learning accuracy of a siamese neural net over k one-shot tasks.\n",
    "        \n",
    "        Thanks here to Soren Bouma for a helpful function! - https://sorenbouma.github.io/blog/oneshot/ \n",
    "        \"\"\"\n",
    "        if model == None:\n",
    "            model = self.discriminator\n",
    "        n_correct = 0\n",
    "        if verbose:\n",
    "            print(\"Evaluating model on {} unique {} way one-shot learning tasks ...\".format(k, N))\n",
    "        for i in range(k):\n",
    "            inputs, targets = self.get_oneshot_set(N)\n",
    "            probs = model.predict(inputs)\n",
    "            if np.argmax(probs) == 0:\n",
    "                n_correct+=1\n",
    "        percent_correct = (100.0*n_correct / k)\n",
    "        if verbose:\n",
    "            print(\"Got an average of {}% {} way one-shot learning accuracy\".format(percent_correct, N))\n",
    "        return percent_correct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "tester = Siamese_Face_Tester()\n",
    "vectors = tester.get_image_vectors()\n",
    "tester.discriminator.compile(loss=\"binary_crossentropy\", optimizer=Adam())\n",
    "X_train = [[np.array(vectors[int(pair[0])]), np.array(vectors[int(pair[1])])] for pair in tester.train_pairs]\n",
    "X_test = [[np.array(vectors[int(pair[0])]), np.array(vectors[int(pair[1])])] for pair in tester.test_pairs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 2688 samples, validate on 896 samples\n",
      "Epoch 1/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.6340 - val_loss: 0.6043\n",
      "Epoch 2/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.5681 - val_loss: 0.5848\n",
      "Epoch 3/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.5451 - val_loss: 0.5754\n",
      "Epoch 4/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.5250 - val_loss: 0.5687\n",
      "Epoch 5/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.5061 - val_loss: 0.5621\n",
      "Epoch 6/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4882 - val_loss: 0.5591\n",
      "Epoch 7/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4712 - val_loss: 0.5547\n",
      "Epoch 8/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4550 - val_loss: 0.5513\n",
      "Epoch 9/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4397 - val_loss: 0.5490\n",
      "Epoch 10/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4249 - val_loss: 0.5471\n",
      "Epoch 11/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.4109 - val_loss: 0.5449\n",
      "Epoch 12/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3974 - val_loss: 0.5442\n",
      "Epoch 13/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3846 - val_loss: 0.5437\n",
      "Epoch 14/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3724 - val_loss: 0.5431\n",
      "Epoch 15/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3608 - val_loss: 0.5433\n",
      "Epoch 16/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3495 - val_loss: 0.5385\n",
      "Epoch 17/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3387 - val_loss: 0.5451\n",
      "Epoch 18/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3284 - val_loss: 0.5448\n",
      "Epoch 19/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3186 - val_loss: 0.5453\n",
      "Epoch 20/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3091 - val_loss: 0.5486\n",
      "Epoch 21/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.3001 - val_loss: 0.5473\n",
      "Epoch 22/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2913 - val_loss: 0.5523\n",
      "Epoch 23/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2829 - val_loss: 0.5526\n",
      "Epoch 24/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2749 - val_loss: 0.5521\n",
      "Epoch 25/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2671 - val_loss: 0.5502\n",
      "Epoch 26/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2597 - val_loss: 0.5529\n",
      "Epoch 27/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2524 - val_loss: 0.5596\n",
      "Epoch 28/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2455 - val_loss: 0.5618\n",
      "Epoch 29/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2388 - val_loss: 0.5633\n",
      "Epoch 30/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2325 - val_loss: 0.5675\n",
      "Epoch 31/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2263 - val_loss: 0.5695\n",
      "Epoch 32/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2204 - val_loss: 0.5713\n",
      "Epoch 33/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2146 - val_loss: 0.5802\n",
      "Epoch 34/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2090 - val_loss: 0.5736\n",
      "Epoch 35/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.2037 - val_loss: 0.5774\n",
      "Epoch 36/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.1985 - val_loss: 0.5805\n",
      "Epoch 37/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.1934 - val_loss: 0.5846\n",
      "Epoch 38/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.1886 - val_loss: 0.5857\n",
      "Epoch 39/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.1839 - val_loss: 0.5916\n",
      "Epoch 40/40\n",
      "2688/2688 [==============================] - 0s - loss: 0.1794 - val_loss: 0.5878\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x7f686d4caf10>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tester.discriminator.fit(x=X_train, y=tester.train_target, epochs=40, validation_data=(X_test, tester.test_target))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_pred = tester.discriminator.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "fpr, tpr, thresholds = roc_curve(tester.test_target, y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJalBhrskNchwl6QGGe6S1KD/B58rPNg/ibIqAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6870229810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fpr, tpr)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ROC Curve\n",
    "Not too bad for only 40 Epochs of training on the final layer. This is an indication of performance for a 1 of 2 one-shot learning task. So not really very good, but let's go on to check the one-shot performance for larger sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "82.0"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tester.test_oneshot(5, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Plot percent correct versus number in one-shot task set. We take an average over 1000 trials\n",
    "# of the one-shot task for set sizes from 2 - 21.\n",
    "accuracy = []\n",
    "for i in range(20):\n",
    "    accuracy.append(tester.test_oneshot(i+2, 1000))\n",
    "x = np.array(range(20)) + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAusAAAJ6CAYAAACRwwzbAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nB6tyJsEhpHqUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f686cba6050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "plt.figure(figsize=(12,10))\n",
    "plt.plot(x, accuracy)\n",
    "plt.title('One-Shot Task Accuracy vs. Number in Set', fontsize = 28)\n",
    "plt.xlabel('Number of Pairs in One-Shot Task', fontsize = 24)\n",
    "plt.ylabel('Accuracy (%)', fontsize = 24)\n",
    "plt.xticks(fontsize = 18)\n",
    "plt.yticks(fontsize = 18)\n",
    "plt.xlim([0, 22])\n",
    "plt.ylim([0, 100])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## So, accuracy drops off pretty quickly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary Notes:\n",
    "## What an awesome experience this was\n",
    "* This is actually the first time I have really done a deep learning project on my own. It was at a perfect level for me to get into it. Previously I have only run things with a lot of hand holding.\n",
    "* I loved the discovery of how easy it is to do transfer learning.\n",
    "* I did not have time to go back and create the full model that would take two images to compare, but it would not be difficult to save the trained weights from the discriminator and load them into the combined model.\n",
    "* Running the calculation of the image vectors actually took quite a while so it would have been a real waste of time to train on the complete network.\n",
    "\n",
    "## Steps for improvement\n",
    "* First step would probably be to come up with some ways to augment the training data. The Olivetti set is just so small.\n",
    "    * Some of those might be to add noise to the images.\n",
    "    * Add a constant offset for all values.\n",
    "    * Small affine distortions that do not result in unnatural faces, but look more like side, top or bottom views.\n",
    "    * Find more face data. Seems like many likely candidates here - http://www.face-rec.org/databases/\n",
    "* Additional performance could be achieved by training the second to last fully connected layer from the VGGFace model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}