{
 "metadata": {
  "name": "08B_unsupervised_clustering"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Clustering"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clustering is the task of gathering samples into groups of similar\n",
      "samples according to some predefined similarity or dissimilarity\n",
      "measure (such as the Euclidean distance).\n",
      "In this section we will explore a basic clustering task on the\n",
      "iris data."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "By the end of this section you will\n",
      "\n",
      "- Know how to instantiate and train KMeans, an unsupervised clustering algorithm\n",
      "- Know several other interesting clustering algorithms within scikit-learn"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's re-use the results of the 2D PCA of the iris dataset in order to\n",
      "explore clustering.  First we need to repeat some of the code from the\n",
      "previous notebook"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# make sure ipython inline mode is activated\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      }
     ],
     "prompt_number": 0
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# all of this is copied from the previous notebook, '06_iris_dimensionality' \n",
      "from sklearn.datasets import load_iris\n",
      "from sklearn.decomposition import PCA\n",
      "import pylab as pl\n",
      "from itertools import cycle\n",
      "\n",
      "iris = load_iris()\n",
      "X = iris.data\n",
      "y = iris.target\n",
      "\n",
      "pca = PCA(n_components=2, whiten=True).fit(X)\n",
      "X_pca = pca.transform(X)\n",
      "\n",
      "def plot_2D(data, target, target_names):\n",
      "    colors = cycle('rgbcmykw')\n",
      "    target_ids = range(len(target_names))\n",
      "    pl.figure()\n",
      "    for i, c, label in zip(target_ids, colors, target_names):\n",
      "        pl.scatter(data[target == i, 0], data[target == i, 1],\n",
      "                   c=c, label=label)\n",
      "    pl.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python2.7/site-packages/scikits/__init__.py:1: UserWarning: Module argparse was already imported from /usr/local/Cellar/python/2.7.5/Frameworks/Python.framework/Versions/2.7/lib/python2.7/argparse.pyc, but /usr/local/lib/python2.7/site-packages is being added to sys.path\n",
        "  __import__('pkg_resources').declare_namespace(__name__)\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "To remind ourselves what we're looking at, let's again plot the PCA components\n",
      "we defined in the last notebook:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_2D(X_pca, iris.target, iris.target_names)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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avdq35+ihQ0vNOmKRovHFV19QcBWoqaOhndqO0vpSYhqID0GhqsDZX87OUf/Y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\njFkQLuqMMWZB/j+1Gd6mP+lysQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now we will use one of the simplest clustering algorithms, K-means.\n",
      "This is an iterative algorithm which searches for three cluster\n",
