Project 10 - Implement a Siamese network.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c8dc0f63",
   "metadata": {},
   "outputs": [],
   "source": [
    "'''\n",
    "try:\n",
    "# %tensorflow_version only exists in Colab.\n",
    "  %tensorflow_version 2.x\n",
    "except Exception:\n",
    "    pass\n",
    "'''\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow.keras.models import Model\n",
    "from tensorflow.keras.layers import Input, Flatten, Dense, Dropout, Lambda\n",
    "from tensorflow.keras.optimizers import RMSprop\n",
    "from tensorflow.keras.datasets import fashion_mnist\n",
    "from tensorflow.keras.utils import plot_model\n",
    "\n",
    "\n",
    "from tensorflow.keras import backend as K\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image, ImageFont, ImageDraw\n",
    "import random\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11ba2ec3",
   "metadata": {},
   "source": [
    "# load the dataset\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e19ae23e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# load the dataset\n",
    "(train_images, train_labels), (test_images, test_labels) = fashion_mnist.load_data()\n",
    "\n",
    "# prepare train and test sets\n",
    "train_images = train_images.astype('float32')\n",
    "test_images = test_images.astype('float32')\n",
    "\n",
    "# normalize values\n",
    "train_images = train_images / 255.0\n",
    "test_images = test_images / 255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2df77670",
   "metadata": {},
   "source": [
    "# Generating pairs on train and test sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "00bc2200",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "119980"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create pairs on train and test sets\n",
    "\n",
    "def create_pairs(x, digit_indices):\n",
    "    '''Positive and negative pair creation.\n",
    "    Alternates between positive and negative pairs.\n",
    "    '''\n",
    "    pairs = []\n",
    "    labels = []\n",
    "    \n",
    "    # n =5999 (6000 labels in each list inside  digit_indices )\n",
    "    n = min([len(digit_indices[d]) for d in range(10)]) - 1\n",
    "    \n",
    "    # 10 classes\n",
    "    for d in range(10):\n",
    "        # 6000 items for each class \n",
    "        for i in range(n):   \n",
    "            # itterate over 10 class and 6000 images for each class and creating \n",
    "            #pairs between each 2 items of all classes   \n",
    "            z1, z2 = digit_indices[d][i], digit_indices[d][i + 1]   \n",
    "            pairs += [[x[z1], x[z2]]] \n",
    "            inc = random.randrange(1, 10)\n",
    "            dn = (d + inc) % 10\n",
    "            z1, z2 = digit_indices[d][i], digit_indices[dn][i]\n",
    "            pairs += [[x[z1], x[z2]]]    # lenght pair is 119980 \n",
    "            labels += [1, 0]\n",
    "            \n",
    "    return np.array(pairs), np.array(labels)\n",
    "\n",
    "\n",
    "def create_pairs_on_set(images, labels):\n",
    "    # creat a list of lists with 10 items for each labels\n",
    "    digit_indices = [np.where(labels == i)[0] for i in range(10)]   \n",
    "    pairs, y = create_pairs(images, digit_indices)\n",
    "    y = y.astype('float32')\n",
    "    return pairs, y\n",
    "\n",
    "tr_pairs, tr_y = create_pairs_on_set(train_images, train_labels)\n",
    "ts_pairs, ts_y = create_pairs_on_set(test_images, test_labels)\n",
    "\n",
    "len(tr_pairs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "95af4038",
   "metadata": {},
   "source": [
    "# seeing a sample pair of images below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "27c89747",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "def show_image(image):\n",
    "    plt.figure()\n",
    "    plt.imshow(image)\n",
    "    plt.colorbar()\n",
    "    plt.grid(False)\n",
    "    plt.show()\n",
    "\n",
    "# array index\n",
    "this_pair = 17\n",
    "\n",
    "# show images at this index\n",
    "show_image(ts_pairs[this_pair][0])\n",
    "show_image(ts_pairs[this_pair][1])\n",
    "\n",
    "# print the label for this pair\n",
    "print(ts_y[this_pair])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8320d8d8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(119980, 2, 28, 28)\n",
      "(2, 28, 28)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# print other pairs\n",
    "\n",
    "print(tr_pairs.shape)\n",
    "print((tr_pairs[ 0]).shape)\n",
    "\n",
    "show_image(tr_pairs[:,0][0])\n",
    "show_image(tr_pairs[:,0][1])\n",
    "\n",
    "show_image(tr_pairs[:,1][0])\n",
    "show_image(tr_pairs[:,1][1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21a2bb4e",
   "metadata": {},
   "source": [
    "## Build the  base Model\n",
    "\n",
    "Next, you'll define some utilities for building our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3d6e9496",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_base_network():\n",
