{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# K-Means Clustering for Imagery Analysis\n",
    "> In this post, we will use a K-means algorithm to perform image classification. Clustering isn't limited to the consumer information and population sciences, it can be used for imagery analysis as well. Leveraging Scikit-learn and the MNIST dataset, we will investigate the use of K-means clustering for computer vision.\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Machine_Learning, Natural_Language_Processing, Vision]\n",
    "- image: images/mnist_kmeans.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Required Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "import sklearn\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Version Check"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python: 3.7.6 (default, Jan  8 2020, 20:23:39) [MSC v.1916 64 bit (AMD64)]\n",
      "Scikit-learn: 0.22.1\n",
      "NumPy: 1.18.1\n"
     ]
    }
   ],
   "source": [
    "print('Python: {}'.format(sys.version))\n",
    "print('Scikit-learn: {}'.format(sklearn.__version__))\n",
    "print('NumPy: {}'.format(np.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Datasets\n",
    "For the convenience, we will load the MNIST dataset from tensorflow Keras Library. Or you can download it directly from [here](http://yann.lecun.com/exdb/mnist/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from tensorflow.keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training: (60000, 28, 28)\n",
      "Test: (10000, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "(X_train, y_train), (X_test, y_test) = mnist.load_data()\n",
    "\n",
    "# Print shape of dataset\n",
    "print(\"Training: {}\".format(X_train.shape))\n",
    "print(\"Test: {}\".format(X_test.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the original dataset contains 28x28x1 pixel image. Let's print it out, and what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x864 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(3, 3, figsize = (12, 12))\n",
    "plt.gray()\n",
    "\n",
    "# loop through subplots and add mnist images\n",
    "for i, ax in enumerate(axs.flat):\n",
    "    ax.imshow(X_train[i])\n",
    "    ax.axis('off')\n",
    "    ax.set_title('Number {}'.format(y_train[i]))\n",
    "    \n",
    "# display the figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preprocessing\n",
    "\n",
    "### Reshape\n",
    "Images stored as NumPy arrays are 2-dimensional arrays. However, the K-means clustering algorithm provided by scikit-learn ingests 1-dimensional arrays; as a result, we will need to reshape each image. (in other words, we need to **flatten** the data)\n",
    "\n",
    "Clustering algorithms almost always use 1-dimensional data. For example, if you were clustering a set of X, Y coordinates, each point would be passed to the clustering algorithm as a 1-dimensional array with a length of two (example: [2,4] or [-1, 4]). If you were using 3-dimensional data, the array would have a length of 3 (example: [2, 4, 1] or [-1, 4, 5]).\n",
    "\n",
    "MNIST contains images that are 28 by 28 pixels; as a result, they will have a length of 784 once we reshape them into a 1-dimensional array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784)\n"
     ]
    }
   ],
   "source": [
    "# Convert each image to 1d array (28x28 -> 784x1)\n",
    "X_train = X_train.reshape(len(X_train), -1)\n",
    "print(X_train.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalization\n",
    "Also, One approach to help training is **normalization**. In order to do this, we need to convert each pixel value into 0 to 1 range. The maximum value of pixel in grayscale is 255, so it can normalize it by dividing 255. Of course, its overall shape is same as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalize the data to 0 - 1\n",
    "X_train = X_train.astype(np.float32) / 255."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Applying K-means Clustering\n",
    "Since the size of the MNIST dataset is quite large, we will use the **mini-batch** implementation of k-means clustering (`MiniBatchKMeans`) provided by scikit-learn. This will dramatically reduce the amount of time it takes to fit the algorithm to the data.\n",
    "\n",
    "Here, we just choose the `n_clusters` argument to the `n_digits`(the size of unique labels, in our case, 10), and set the default parameters in `MiniBatchKMeans`.\n",
    "\n",
    "And as you know that, K-means clustering is one of the unsupervised learning. That means it doesn't require any label to train."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import MiniBatchKMeans\n",
    "\n",
    "n_digits = len(np.unique(y_train))\n",
    "print(n_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MiniBatchKMeans(batch_size=100, compute_labels=True, init='k-means++',\n",
       "                init_size=None, max_iter=100, max_no_improvement=10,\n",
       "                n_clusters=10, n_init=3, random_state=None,\n",
       "                reassignment_ratio=0.01, tol=0.0, verbose=0)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans = MiniBatchKMeans(n_clusters=n_digits)\n",
    "kmeans.fit(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can find the labels of each input that is generated from K means model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([7, 8, 3, ..., 7, 9, 7])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But these are not real label of each image, since the output of the `kmeans.labels_` is just group id for clustering. For example, 6 in `kmeans.labels_` has similar features with another 6 in `kmeans.labels_`. There is no more meaning from the label.\n",
    "\n",
    "To match it with real label, we can tackle the follow things:\n",
    "\n",
    "- Combine each images in the same group\n",
    "- Check Frequency distribution of actual labels (using `np.bincount`)\n",
    "- Find the Maximum frequent label (through `np.argmax`), and set the label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def infer_cluster_labels(kmeans, actual_labels):\n",
    "    \"\"\"\n",
    "    Associates most probable label with each cluster in KMeans model\n",
    "    returns: dictionary of clusters assigned to each label\n",
    "    \"\"\"\n",
    "\n",
    "    inferred_labels = {}\n",
    "\n",
    "    # Loop through the clusters\n",
    "    for i in range(kmeans.n_clusters):\n",
    "\n",
    "        # find index of points in cluster\n",
    "        labels = []\n",
    "        index = np.where(kmeans.labels_ == i)\n",
    "\n",
    "        # append actual labels for each point in cluster\n",
    "        labels.append(actual_labels[index])\n",
    "\n",
    "        # determine most common label\n",
    "        if len(labels[0]) == 1:\n",
    "            counts = np.bincount(labels[0])\n",
    "        else:\n",
    "            counts = np.bincount(np.squeeze(labels))\n",
    "\n",
    "        # assign the cluster to a value in the inferred_labels dictionary\n",
    "        if np.argmax(counts) in inferred_labels:\n",
    "            # append the new number to the existing array at this slot\n",
    "            inferred_labels[np.argmax(counts)].append(i)\n",
    "        else:\n",
    "            # create a new array in this slot\n",
    "            inferred_labels[np.argmax(counts)] = [i]\n",
    "        \n",
    "    return inferred_labels  \n",
    "\n",
    "def infer_data_labels(X_labels, cluster_labels):\n",
    "    \"\"\"\n",
    "    Determines label for each array, depending on the cluster it has been assigned to.\n",
    "    returns: predicted labels for each array\n",
    "    \"\"\"\n",
    "    \n",
    "    # empty array of len(X)\n",
    "    predicted_labels = np.zeros(len(X_labels)).astype(np.uint8)\n",
    "    \n",
    "    for i, cluster in enumerate(X_labels):\n",
    "        for key, value in cluster_labels.items():\n",
    "            if cluster in value:\n",
    "                predicted_labels[i] = key\n",
    "                \n",
    "    return predicted_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[8 0 4 1 7 2 1 8 1 7 3 1 3 6 1 7 2 8 6 7]\n",
      "[5 0 4 1 9 2 1 3 1 4 3 5 3 6 1 7 2 8 6 9]\n"
     ]
    }
   ],
   "source": [
    "cluster_labels = infer_cluster_labels(kmeans, y_train)\n",
    "X_clusters = kmeans.predict(X_train)\n",
    "predicted_labels = infer_data_labels(X_clusters, cluster_labels)\n",
    "print(predicted_labels[:20])\n",
    "print(y_train[:20])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a result, some predicted label is mismatched, but most of case, the k-means model can correctly cluster of each group."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating Clustering Algorithm\n",
    "With the functions defined above, we can now determine the accuracy of our algorithms. Since we are using this clustering algorithm for classification, accuracy is ultimately the most important metric; however, there are other metrics out there that can be applied directly to the clusters themselves, regardless of the associated labels. Two of these metrics that we will use are **inertia** and **homogeneity**. (See the detailed description of [homogeneity_score](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.homogeneity_score.html))\n",
    "\n",
    "Furthermore, earlier we made the assumption that K = 10 was the appropriate number of clusters; however, this might not be the case. Let's fit the K-means clustering algorithm with several different values of K, than evaluate the performance using our metrics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import homogeneity_score\n",
    "\n",
    "def calc_metrics(estimator, data, labels):\n",
    "    print('Number of Clusters: {}'.format(estimator.n_clusters))\n",
    "    # Inertia\n",
    "    inertia = estimator.inertia_\n",
    "    print(\"Inertia: {}\".format(inertia))\n",
    "    # Homogeneity Score\n",
    "    homogeneity = homogeneity_score(labels, estimator.labels_)\n",
    "    print(\"Homogeneity score: {}\".format(homogeneity))\n",
    "    return inertia, homogeneity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Clusters: 10\n",
