K-Means.ipynb

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    "<h2 align=\"center\">Image Compression with K-means Clustering</h2>"
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    " "
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    "### Task 1: Importing Libraries\n",
    "---"
   ]
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   "source": [
    "from __future__ import print_function\n",
    "%matplotlib inline\n",
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as image\n",
    "plt.style.use(\"ggplot\")\n",
    "\n",
    "from skimage import io\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual, IntSlider\n",
    "import ipywidgets as widgets"
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    "plt.rcParams['figure.figsize'] = (20, 12)"
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    " "
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    "### Task 2: Data Preprocessing \n",
    "---"
   ]
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    "### Task 3: Visualizing the Color Space using Point Clouds\n",
    "---"
   ]
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    "\n"
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   "source": [
    "### Task 4: Visualizing the K-means Reduced Color Space\n",
    "---"
   ]
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   "source": [
    "<a title=\"Incheol [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons\" href=\"https://commons.wikimedia.org/wiki/File:Kmeans_animation.gif\"><img width=\"300\" alt=\"Kmeans animation\" src=\"https://upload.wikimedia.org/wikipedia/commons/d/d5/Kmeans_animation.gif\"></a>\n",
    "<h5 align=\"center\">Incheol [<a href=\"https://creativecommons.org/licenses/by-sa/4.0\">CC BY-SA 4.0</a>], <a href=\"https://commons.wikimedia.org/wiki/File:Kmeans_animation.gif\">via Wikimedia Commons</a></h5>"
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    "**K-means Algorithm**:\n",
    "\n",
    "1. Initialization: Randomly sample $k$ colors from the input image. These are the initial $k$ means $\\mu_1,\\mu_2,...,\\mu_k$.\n",
    "\n",
    "\n",
    "2. For each pixel in the image, assign it to its nearest mean given by $$c^{(i)} := \\textrm{argmin}_{j}\\left \\|x^{(i)} - \\mu_j \\right \\|^2$$\n",
    "\n",
    "\n",
    "3. Update the means using the pixel assignments from Step 2. $$\\mu_j := \\frac{\\sum_{i}^{n}1\\left \\{c^{(i)} = j  \\right \\}x^{(i)}}{\\sum_{i}^{n}1\\left \\{c^{(i)} = j  \\right \\}}$$\n",
    "\n",
    "\n",
    "4. Repeat Steps 2 and 3 until convergence."
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   "source": [
    "### Task 5: K-means Image Compression with Interactive Controls\n",
    "---"
   ]
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