    "    input = Input(shape= (28,28,) , name = \"base_input\")\n",
    "    x = Flatten(name = \"flatten_input\")(input)\n",
    "    x = Dense(128, activation = 'relu', name= \"first_base_dense\")(x)\n",
    "    x = Dropout(0.1, name = \"first_dropout\")(x)\n",
    "    x = Dense(128, activation = 'relu', name = \"second_base_dense\")(x)\n",
    "    x = Dropout(0.1, name = \"second_dropout\")(x)\n",
    "    x = Dense(128, activation = 'relu', name = \"third_base_dense\")(x)\n",
    "    return Model(inputs = input, outputs = x)\n",
    "\n",
    "\n",
    "def euclidean_distance(vects):\n",
    "    x, y = vects\n",
    "    sum_square = K.sum(K.square(x - y), axis=1, keepdims=True)\n",
    "    return K.sqrt(K.maximum(sum_square, K.epsilon()))\n",
    "\n",
    "\n",
    "def eucl_dist_output_shape(shapes):\n",
    "    shape1, shape2 = shapes\n",
    "    return (shape1[0], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "cfb63ab1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_network = initialize_base_network()\n",
    "plot_model(base_network, show_shapes=True, show_layer_names=True, to_file='base-model.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1c539144",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create the left input and point to the base network\n",
    "input_a = Input(shape=(28,28,), name = \"left_input\")\n",
    "vect_output_a = base_network(input_a)\n",
    "\n",
    "# create the right input and point to the base network\n",
    "input_b = Input(shape=(28,28,), name=\"right_input\")\n",
    "vect_output_b = base_network(input_b)\n",
    "\n",
    "# measure the similarity of the two vector outputs\n",
    "output = Lambda(euclidean_distance, name = \"output_layer\",\n",
    "                output_shape = eucl_dist_output_shape)([vect_output_a, vect_output_b])\n",
    "\n",
    "# specify the inputs and output of the model\n",
    "model = Model([input_a, input_b], output)\n",
    "\n",
    "# plot model graph\n",
    "plot_model(model, show_shapes = True, show_layer_names = True, to_file='outer-model.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e69d6274",
   "metadata": {},
   "source": [
    "# define the custom loss and training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "59903c08",
   "metadata": {},
   "outputs": [],
   "source": [
    "def contrastive_loss_with_margin(margin):\n",
    "    def contrastive_loss(y_true, y_pred):\n",
    "        '''Contrastive loss from Hadsell-et-al.'06\n",
    "        http://yann.lecun.com/exdb/publis/pdf/hadsell-chopra-lecun-06.pdf\n",
    "        '''\n",
    "        square_pred = K.square(y_pred)\n",
    "        margin_square = K.square(K.maximum(margin - y_pred, 0))\n",
    "        return K.mean(y_true * square_pred + (1 - y_true) * margin_square)\n",
    "    return contrastive_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "92d9dcfc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(119980, 2, 28, 28)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tr_pairs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "81434b39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((119980, 28, 28), (119980, 28, 28))"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tr_pairs[:,0].shape, tr_pairs[:,1].shape # Left image and right image to fed to net "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e4f26eb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/8\n",
      "1875/1875 [==============================] - 21s 10ms/step - loss: 0.1070 - val_loss: 0.0825\n",
      "Epoch 2/8\n",
      "1875/1875 [==============================] - 19s 10ms/step - loss: 0.0798 - val_loss: 0.0718\n",
      "Epoch 3/8\n",
      "1875/1875 [==============================] - 21s 11ms/step - loss: 0.0712 - val_loss: 0.0712\n",
      "Epoch 4/8\n",
      "1875/1875 [==============================] - 25s 13ms/step - loss: 0.0678 - val_loss: 0.0694\n",
      "Epoch 5/8\n",
      "1875/1875 [==============================] - 20s 11ms/step - loss: 0.0655 - val_loss: 0.0668\n",
      "Epoch 6/8\n",
      "1875/1875 [==============================] - 24s 13ms/step - loss: 0.0643 - val_loss: 0.0665\n",
      "Epoch 7/8\n",
      "1875/1875 [==============================] - 24s 13ms/step - loss: 0.0628 - val_loss: 0.0675\n",
      "Epoch 8/8\n",
      "1875/1875 [==============================] - 21s 11ms/step - loss: 0.0616 - val_loss: 0.0656\n"
     ]
    }
   ],
   "source": [
    "rms = RMSprop()\n",
    "model.compile(loss= contrastive_loss_with_margin(margin=1), optimizer=rms)\n",
    "history = model.fit([tr_pairs[:,0], tr_pairs[:,1]], tr_y, epochs=8, batch_size=64, validation_data=([ts_pairs[:,0], ts_pairs[:,1]], ts_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "810788ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_accuracy(y_true, y_pred):\n",
    "    '''Compute classification accuracy with a fixed threshold on distances.\n",
    "    '''\n",
    "    pred = y_pred.ravel() < 0.5    # returns a true and false array with using treshold \n",