      "Inertia: 2383375.0\n",
      "Homogeneity score: 0.46576292303121536\n",
      "Accuracy: 0.56465\n",
      "\n",
      "Number of Clusters: 16\n",
      "Inertia: 2208197.5\n",
      "Homogeneity score: 0.5531322770474518\n",
      "Accuracy: 0.65095\n",
      "\n",
      "Number of Clusters: 36\n",
      "Inertia: 1961340.875\n",
      "Homogeneity score: 0.6783212163972349\n",
      "Accuracy: 0.767\n",
      "\n",
      "Number of Clusters: 64\n",
      "Inertia: 1822361.625\n",
      "Homogeneity score: 0.727585914263205\n",
      "Accuracy: 0.7895166666666666\n",
      "\n",
      "Number of Clusters: 144\n",
      "Inertia: 1635514.25\n",
      "Homogeneity score: 0.8048996371912126\n",
      "Accuracy: 0.8673833333333333\n",
      "\n",
      "Number of Clusters: 256\n",
      "Inertia: 1519708.25\n",
      "Homogeneity score: 0.8428113183818001\n",
      "Accuracy: 0.9000333333333334\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "clusters = [10, 16, 36, 64, 144, 256]\n",
    "iner_list = []\n",
    "homo_list = []\n",
    "acc_list = []\n",
    "\n",
    "for n_clusters in clusters:\n",
    "    estimator = MiniBatchKMeans(n_clusters=n_clusters)\n",
    "    estimator.fit(X_train)\n",
    "    \n",
    "    inertia, homo = calc_metrics(estimator, X_train, y_train)\n",
    "    iner_list.append(inertia)\n",
    "    homo_list.append(homo)\n",
    "    \n",
    "    # Determine predicted labels\n",
    "    cluster_labels = infer_cluster_labels(estimator, y_train)\n",
    "    prediction = infer_data_labels(estimator.labels_, cluster_labels)\n",
    "    \n",
    "    acc = accuracy_score(y_train, prediction)\n",
    "    acc_list.append(acc)\n",
    "    print('Accuracy: {}\\n'.format(acc))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(16, 10))\n",
    "ax[0].plot(clusters, iner_list, label='inertia', marker='o')\n",
    "ax[1].plot(clusters, homo_list, label='homogeneity', marker='o')\n",
    "ax[1].plot(clusters, acc_list, label='accuracy', marker='^')\n",
    "ax[0].legend(loc='best')\n",
    "ax[1].legend(loc='best')\n",
    "ax[0].grid('on')\n",
    "ax[1].grid('on')\n",
    "ax[0].set_title('Inertia of each clusters')\n",
    "ax[1].set_title('Homogeneity and Accuracy of each clusters')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As a result, we found out that when the K value is increased, the accuracy and homogeneity is also increased. We can also check the performance on test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.8877\n"
     ]
    }
   ],
   "source": [
    "X_test = X_test.reshape(len(X_test), -1)\n",
    "X_test = X_test.astype(np.float32) / 255.\n",
    "\n",
    "kmeans = MiniBatchKMeans(n_clusters=256)\n",
    "kmeans.fit(X_test)\n",
    "\n",
    "cluster_labels = infer_cluster_labels(kmeans, y_test)\n",
    "\n",
    "test_clusters = kmeans.predict(X_test)\n",
    "prediction = infer_data_labels(kmeans.predict(X_test), cluster_labels)\n",
    "print('Accuracy: {}'.format(accuracy_score(y_test, prediction)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There we have MiniBatchKmeans Clustering model with almost 90% accuracy. One definite way to check the model performance is to visualize the real image.\n",
    "\n",
    "For the convenience, we decrease the `n_clusters` to 36."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x1440 with 36 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialize and fit KMeans algorithm\n",
    "kmeans = MiniBatchKMeans(n_clusters = 36)\n",
    "kmeans.fit(X_test)\n",
    "\n",
    "# record centroid values\n",
    "centroids = kmeans.cluster_centers_\n",
    "\n",
    "# reshape centroids into images\n",
    "images = centroids.reshape(36, 28, 28)\n",
    "images *= 255\n",
    "images = images.astype(np.uint8)\n",
    "\n",
    "# determine cluster labels\n",
    "cluster_labels = infer_cluster_labels(kmeans, y_test)\n",
    "prediction = infer_data_labels(kmeans.predict(X_test), cluster_labels)\n",
    "\n",
    "# create figure with subplots using matplotlib.pyplot\n",
    "fig, axs = plt.subplots(6, 6, figsize = (20, 20))\n",
    "plt.gray()\n",
    "\n",
    "# loop through subplots and add centroid images\n",
    "for i, ax in enumerate(axs.flat):\n",
    "    \n",
    "    # determine inferred label using cluster_labels dictionary\n",
    "    for key, value in cluster_labels.items():        \n",
    "        if i in value:\n",
    "            ax.set_title('Inferred Label: {}'.format(key), color='blue')\n",
    "    \n",
    "    # add image to subplot\n",
    "    ax.matshow(images[i])\n",
    "    ax.axis('off')\n",
    "    \n",
    "# display the figure\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "Through this post, we built the K means clustering model for MNIST digit classification. To do this, we applied preprocessing steps like reshape and normalization. And the model performance is changed in depends on n_clusters. After that, we can make MNIST classifier with almost 90%."
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}