      "centers such that the distance from each point to its cluster is\n",
      "minimizied. First, let's step back for a second,\n",
      "look at the above plot, and think about what this will do.\n",
      "The algorithm will look for three cluster centers, and label the\n",
      "points according to which cluster center they're closest to.\n",
      "\n",
      "**Question:** what would you expect the output to look like?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.cluster import KMeans\n",
      "from numpy.random import RandomState\n",
      "rng = RandomState(42)\n",
      "\n",
      "kmeans = KMeans(n_clusters=3, random_state=rng)\n",
      "kmeans.fit(X_pca)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "KMeans(copy_x=True, init='k-means++', k=None, max_iter=300, n_clusters=3,\n",
        "    n_init=10, n_jobs=1, precompute_distances=True,\n",
        "    random_state=<mtrand.RandomState object at 0x1064aa9a8>, tol=0.0001,\n",
        "    verbose=0)"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "np.round(kmeans.cluster_centers_, decimals=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[ 1.02, -0.71],\n",
        "       [ 0.33,  0.89],\n",
        "       [-1.29, -0.44]])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The ``labels_`` attribute of the K means estimator contains the ID of the\n",
      "cluster that each point is assigned to."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kmeans.labels_"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2,\n",
        "       2, 2, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1,\n",
        "       1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1,\n",
        "       0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0,\n",
        "       1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1], dtype=int32)"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The K-means algorithm has been used to infer cluster labels for the\n",
      "points.  Let's call the ``plot_2D`` function again, but color the points\n",
      "based on the cluster labels rather than the iris species."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_2D(X_pca, kmeans.labels_, [\"c0\", \"c1\", \"c2\"])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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BrVqN8Msv3ti69RWMH/89pkyZ4ZB4C6ulPy2F9wVvOP/sDOkHCS2qtkhfpjQr\nlixZgiGjh2CP8x5sx3bEJ8anbiptABCRVoiA5q4G165ew6ZNm574wdysUTNoT2oBCwATIJ2R0KJJ\nC+zfuR+NFY3h+bsnGpgb4MDuA5AkKVv9nL9oPpLqJwE1AFQEjK2NmPPdnPTjSqUS+3bsw7R+0zCo\nxCB8Nekr/Pj9j9lqQxDS2WlK5RPlQxPZNmvWbOp07QmYCJAKxRS2b98zU5l58+ZRp+uXYeOMa9Tr\n3R0UceGVmJjIw4cP8+zZs9l+OrJyrcqp873/XQa3FYgAEINASCCqgOrSasq0Mmpf0tLga2D33t0f\n247RaGTbTm2p0qqo1CjZd0Bfu21QMWjYoNTY/o2zC2jwNNCntA/bdcn+ZsfCiyGnufOFnP0yevRI\nbN68G0ePVoBc7gx3dxMWLNieqYzVagWpzvCOOttLrArPJkkS6tevn6NzH5kZQkAWLANupP47QBOA\nM5fPgEOJ5CLJgAXYunAr9u/fj6ZNm2Y6VafTYfOGzYiNjYVcLoeTk1POOvQYI4ePxMrmK2FUGgEF\nINshg7GxEQkVEnDn3B00adkEwaeDoVS+kH+Ogp29kMMvarUaO3ZswMGDa7F9+3xcvHgSPj4+mcp0\n7doVavUmyGRzACyFRtMOffv2cUzAL5CEhAQMHDoQpSqUQpOWTZ4602TC6AmQtkjAWQDHANUhFVSu\nKrAzwc7ExasXIVfKgSJpJygBeRE57ty588Q6XVxc7JrQAaBmzZrYu2Mverr3RKPERtB56WBrYgO8\nAUtzCyLvRyIkJMSubWaF2WzG6tWrMX/+fAQHB+d7+0LesMvaL09t4Dl9ojQmJgYbNmzA1KkzERoa\nDrW6NJTK29iwYSVatGjh6PAKrVbtWuHAnQNIqZsCWbgMLkddcOncJXh7ez+2/KpVq7BgyQLotDqc\nPX8WNxvcBEqlHTwEGI4bYKxrhK2uDQgDpDUSzp86j1KlSj22vrx2+vRpNGrdCIlvJAIKAGZA+60W\nF09fhJ+fX77FYTKZ0LhFYwTfCYbV3QrZJRlWr1iN9u3bP/tkIV/kNHeKpJ6BzWbDrFlf4scfV+Dm\nzVCo1a5ISooGcB5AMQC74OzcG9HREZkWhhLsIzExEa7urrBMsKQmPABOa5zw0+Sf8Oqrrz7z/Br1\nauCM/xmgQtobe4COzh1x4fIFXL98Ha6erlixZAXatm2bZ314FpvNhrad2uLA1QNIKp0E6YqE9i+1\nx6oVq7JJTBjVAAAgAElEQVT0oJHNZsOvv/6KkJAQVK9eHd26dXvmecHBwZjz1RzcuX8HTRs0xZjR\nY7Bs2TKM+GQEEoMSU6eUXgeK7i6KiJsRT61LyD85zZ1iEC+DGTM+xeefr4XROAfAbSQljQAQgNSE\nDgAtkJJixu3bt3H16lXIZDLUr1//qWtvC1mnUqlS/5ECQAJAgEZmeb72jEkz0GdwHxhjjUAiID8q\nxw7tDsgVctSqVwu7t+62+9BKdsnlcixesBjdenbDzfM3EVAlAEsWLslSQieJnn16YuuxrUgskQj9\nIj0G7B2AeV/Ne2x5i8WCnkE9sX7jerAcgbLA9u+34/ip46hVrRZSvFJSEzoAFAUeRD2wY08Fh7HP\nfdony4cm7MbHpyKBkxlmvEwj4EzgZtrrv6hQOFGhcKVSWZVOTrVYrlwA79+/7+jQC40x48dQX1JP\ntAc1NTWsWL0ik5KSsnz+jh072GdAH1arVY2aqhpiKoipoKa2hm+MeMMuMZ45c4br1q3L8lZyVquV\nkZGRTE5OZmJiIv3K+lHVSEUEgbqqOrbv0j5L9Zw+fZqSp0S8nzaLZiKoMWh4+/ZtkuS9e/d46NAh\nhoeHkyTnzJ1DjY+GKI6Ha8ZPAlU6Fbdu3UrJTSKGp25wrWqgYos2LXL2AxHyRE5z5wt5o/RJVCo1\ngPgM78QhdTm9ilAqywLoAau1NKzWPrBYziA+/jhu3myASZM+cEi8hdGXs77Etx98i/7F+mNil4k4\neuBotp6sbNmyJZb/vBxeRbyQUjkldSqAHEiplIITp3O+9du/C3lNmzEN9ZvVR//3+6Na7WpY+svj\nlzVISEhASEgITp06hZL+JVGqfCm4uLtg0uRJiEY0zC+bgQpAUtck7Ni+A/fv339mDLGxsVC5qh5+\nv9YCKr0KcXFx2LhxI/zK+qFtv7YoW6ksvv72axw9eRQpPimpT8T+e0WuBOQKOWrWrIl5c+ZBv0IP\n+Sdy1NXWxcplK3P88xEKEDt/uDwiH5qwmyVLllKSfAl8R+A9AhIBLRUKX8pkzQnUJdCWwMYMV/Nr\n2aRJR0eHLvzHmLfHUFNLk3qFOg1U11dz4LCB2a7nxIkT9PX3pUwuY1HfotQYNMQ7aVe9I0CtQcv4\n+PhM56xctZI6Jx0NRQyUqWVE/bTyI0GNs4aSr/Twyvl9UC2ps/RtLzY2lh5FPSjrJCPeBuUvy+nr\n78vY2FjqnfXE0LQ6x4A6Fx3Hvj2Wmkoawg1EYOr8fXlVOZu2bJpprr695uML9pXT3Cmu1NPExcVB\no1Hjrbd64ZVXDmHYsHjMmjUdkuQHq/UqyHeRujhHTQA/AzADMEGjWQy5PAVz5sx56lQ5IX/NmDYD\nlZSVYPjRAKeFTvA3+uOLmV9kq47ExES0atcKYQFh4PtEZP1IpJhTHl4pewEKnSLT//dbt25h0NBB\nSOqbhIThCWAQgTNI/XXxAJTllZBMElTbVcAJQD5PDqVOidHjRyM29unrtzs7O2Pfzn2oFlENhkUG\n1Emug3079iEqKip1aYQSaQVdAbWPGs2aNEMtr1qQ1BKU/yih/F2J3rV6Y9O6TZnG8MVN/8JF3CgF\ncPfuXdSu3QQxMWUAaKHRHMfRo3tx+vRpKJXlAKgANEfqd9gLAEIBeEAuB8xmOQ4c6IfDh8/i449f\nwqlTh1GiRImntCbkBycnJxw7eAynT5+GzWZDjRo1oFarn31iBhcvXoRVawX+XeqlCoCdAIKRev/8\nEmBJsmD16tV466234OzsjEuXLkFVTAX8uytiaaQOf8QCMAC8Rcz/bj7W/bkOv636DZa6Fhj9jVh1\nahVCOoXg8N7DT71pWrlyZZw+djrTe8nJyZCZZcBNAH4A7gOmWyZUq1YN+3ftx8mTJ5GSkoJatWpl\ne4kD4Tlk528Mj8iHJnJt+PAxVKlGpQ+pyOWfslOn3rx16xYNBi8CawisIuBLpVLDjh178rPPZrF2\n7WYEFqWfp1CM5//+N87R3RGywGw289atW0xJSXlimdDQUGqdtMS7acMaE0CVQUWNXkOVk4pQgagN\nagI09K/oz/j4eF69epU6Fx0xNu2ct0AoQYWbgpCBcqWc02dM55YtW+hc3vnh0gFTQa2zNsdLBmzd\nupUGVwOdSzpTa9By/oL5Of3RCAVETnOnGH4BcPNmBMzmuumvbbY6CA29jeLFi2Pr1nVwcxsOYACA\nAFgstfDnn5vRvn07JCYmAyiXfp7VWhZRUTH5Hr+QPYcPH4a3jzf8K/vDzcsNGzZseGw5X19fjB45\nGvoleug266BfoseoEaMQez8WGoUGGAygE5DSNQWRikisWrUKZcqUwYxpM6BbpIPLby7QLdOhTp06\nkJeQA5MA2ygbZv0wC4cPHwZT+HC5XQtgs9iy/W3iX61bt0b4jXDsWbcHoddC8fqw13P2wxGeeyKp\nA2jdujEkaR6AaADhUCjeQGhoGLp06YNSpUohNtYC4EsAGwAcBNAF7dt3Qffu7SFJkwBcB3AakvQ5\nuncXT+QVZMnJyWjfpT0etHyA5LHJMPYyIqh/EG7fvv3Y8jM/nok/f/sTs/vPxoblGzB75mxoNBqY\nUkypK0KmsThZcOPGDbzU8CVMmz4NPj4+mDV2Fi6evYjIe5EwNzKnjuI5A8bqRoTeCoV/EX9o1mmA\nE4C0SkLPV3vC3d09x31zcXFBzZo14eXlleM6hOefSOoARo58CwMG1INCUQxARZCBePBgOf76qwwa\nNGiZtpBXnbTSMgAN8OBBEqZPn4QhQ+rBxaUhPDw645NPxqBHj+6O64jwiJ8W/oRqdaohoH4AVq9e\njbCwMFhklodPnfoAqmKqp64xExgYiLfeeivT8hDtO7aHdrM29TrgIiC/IMeCxQvwj/M/ML5hxNWy\nVzFp6iS4urqiaNGimZYCVt9Vo1TJUjiw6wAmdJuAXi69MHP0TCz5aUme/RyEF4idh4EekQ9N2M2l\nS5coST4ErOnj5M7OtanXFyXQhUASgQgCZdmiRUtHhys8w6LFiygVkVKX5+0DSh4SV69eTY1eQ/wv\nbSz7HVDnquPFixezVXdCQgL7DOhDz+KeLFe1HBcvXkxDUcPDMfLpoLO/M/fv388TJ07Qyd2J+tp6\nGioaWLZSWcbExORRr7Pv7t27PHfuHI1Go6NDETLIae4Us18ykCQJNlsKABNSN9CwwmZLxIoV89Gz\n52CYTAYAMhQv7odt27Y+sR6bzYaVK1fi2rVrqFmzplgkyUG+X/Q9jC2MgH/qa2OCEctWLcO8b+Zh\n5NiRUPmpYAm3YPzY8ahQocLTKwMQFRWFGR/PwM3wm2jdvDV+WfRwk+yIiAiYR5qBJAA6AGbAEmuB\nq6srqlatigunL2D79u3Q6XTo3LlzgZmF8uWsWZgxdSqKqtWIVyqxfts2vPTSS44OS8gNO3+4PCIf\nmrAbm83Gzp17U5JeJrCQWm0P1q0bmP5wxv379595NWOz2dilSxD1+rqUyydQry/PiROn5kf4wn80\nadWEeCXD5hRtwF79epFM/Va2Zs0anjp1Kkt1xcXF0beML1X1VUQ3UCotccSoEZnKjBg9gvoSesqa\nyKgvpeerfV7N9sYf+en48eP0kSSGpX0tXQ2wlLd3eswmk4knTpzg6dOnabVaHRztiyenuTPXGXfz\n5s2sUKECy5Yty5kzZ9otMEcxm82cNesLdu/en1Onzsj2V9Jjx45Rry+TNlRDAnepVjuJ9WEcYOfO\nnanTC9uAaAnqXfQ8ceJEjupauXIlDZUzDK9MAJVqJc1mc3oZm83GtWvX8oMPPuCKFSsKfCL8+eef\n2ddg+PfRaNoAapVKxsfH8969e6xVoQIrGQwso9ezVYMGYngmnzkkqVssFvr7+/P69es0mUysUaMG\nL1y4YJfACjKTyfTEX/Bt27bRxSUwwzICNkpSCV6/fj1/gxRIkgcPHuSAIQM45PUhz7wqv3HjBo8e\nPcq4uLhHji1btoyGGhmS+mRQoVI8dZ57QXfo0CH6SRLvpf2ybgVYzM2NNpuNQ/r04Ui1mjaAFoA9\ntFpOmzzZ0SG/UByS1A8dOsQ2bdqkv/7000/56aef2iWwgshms3H06HeoVGqoUGjYpk03JiQkZCoT\nFRVFF5eiBJYRuEe5/FP6+VUW62sUcO9OepdaZy2dSznT1cuVx44dy3T87t27dC/iTnlrOTEQ1FXR\nsXuv7g6K1n6mvPsuvXU6NnBxobeTE/fs2UOSbFytGnc/vDLhLwB7tc/aapKCfeQ0d+bqRumtW7fg\n6+ub/rpEiRI4cuTII+WmT5+e/u/AwEAEBgbmplmHWbz4Z/z4405YLLcAOGHv3v4YM2Yifvzxm/Qy\nHh4e2LVrE3r3Horw8BGoUqUmVq/eJNbXKMD27t2LeQvnIfnNZCRLycB5oGvPrgi/Hp5exsvLC0cO\nHMGo8aMQfi4crdq1wqcfferAqFNZLBbs3LkTixYswKV//oGnpyc+mDMHjRo1ytL5Mz77DP2HDUNE\nRAQqV64MDw8PAEDlgACsvHQJzUwmWAD8odOhVu3aedgTYc+ePdizZ0/uK8rNJ8nvv//OoUOHpr/+\n5Zdf+L///c8unzYFUVDQEAI/ZBhaOUJ//1qODkvIpR9++IFSPSnTI/syuSzTeHlBlJKSwpcbNmQl\nlYqBAD0BfgTQU5J4/vz5XNUdHR3NelWr0t9gYAlJYrtmzbK1rr2QeznNnbm6Uvfx8UFYWFj667Cw\nsOd6Matr165h8+bNkCQJ3bt3h7Ozc6bjpUoVh1r9N0ym1wHIIJP9DV/f4o4JVrCbSpUqQXZdBhiR\nuuNSMFC8ZHEolVn/87BarVi4cCEunTuHKgEBGDhwYPp0R3sxGo3YsWMHzGYzmjdvjpUrV0J+6hTO\nms1QAFgKYD6A/ikpWLd2LSpXrpzjttzc3HDgn39w6dIlKJVKlC9fPku7MwkFQG4+ScxmM8uUKcPr\n168zJSXlub5ReuTIERoMXtRqh1Cv78ySJSs+MmMlJiaG5crVoJNTMzo5daGrazEGBwc7KGLBnt57\n/z1qnbR09nOmm7fbI2PqT2Oz2dirUyc2lSR+BrChJHFgr152nc4YHR3Nav7+bOrkxHZOTvT19OSb\nr7/ODzOMe18HWALgYLWan3/+ud3aFhwjp7kz1xn3r7/+Yvny5env789PPvnEboHlt9q1AwksTR9a\nUauHcMqU6Y+US0xM5Nq1a/nbb7/xzp07T60zPj6eH3zwEQcMeJM//7ykQM9ZFlJXZTx+/Pgjm148\ny7lz5+grSUxK++VJBOit0/HatWt2i23CuHEcljYbhQA/kcvZtFYtVtLreQegFeAogFUAlvDwyPFq\nj0LBkdPcmesnStu1a4d27drlthqHu3v3Hh4unA2YTNVw+3YI4uLiEBQ0FNu2bYQkuWDOnJkYPHjg\nM+tLTk5G3brNce1aOaSkNMTq1XNw6tQFzJkzM+86IeSKr69vphv/WZWYmAh3pRL/brqnA+CqUCAh\nIcFusYVfvYqXTab0Xeka2Wz4MyUFHlWqoMzRoyAAtUKB3gMH4v0PPkhdb0Z4IRXaBb1I4uzZszhw\n4ADi4uKeWb5du5bQ6aYDiAEQAkmahw4dWmLQoBHYuVMLi+UO4uK2YuTI97Fv375M55pMJixcuBAf\nffQRdu/eDQDYvn07wsM1SElZDuB/MBq349tv58JkMtm9r4JjVatWDYkGAz6Ty3EZwAyFAgoPjywt\nPZBVDVq2xAJJQiyAFABfa7VQubjgxtGjOATgNIBSVivCQkPh4+OT6dzQ0FDMnz8fS5YsydLfgvCc\ns+8XhkflQxOPsFqt7NHjNUqSL11c6tHDw/eZswGMRiN79hxAlUpHvd6ds2Z9QZJpc87D