Image Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Image Clustering with K-Means\n",
    "\n",
    "References:\n",
    "- Tutorial on PCA vs ZCA: http://ufldl.stanford.edu/tutorial/unsupervised/PCAWhitening/\n",
    "- Functions for image featurization: https://machinelearningmastery.com/image-augmentation-deep-learning-keras/ \n",
    "- Kmeans with VCG16 https://towardsdatascience.com/how-to-cluster-images-based-on-visual-similarity-cd6e7209fe34 \n",
    "- Kmeans with Resnet50 https://towardsdatascience.com/image-clustering-using-transfer-learning-df5862779571\n",
    "  \n",
    "Things we want to do in this tutorial:\n",
    "- K-means clustering on MNIST data (standardization + whitening) -- decent quality\n",
    "- K-means clustering on MNIST data (standardization + whitening + rotations) -- worse quality\n",
    "- K-means clustering on MNIST data (standardization + whitening + rotations + transfer learning - VCG16 and Resnet50 with PCA) -- significant improvement in clustering quality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.datasets import mnist\n",
    "from keras.preprocessing.image import ImageDataGenerator\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train), (_, _) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 28, 28)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "datagen = ImageDataGenerator(featurewise_center=True,\n",
    "                             featurewise_std_normalization=True,\n",
    "                             #zca_whitening=True\n",
    "                            )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "datagen.fit(x_train.reshape(x_train.shape[0], 28, 28, 1).astype('float32'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 28, 28)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as pyplot\n",
    "for X_batch, y_batch in datagen.flow(x_train.reshape(x_train.shape[0], 28, 28, 1).astype('float32'),\n",
    "                                     y_train,\n",
    "                                     batch_size=10):\n",
    "    print(X_batch.reshape(10, 28, 28).shape)\n",
    "    # create a grid of 3x3 images\n",
    "    for i in range(0, 9):\n",
    "        pyplot.subplot(330 + 1 + i)\n",
    "        pyplot.imshow(X_batch[i].reshape(28, 28), cmap=pyplot.get_cmap('gray'))\n",
    "    # show the plot\n",
    "    pyplot.show()\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.gray();\n",
    "plt.figure(figsize = (5,5));\n",
    "for i in range(9):\n",
    "    plt.subplot(3,3,i+1);\n",
    "    plt.imshow(x_train[i]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MnistDataset:\n",
    "    \n",
    "    def __init__(self, zca_whitening=False, rotate=False):\n",
    "        (self.x_train, self.y_train), (_, _) = mnist.load_data()\n",
    "        self.width = 28 # image width in pixels\n",
    "        self.height = 28 # image height in pixels\n",
    "        self.channels = 1\n",
    "        if zca_whitening:\n",
    "            self._zca_whitening()\n",
    "        if rotate:\n",
    "            self._random_rotations()\n",
    "        \n",
    "    def _process_for_imagedatagenerator(self, image_matrix):\n",
    "        \"\"\"Convert image matrix for processing with ImageDataGenerator\"\"\"\n",
    "        reshaped_matrix = image_matrix \\\n",
    "            .reshape((image_matrix.shape[0], self.width, self.height, self.channels))\n",
    "        return reshaped_matrix.astype('float32')\n",
    "    \n",
    "    def _zca_whitening(self):\n",
    "        \"\"\"ZCA whitening of dataset images\"\"\"\n",
    "        x_processed = self._process_for_imagedatagenerator(self.x_train)\n",
    "        datagen = ImageDataGenerator(zca_whitening=True)\n",
    "        datagen.fit(x_processed)\n",
    "        for x_batch, y_batch in datagen.flow(x_processed,\n",
    "                                     self.y_train,\n",
    "                                     batch_size=x_processed.shape[0]):\n",
    "            self.x_train = x_batch.reshape(x_processed.shape[0], self.width, self.height)\n",
    "            break\n",
    "        \n",
    "    def _random_rotations(self):\n",
    "        \"\"\"Rotate images by 90 degrees\"\"\"\n",
    "        x_processed = self._process_for_imagedatagenerator(self.x_train)\n",
    "        datagen = ImageDataGenerator(rotation_range=90)\n",
    "        datagen.fit(x_processed)\n",
    "        for x_batch, y_batch in datagen.flow(x_processed,\n",
    "                                     self.y_train,\n",
    "                                     batch_size=x_processed.shape[0]):\n",
    "            self.x_train = x_batch.reshape(x_processed.shape[0], self.width, self.height)\n",
    "            break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/karan/opt/miniconda3/lib/python3.8/site-packages/keras_preprocessing/image/image_data_generator.py:337: UserWarning: This ImageDataGenerator specifies `zca_whitening`, which overrides setting of `featurewise_center`.\n",
      "  warnings.warn('This ImageDataGenerator specifies '\n"
     ]
    }
   ],
   "source": [
    "baseline_images = MnistDataset()\n",
    "whitened_images = MnistDataset(zca_whitening=True)\n",
    "rotated_images = MnistDataset(zca_whitening=True,\n",
    "                              rotate=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import MiniBatchKMeans\n",
    "def get_clustering_labels(image_dataset):\n",
    "    X = image_dataset.x_train.reshape(len(image_dataset.x_train),-1)\n",
    "    Y = image_dataset.y_train\n",
    "    n_digits = 10\n",
    "\n",
    "    kmeans = MiniBatchKMeans(n_clusters = n_digits)\n",
    "    kmeans.fit(X)\n",
    "    return kmeans.labels_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kmeans_label\n",
       "0    2\n",
       "1    7\n",
       "2    6\n",
       "3    6\n",
       "4    2\n",
       "5    4\n",
       "6    0\n",
       "7    7\n",
       "8    2\n",
       "9    5\n",
       "Name: digit, dtype: int64"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "baseline_pred_labels = get_clustering_labels(baseline_images)\n",
    "data = pd.DataFrame({ 'kmeans_label' : baseline_pred_labels.tolist(),\n",
    "                      'digit': Y.tolist()})\n",
    "data.groupby('kmeans_label')['digit'].apply(np.mean).apply(round)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kmeans_label\n",
       "0    7\n",
       "1    6\n",
       "2    6\n",
       "3    6\n",
       "4    4\n",
       "5    4\n",
       "6    3\n",
       "7    5\n",
       "8    3\n",
       "9    4\n",
       "Name: digit, dtype: int64"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "whitened_pred_labels = get_clustering_labels(whitened_images)\n",
    "data = pd.DataFrame({ 'kmeans_label' : whitened_pred_labels.tolist(),\n",
    "                      'digit': Y.tolist()})\n",
    "data.groupby('kmeans_label')['digit'].apply(np.mean).apply(round)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "kmeans_label\n",
       "0    6\n",
       "1    4\n",
       "2    4\n",
       "3    4\n",
       "4    5\n",
       "5    4\n",
       "6    4\n",
       "7    6\n",
       "8    3\n",
       "9    5\n",
       "Name: digit, dtype: int64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rotated_pred_labels = get_clustering_labels(rotated_images)\n",
    "data = pd.DataFrame({ 'kmeans_label' : rotated_pred_labels.tolist(),\n",
    "                      'digit': Y.tolist()})\n",
    "data.groupby('kmeans_label')['digit'].apply(np.mean).apply(round)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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