    "    return np.mean(pred == y_true)   # compare trues in pred and 1s in y_true "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d2893ffd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(19980,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c1e0cf43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 0., 1., ..., 0., 1., 0.], dtype=float32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "49865026",
   "metadata": {},
   "outputs": [],
   "source": [
    "tf.compat.v1.reset_default_graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8319d06e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "625/625 [==============================] - 2s 3ms/step - loss: 0.0656\n",
      "3750/3750 [==============================] - 11s 3ms/step\n",
      "625/625 [==============================] - 1s 2ms/step\n",
      "Loss = 0.06561069935560226, Train Accuracy = 0.9255292548758126 Test Accuracy = 0.9108608608608608\n"
     ]
    }
   ],
   "source": [
    "loss = model.evaluate(x = [ts_pairs[:,0], ts_pairs[:,1]], y = ts_y)\n",
    "\n",
    "y_pred_train = model.predict([tr_pairs[:,0], tr_pairs[:,1]])\n",
    "train_accuracy = compute_accuracy(tr_y, y_pred_train)\n",
    "\n",
    "y_pred_test = model.predict([ts_pairs[:,0], ts_pairs[:,1]])\n",
    "test_accuracy = compute_accuracy(ts_y, y_pred_test)\n",
    "\n",
    "print(\"Loss = {}, Train Accuracy = {} Test Accuracy = {}\".format(loss, train_accuracy, test_accuracy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "cb55ba11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_metrics(metric_name, title, ylim=5):\n",
    "    plt.title(title)\n",
    "    plt.ylim(0,ylim)\n",
    "    plt.plot(history.history[metric_name],color='blue',label=metric_name)\n",
    "    plt.plot(history.history['val_' + metric_name],color='green',label='val_' + metric_name)\n",
    "    plt.legend()\n",
    "\n",
    "plot_metrics(metric_name='loss', title=\"Loss\", ylim=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8377f07a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Matplotlib config\n",
    "def visualize_images():\n",
    "    plt.rc('image', cmap='gray_r')\n",
    "    plt.rc('grid', linewidth=0)\n",
    "    plt.rc('xtick', top=False, bottom=False, labelsize='large')\n",
    "    plt.rc('ytick', left=False, right=False, labelsize='large')\n",
    "    plt.rc('axes', facecolor='F8F8F8', titlesize=\"large\", edgecolor='white')\n",
    "    plt.rc('text', color='a8151a')\n",
    "    plt.rc('figure', facecolor='F0F0F0')# Matplotlib fonts\n",
    "\n",
    "# utility to display a row of digits with their predictions\n",
    "def display_images(left, right, predictions, labels, title, n):\n",
    "    plt.figure(figsize=(17,3))\n",
    "    plt.title(title)\n",
    "    plt.yticks([])\n",
    "    plt.xticks([])\n",
    "    plt.grid(None)\n",
    "    left = np.reshape(left, [n, 28, 28])\n",
    "    left = np.swapaxes(left, 0, 1)\n",
    "    left = np.reshape(left, [28, 28*n])\n",
    "    plt.imshow(left)\n",
    "    plt.figure(figsize=(17,3))\n",
    "    plt.yticks([])\n",
    "    plt.xticks([28*x+14 for x in range(n)], predictions)\n",
    "    for i,t in enumerate(plt.gca().xaxis.get_ticklabels()):\n",
    "        if predictions[i] > 0.5: t.set_color('red') # bad predictions in red\n",
    "    plt.grid(None)\n",
    "    right = np.reshape(right, [n, 28, 28])\n",
    "    right = np.swapaxes(right, 0, 1)\n",
    "    right = np.reshape(right, [28, 28*n])\n",
    "    plt.imshow(right)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c0241429",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(119980, 1)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred_train.shape "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "2cd10910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([110499,  64829,  39598,  71352, 117548, 101274,  60650, 105709,\n",
       "        15508,  64057])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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      "text/plain": [
       "<Figure size 1700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_train = np.squeeze(y_pred_train)  # Remove axes of length one from a.\n",
    "indexes = np.random.choice(len(y_pred_train), size =10)# 10 random nums between 0 and 119980\n",
    "display_images(tr_pairs[:, 0][indexes], tr_pairs[:, 1][indexes], y_pred_train[indexes], tr_y[indexes], \"clothes and their dissimilarity\", 10)\n",
    "\n",
    "indexes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9424123",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
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     "delete_cmd_postfix": ") ",
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     "varRefreshCmd": "cat(var_dic_list()) "
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   },
   "oldHeight": 367.841,
   "position": {
    "height": "268px",
    "left": "285.364px",
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