0odlZLL3\nOXXqtPTzTCYT69VrQUlqRbl8IiWpJL/66luuWrWKTk6dM8yUMVGp1GX7q72Q/zZt2sTeHTvytVde\n4ZEjR7J0zrVr19iuSROW9vJip+bNGRoaateYrFYr/zd0KDUKBXVKJbu3a8da5ctzYYYx9Z0AvZXK\nTOf9888/9HZy4gBJYme9nuVLlGBUVJRdYxPyRk5zZ6FM6suWLaNeX4+AMS0R/8AaNRpl6dz/jnv7\n+VUlsDn96VCNpgv79u3LnTt30mazcf369TQY6mVY2fEq1Wo9IyMj6epajDLZtwROUqN5jc2biw2q\nC7o1a9awuE7HRQC/TpsemJ2bpnnNaDSmXxg0qFmT72VI6j8C9FarM5Vv07AhF2Qo86ZKxUnvvuuI\n0IVsymnuLJTDLyEhIUhMfBmpo5sA2RlXr17O0rn/nba1YMEXkKTXoNG8BbW6NUym3Vi71orOnd/C\n4MEjEB0djdRlAP/9UfrBajXDxcUFhw7tRMOGf8LPbwB69tRh/foVduujkDe+/fhjfJeUhEEARgKY\naDRiwVdfOTqsdDqdDgaDAQAwc+5cfIXUDZhGARgNoENQUKbydyMjUSPD6+pmM+6lbQhy8eJFvDNm\nDMaNHInjx4/nR/hCfrDzh8sj8qGJR/z+++/U66sTeJC25+hnrFu3RY7rO3/+PGfPnk2lUkPgVNpF\nTzz1+jL8448/qNd7EthIIJRyeUPq9b7s23cob9++bcdeCfmhWUAAN2W4sp0EsHzRomxYpQonjh3L\n5ORkR4eYye7du+nv50e1TMaaGg29dTp+PG1a+vG3R4xgJ52OMQBvAKwsSVyxfDnPnj1LL4OB78tk\n6Q8s7d2713EdER6R09xZKJO6zWbjm2+OoUbjRoPBn76+FXI9vSwiIoJarWeGMXLS2bkT16xZw927\nd7NUqaqUy10olzcnsJFK5QQWK+bP2NhYO/VKyA+/LF3K0pLENQC/ASgBnC2TcS/ADjod+/fs6egQ\nM0lOTqabJPFo2i9lJMBiOh3PnDlDkkxKSuLAXr2oUSgoKZXs3b07zWYzh/Xrx09lsvRf5iUAOzRt\n6uDeCBmJpP4Yt27d4oULF2gymXJdl9VqZfHiZSmT/ZA2fr6JOp07b9y4QTJ1JxylUksgMT3pOzm1\n4tq1a3PdtpC/VixfzrYNGrBmxYrsptWmJ754gGqF4pHlAw4fPsxxI0dy0oQJ6b8P+SU8PJxFdDpm\nvNro4OzMdevWpZf5du5cltDpOEapZEO9np1btWKfzp35U4Zz/gLYonbtfI1deDqR1PPBhQsX6Otb\ngYCBgESlUs++fYfQYrEwMTExLaknZEjqLTL9cQnPlxUrVrB9hvXG7wLUKJWZVtz866+/Uoc8AL4t\nl7Ooi8sTvxUmJibyyy+/5PgxY7L0YR8eHs4hffqwTf36nD5p0mOX+TWbzSzm6sqNaTFeBOil0zEk\nJIRk6uwsSa3mtbTjZoDVDQZOnz6dJSWJOwAeTBuW+eG773L4kyp4CsODfiKp55PBg0dQo3mNgJlA\nPCWpKefO/Zok2avXQOp0LxNYQ6XybZYoUf6xa3MLz4fY2FiWL1GC/1Op+DPAlySJE8aMyVSmcfXq\nXJvhivdduZzv/KcMmTpM0qB6dXbVavkpwAqSxI+nP/rEss1m4/379/ngwQP6FyvGiUolNwJsq9Px\ntR49HhvnwYMHWdTFhaUNBjprNPx54cL0YzExMdSrVOlPohJgdycn/vbbb/xl6VLWLleOAWXK8Ksv\nvywUiTAuLo7d27alWqGgh8HwXH9QiaRuZ5cuXWKTJu1YokRl9uw5gNHR0STJihXrETiQ4dvuQnbv\n3p9k6lXR9Okfs1mzThw0aDgjIyMd2QXBDu7evcu3R45k3y5dOP/77x9JfLX8/XkoQ8L8EuCIIUMe\nqWfdunVsaDCkJ9dbSN1lKONV/7Fjx1jSy4vOajUNWi1bZBhWSUwrn5iY+Ng4k5KSePny5cfew6lb\npQqnKBSMSRtm8dTrefPmzSz1//bt25w5cyY/mD6dZ8+ezdI5jtS/Rw++ptEwAeAFIPXbyI4djg4r\nR0RSt6Po6Gh6eJSgTDaXwGmq1a+zTp1A2mw2dujwKhWKGRnmrffje+9NcXTIgoN88sEHrCtJPA5w\nG0BXgM5aLRf99FOmcsuXL2ePDEM5ZoAahSJ9B63k5GT6uLvz97TjHwOsn+HDIuE/5bMjPDycLevV\no16tZnkfH+7atStL54WGhtLH3Z2vq1R8Ry6npyRx//792W4/P/m4ufF6hp/bdJmMk997z9Fh5YhI\n6na0ceNGOju3ynA1bqFG48q7d+/yxo0bLFKkNJ2dA+nk9BKrVKkrhlheYFarlR9Nm8YiWi19AS4H\neBZg8f8kwPDwcHo7OXEpwMsAh6rVbNukSfrxy5cvs3SGpB8H0E0m41iFgmsAtpIkDurdO8/6YbPZ\n+POiRWzfqBF7tG3LI0eO8O1Ro/iOQpEe0zKALevUybMY7CHA35/r8XDP1e5aLefOnevosHJEJHU7\n2rlzJw2GmhmeEn1ApVJi79596OZWmu7uZTho0CDu2LGjwM1bFvLe4kWL2DkwkEGdO6dvZO0mSbyT\ncWxdoeBHH32U6bzjx4+zcY0aLO3lxddeeYUPHjxIPxYTE0NnjYZX0s6PAuil1TKoa1d2ataMn3zw\nQZ5u2vHdt9+yfNpUzh8AekgSX+nQgfMy9OkgwDrly+dZDPawa9cuekoSh+l0bK3Xs1bFio9sOfm8\nEEndjkwmE2vVakKtthuBryiTVSEgEdATmEtgBYFi/PDDjx0dqpCPbty4wXLFilEO0AXg4LTx6XPn\nzrGCjw+3ZbhCbCtJXLBgQbbqn//ddyyi07GHkxNLShKn5NHj/EajkePeeov1K1XiK61bMyQkhAFl\nyvBAhgQ+DeArnTqxlCTxCMBLABtqtRw+dKhdpgjnpUuXLnHevHn85ZdfcjRcVVDkNHfK0k7OMzKZ\nDHncRJ5ISkpC3779sWHDXlitQQCWABgDYHpaib1wdx+I+/evOyxGIX/VqVwZXYKDMQnAPwDaAegO\nwHncOLRo3Rr9XnkFXUmEKBSwlC2LHYcPQ6vVPr3S/zh37hzOnTsHf39/1KlTJw96AbzasSOsO3di\nbHIyDsvl+MrVFR7Ozvjmxg00TSszFUDy2LEoX7EiZk6divtRUVDL5XBVq+FaqhS27N8PNze3x9Zv\ntVqxaNEiXDp/HlVq1MCAAQPsvgvUiyDHudOOHyyPlQ9N5JlKleoT2JF28eJBYHqGcfZ9dHUtKZ4Y\nfUEYjUaqFYpMUwP7AewM8J2xY0mSwcHB/P777/nrr78WmGG5y5cvc/369Tx37hzJ1H5oFIr0DT0I\nsJOTE18fNoxlJIkrAM7N8A2EJCeMHcu+Gg2tad9CXlerH5nhY7PZeOHCBf7999/s0b49m0gSZwJs\nkHYvoDBMl8xvOc2dIqk/RdWqjQj8lfa7Py5t+OV7Ar8T8KFcrqNKJaU/gCQUXjabja6SxFNpiTAF\nYCWAzhpNgZ3qt+jHH+ml07G9szOL6nSc9fHHTElJoUapZHSGoaLmBgPXrFnDN4cNo6dSSWe5nO2a\nN08fi+7aogVXZ/gQ2Ayw5UsvpbdjsVjYr3t3+kgSqxsMNAA8n2HWjr13gXpR5DR3iu9ETzF58khI\n0usAFgMoBsAM4D0olW9BofCBzRYLs/kO1q69grlzv3nk/JCQEIwZ8w7efHMUDh06lM/RC/Ykk8nw\nw8KFaC1J6KfRoLpCAbO3N3bs34+qVas6OrxHxMTEYOzIkTiQlIRNcXE4mZSEzz/6CGFhYRg+bBja\nShIWAXhDrcY9b29otVpsXL4c2ywWXLfZ4Hz4MEYNHQoAqFK7NlZptbAAsAFYqdGgSq1a6W0tXboU\n17ZsQYjRiNMJCZiC1BUjAUAPwE2ptOsuUMIz2PnD5RH50ESe2rBhAzt2DGLXrn24fPlyRkVFsUqV\nhgT2ZhiKWcJOnYJIkleuXOHWrVu5c+dOOjl5USabRGAmJcmbW7ZscXBvhNw6e/Ysf/rpJ27atIlW\nq/WpZXft2sUqfn50lyR2adWK9+7ds3s8JpOJE8eOZaUSJVi3YkVu3ryZZOrKouUyTJEkwMYuLty9\nezetViu/nzePr3XrxgnjxjE6OpqT33uP0zIs8HUNYAk3N5Kpyxu83KgRfSWJpfR6Nq5ZM9Ow44Tx\n4/lRhnauAfRMm7o5Q6FgJT+/xy5xIDxdTnOnSOo50KlTbyoUH6Q/gKRWD+bbb0/k3LnfUqfzootL\nCyoULgS6ZfibWs2XXsr58r/C8+Xq1av0lCT+CfAOwJEqFVvWr2/3dsaPHMnmacNCG5C67suxY8eY\nmJhIb2dnbk77Bfw7bZrikzak/vLLL/lqhsXLNgGsUaZM+nGr1crg4GBeuHDhkaHGJUuWsK5ez4R/\nH5xSKFjCyYmlPD3ZoVkzu+8C9aIQST0f3bx5k97epahUNqBMVpVarSfXrFlDnc6DwI20v4uLBJwI\n3E97vYvFipVlmzY92K/fMF65csXR3RDy0OLFi9lXr8/0BKlKLrf7DdRSnp68lOEq+X2ZjFMmTyZJ\n7tu3j0VcXFhUp6ObJHHD+vVPrCcuLo7V/P3ZSZL4P7WanpLErVu3ZikGq9XKIX370kurZUUnJ1bw\n9eX169ft0b0XWk5zp9KRQz/Pq5IlS6JUqdKIjlaBHIjkZDNee20oVKrySErySytVAYAbgN8ABECl\n6o/79/XYurUb5PIr2LixMc6dO4YSJUo4riNCjpnNZiiVykd2yvqXq6srrslksCF1T6ybANRKJdRq\ntV3jkHQ6RAIon/Y6UqmEv14PAGjSpAnC7t1DZGQkvL29odFonljPrVu38Oa4cQgODkapUqWwu02b\nLN8rkMvl+GnZMlz/8EPEx8ejQoUKT20rJ3bs2IEvpk2DKSUF/YYPx6AhQ+xaf6Fi5w+XR+RDE/ku\nJiaGKpWegCV9eMVgaE2NxpXAsbT39lCrdWX58i+xTJma1Ok8CVxIL69WD+Ps2bMd3RUhm8LCwtiw\nRg0qZDJ6Ojlx9apVjy1nMpnYvG5dvixJnCiXs6Qk8btvvrF7PL+uWMHiadMH31IqWdLLK9sLya1f\nvw7giHoAABb0SURBVJ5eksT+ej1rGQzs3KpVgZrNtX//fnqnTbf8E2A5SeKP8+c7Oqw8l9PcmeOM\nu2rVKlauXJlyuTz9UWl7BlaQJSUlpa2dfjctSVtpMNTllClTKEluNBhK0WDw5LZt29LPcXEpRiAk\nPamrVCP42WefObAXQk40qF6d0xQKWgAeSxvD/nc+93+lpKTwp59+4ocffsjdu3fnWUw7d+7k2BEj\nOG3KlCeOmT9NMVfX9JUmzQDrGgz8448/8iDSnHmjf39+mWGIaRvARlWrOjqsPJfvST04OJiXLl1i\nYGDgC5fUSXL8+EmUpCoE/t/enYdHVd97HH/PZCOTsIQtRIJAs5AQYBIaCEvVQJhIgqFAg7JVLFZU\nrFweb1FaawWuRBaxbggViiCPPi5VjAuhiVzCJhjDEopY4BIDWQhbBJMM2Ybf/QPMg2RxMpmZM0y+\nr78yMyfnfOZL/D7H3/md33lYeXvHq0GDhqvq6mpVUVGhTpw40eD25Cef/IsyGIYo2KJ0uleUv383\ndfLkSY3SC1vU1NQoT71e1d3QYB4wGNTatWtt3ufRo0fV7+67T00eO1a98/bbdkxrHYvFojz0elV9\nw3ea7eurVq1a5fQsTXnswQdV2g350kHdFR2tdSyHs7V32jymHhERYZ/xn1vQwYMHyc//jpqaIjw9\nc4EyOnWKQKfT4efnR2hoaIPfef75RXTt2pkPPniRLl06sXz5Nn7xi184P7ywmaenJx18fTlcWUkM\n1+5aOKzXMykw0Kb9nTx5kruGDuW/KysJVopnd+7k+7Iy5vzhD3bN3Ry9Xs/I6Giey8tjocXCUSAd\neGT4cKdl+DkPPf44Y959F6/KSjoCCw0GXvvrX7WO5bJavfbLqFGjWLlyJYNvuBnhJwfQ6Xj22Wfr\nX8fHxxMfH9+aQ2oqNzeXu+5KwmzuBjwCzAVq8fVN5oUXJjJnzhyNEwpHev+993h81izGAXl6Pb1H\njuSfW7bYtLbJomef5YclS1hpsQCQA8zs2ZNvi4rsG/pnFBcXc29yMl8fOYLBx4dVb7zB9BkznJrh\n5xw6dIjXVqyg5soVps2ezdixY7WOZHfZ2dlkZ2fXv160aJFNa780e6ZuMpkoLS1t8H5aWhopKSlW\nH2ThwoUtDuaqli59FbP5aeAVri3pBODFlStj+M9/TmqYTDjDvffdR2T//uzdu5cJPXpwzz332LxY\nlcViwevq1frX3tffc7aePXuyJy+P6upqvL29G53Rc/XqVQoKCvDy8iI4OLjJWT/2cuDAAR5/4AEK\ni4sZNmwYr2/cyLq333boMbV28wnvokWLbNpPs009KyvLpp26sytXqoFOQDSwDlgK/ICf3wcMHTpP\n02zCOQYOHMjAgQNbvZ+p06dz50sv0aeykl7An/38eGju3NYHtFFT0xAvX77Mr8eM4cTRo9Revcqd\no0bxzscf23165o9KS0tJio/nhfJyfgX8LSuL1KQksr/+2iHHczd2WfullSM4t5RHHpmOwfAMMAn4\nJ9AeD48gpk4dzvTp0zVOJ24lkZGRZGRnk5WYyCtxcTyydCl/XLBA61gN/GnePEIOH+a02UxhVRXm\n7Gz+tmKFw463e/duhul0/BboC7xUW8v+vDwuX77ssGO6E5svlG7evJm5c+dy4cIFxo0bR0xMDBkZ\nGfbM5pJSUlJYt66SBQsWU1h4Hm/v0Xh4HKW6ukbraOIWFBsby4f/+pfWMZp1ODeXJTU1eAAewNQr\nV8jYt89hx2vfvj3FStXfuHUOqFOqxWvTt1U2n6lPnDiRwsJCrly5QmlpaZto6KdOnWLgwGtn5KdP\n56PUdqqrP8FszmPz5h3s2LFD64hC2F1oZCSfe3mhuLZKY0a7doQ6cGXKhIQEOvbvzz2+vjwHjPLz\n488LFtj9LlV3JU8+aoHIyFiOH5/E1auPArcBZuDaBSN//6msXj2OGS42a0CI1jp79iwJw4fjc+EC\nVUrROSyMrbt24Xd9OQJHqK6uZt26dRSdOkXciBFMmDDBYcdyVbb2TmnqVqqoqCAgoBt1dT828ijg\nMWAOcARf3wRyc7fTv39/TXMK4QhVVVXk5ubi6elJbGwsnp6ybJSjSVN3sKtXr+Ln14mqqq+ASOAI\nOt2vgFqUqkOnU0ybdj8bNqyRP3ghRKvZ2jvlyUdW0uv1rF79GgbDaAyG3+Pvfz99+tyOt/cdwEWU\nKmPz5nxWrPib1lGFEG2YNPUWeOCB+9m9ewsvvjiEd95ZREBAV6qrnwD8AX/M5ofZvv0rrWMKF1NW\nVsa948bRMyCAIRER7HPgzBFXVVlZyUMzZtC3e3eGRET85M5JYV8yTtBCMTExxMTEALBp04fk5e3G\nYkkEwMtrNyEhsj66+Kn77rmH8Nxc9tbWsu/SJcabTOw/epRevXppHc1pZs+YgWXrVjKrqvjm/Hkm\njxvH7gMH6Nevn9bR3I6MqbdCYWEhQ4bchdkcCtTQufM5cnN30rVrV62jCRdhNpvp3KEDlRYLHtff\nu9ffn1+vWdOmblYzeHtzpraWjtdfP9KuHVHLl/P4449rmsuV2do75Uy9FXr16sWxYwfZvn07er2e\nhIQEh07zErceHx8f9Ho9JRYLvbg2z/s00KFDB42TOZd/u3YU3dDUi/R64vz9Nc3krmRMvZU6duzI\nhAkTGD9+fKMN/YsvviAqaji9ekUxb95T1NbWapBSaMXDw4PFixczymBgEZDi64tPv35uucpgc/5n\n2TLGGQwsAab5+HA6KIjJkydrHcstyfCLAx06dIiRIxMxm98A+uLr+0ceeGAgr7/+otbRhJNlZGSw\nZ9cubgsOZtasWW3ylvfMzEz+NzOTrj16MHv27Db3fystJfPUXdCiRYtZvNjM1atLr7+TT0DAXZSV\nFWqaSwhH+vTTT1m7ciU6nY45CxZw9913ax3pliRj6i7Iz8+Ap2cBNfVrfZ3F19egZSQhHOqTTz7h\n0SlTeOHKFSzAzK++YlN6OiaTSetobYacqbeAxWK5/ii7fEJDQ4mJiWn2YQHnz59nwIAhlJUlU1fX\nF4PhFVavTuP++3/rxNRCOM/4+Him7djBlOuv1wOZycm8+/nnWsa6JcmZuoOdOXOGYcMSOH36HFCF\np6cvEycm8957G5ps7N26dePw4a9YtWo1Fy+WMHHim4wZM8a5wYVwIp1Ox43PbrIAOhufDCVsI2fq\nVrr77klkZoYAy4FyYAze3ud5++0VpKamapxOCNeQkZHBrNRU0sxm6oCnfX15f8uWW/q5xFqRtV8c\n7NChPOAhrq3Q2AFIpba2GydPynNJhfhRUlISGzdvZmtSEtvGjZOGrgEZfrFSSEgI5859DoQDtUAm\nnp4F9UsGWKOuro4vv/wSs9nMsGHD6NSpk6PiCqGZxMREEhMTtY7RZsnwi5VOnDjBsGGj+f77AJS6\niE5XzpNPzmPp0sVW/X5VVRXx8eP45pvz6PVd8fb+P/bs+YLw8HAHJxdC3IpknroTlJeXk5OTQ0VF\nBSNHjmzRGi8vvLCSZ57ZSVXVR4AHOt1LjBjxL3bvdv/HAAohWk5mvzhB+/btSUhIsOl3jx8voKpq\nFFxf1kmpMRQU/N2O6YQQQi6UOs2IEb/EYHgHuAxcxcvr7wwZ8kutYwkh3IwMvziJUoqHH/4vNmx4\nEw+PdkRE9OOLL9Lp0qWL1tGEEC5IxtRvEZcuXeLKlSv06NGj2btRhRBtmybz1OfPn09kZCRGo5FJ\nkyZx+fLl1uyuTejUqRNBQUHS0IUQDtGqpp6YmMg333xDXl4e4eHhPP/88/bKJYQQwgatauomkwn9\n9XUd4uLiKCoqsksoIYQQtrHblMb169czderURj9buHBh/c/x8fFy27AQQtwkOzub7OzsVu/nZy+U\nmkwmSktLG7yflpZGSkoKAEuWLOHAgQN8+OGHDQ8gF0qFEKLFNJv9smHDBtauXcu2bdsafUSXNHUh\nhGg5Te4o3bp1KytWrGDHjh1t8pmLQgjhalp1ph4WFkZNTQ2dO3cGYPjw4bz++us/PYCcqQshRIvJ\nzUdOcu7cOSZP/h1ffbWLLl16sGHDKnn+ohDC7qSpO8nQoaM4eHAwdXV/Ab7GYJhOXt5eQkNDtY4m\nhHAj8uQjJ6iurmb//j3U1S0HAoBEdLqx7N69W+toQggBSFNvES8vL7y8fID86+9Y0OmO119TEEII\nrUlTbwG9Xs9LL72IwTAaT88/4uc3hkGDOpKcnKx1NCHc2pkzZ/jss8/4+uuv3Wo41xFkTL0Ffvjh\nB7Zt28a3335LXV0dvXv3Ztq0aXh5eWkdTQi3tX37du5NSeGXHh4ct1hImDCBNzZtcvtF8eRCqYOV\nlJQQG3snFRV9AUXHjoXk5u4kMDBQ62hCuLXe3bqx9sIFEgEzEOfvz/L33ycpKUnraA4lF0od7Mkn\nn+X8+VTKy7MoL/+C0tIU/vSnRVrHEsKtWSwWii5e5MeHSBqA4RYLBQUFGqZybdLUrZSfX0Rd3a/q\nX9fVjSQ/X1alFMKRPDw8MIaFseb6UMspIEOnY/DgwdoGc2HS1K00evRwfH1Xce1/ACsxGFYzatQw\nrWMJ4fbe/fRTXr7tNoJ8fYny9ubJ554jLi5O61guS8bUrVRTU8P06b/n448/QClFaupUNm16Qy6S\nCuEEFouFkpISAgIC8Pf31zqOU8iFUieprKxEp9NhMBi0jiKEcGPS1IUQwo3I7BchhBDS1IUQwp1I\nU3cApRRms1nrGEKINkiaup1lZWUREBBEhw4B9OrVj3//+99aRxJCtCFyodSOSkpKCA83Uln5T+BO\n4C26d19IUdFxmfooRCOUUuzatYtTp04RExPDgAEDtI7kMuRCqQs4fPgwnp7RwF2ADphJRUUdRUVy\n56kQjZk7eza/T04mY84cxsTFsWH9eq0j3fLkTN2O8vLyGDHiHszmI0BH4Dt8fIycP19M+/bttY4n\nhEvJyclhyujR5FVW0h44BsT6+HDh8mV8fHy0jqc5OVN3AUajkZkzJ+PnF4uf328xGEayYsUyaehC\nNKKkpIQoDw9+/K+jH9BOp6OsrEzLWLc8OVN3gJ07d5Kfn4/RaCQmJkbrOEK4pFOnThHbvz+fmc0M\nBdYDzwcFcbyoCL1ezjfljlIhxC3ns88+Y+aUKZirq+kdFMRHW7fSv39/rWO5BGnqQohbklKKysrK\nNrNQl7WcPqb+zDPPYDQaiY6OJiEhgcLCQlt3JYRow3Q6nTR0O7L5TL28vLz+AuCrr75KXl4e69at\na3gAOVMXQogWc/qZ+o0zOioqKujatautuxJCCGEnnq355aeffppNmzZhMBjYt29fk9stXLiw/uf4\n+Hji4+Nbc1ghhHA72dnZZGdnt3o/zQ6/mEwmSktLG7yflpZGSkpK/eulS5dy7Ngx3nzzzYYHkOEX\nIYRoMU1nv5w+fZrk5GSOHDlit2BCCNGWOX1M/cSJE/U/p6eny002QgjhAmw+U09NTeXYsWN4eHgQ\nEhLC6tWr6d69e8MDyJm6EEK0mNx8JIQQbkQW9BJCCCFNXQgh3Ik0dSGEcCPS1IUQwo1IUxdCCDci\nTV0IIdyINHUhhHAj0tSFEMKNSFMXQgg3Ik1dCCHciDR1IYRwI9LUhRDCjUhTF0IINyJNXQgh3Ig0\ndSGEcCPS1IUQwo1IUxdCCDciTV0IIdyINHUhhHAj0tSFEMKNSFMXQgg3Ik1dCCHcSKub+sqVK9Hr\n9ZSVldkjj1NkZ2drHaFRrphLMllHMlnPFXO5YiZbtaqpFxYWkpWVRe/eve2Vxylc9R/QFXNJJutI\nJuu5Yi5XzGSrVjX1J554guXLl9srixBCiFayuamnp6cTHBzMoEGD7JlHCCFEK+iUUqqpD00mE6Wl\npQ3eX7JkCWlpaWRmZtKhQwf69u1Lbm4uXbp0aXgAnc6+iYUQoo1opj03qdmm3pQjR46QkJCAwWAA\noKioiJ49e5KTk0P37t1bHEIIIYR92NTUb9a3b1/2799P586d7ZFJCCGEjewyT12GWIQQwjXYpann\n5+fXn6XPnz+fyMhIjEYjkyZN4vLly43+ztatW4mIiCAsLIxly5bZI0aTPvjgA6KiovDw8ODAgQNN\nbtenTx8GDRpETEwMQ4cOdYlMzqwTQFlZGSaTifDwcBITE7l06VKj2zmjVtZ897lz5xIWFobRaOTg\nwYMOydGSTNnZ2XTs2JGYmBhiYmJ47rnnHJpn1qxZBAYGMnDgwCa3cXaNrMnl7DrBtSnYo0aNIioq\nigEDBvDKK680up0z62VNphbXStlZZmamslgsSimlnnrqKfXUU0812Kaurk6FhISo7777TtXU1Cij\n0aiOHj1q7yj1vv32W3Xs2DEVHx+v9u/f3+R2ffr0URcvXnRYjpZmcnadlFJq/vz5atmyZUoppZYu\nXdrov59Sjq+VNd/9888/V0lJSUoppfbt26fi4uIclsfaTNu3b1cpKSkOzXGjnTt3qgMHDqgBAwY0\n+rmza2RtLmfXSSmlzpw5ow4ePKiUUqq8vFyFh4dr/jdlTaaW1sruywSYTCb0+mu7jYuLo6ioqME2\nOTk5hIaG0qdPH7y8vJgyZQrp6en2jlIvIiKC8PBwq7ZVrb/EYBVrMjm7TgCffPIJM2fOBGDmzJl8\n/PHHTW7ryFpZ891vzBoXF8elS5c4e/asppnAeX9DAHfccQcBAQFNfu7sGlmbC5xbJ4AePXoQHR0N\ngL+/P5GRkZSUlPxkG2fXy5pM0LJaOXTtl/Xr15OcnNzg/eLiYnr16lX/Ojg4mOLiYkdGsYpOp2PM\nmDHExsaydu1areNoUqezZ88SGBgIQGBgYJN/0I6ulTXfvbFtGjuJcGYmnU7Hl19+idFoJDk5maNH\njzosjzWcXSNraV2ngoICDh48SFxc3E/e17JeTWVqaa08bTl4U/PX09LSSElJAa7NZff29mbatGkN\ntnPEhVVrMv2cPXv2EBQUxPnz5zGZTERERHDHHXdolslRF6Cbu//g5uM3lcHetbqZtd/95jMYR160\nt2bfgwcPprCwEIPBQEZGBhMmTOD48eMOy2QNZ9bIWlrWqaKigtTUVF5++WX8/f0bfK5FvZrL1NJa\n2dTUs7Kymv18w4YNbNmyhW3btjX6ec+ePSksLKx/XVhYSHBwsC1RrM5kjaCgIAC6devGxIkTycnJ\naVWjam0mR9QJms8VGBhIaWkpPXr04MyZM03ed2DvWt3Mmu9+8zY/3i/hKNZkat++ff3PSUlJzJkz\nh7KyMs2m+zq7RtbSqk61tbX85je/YcaMGUyYMKHB51rU6+cytbRWdh9+2bp1KytWrCA9PZ127do1\nuk1sbCwnTpygoKCAmpoa3nvvPcaPH2/vKI1qamzKbDZTXl4OQGVlJZmZmc3OKHBGJi3qNH78eDZu\n3AjAxo0bG/0jc0atrPnu48eP56233gJg3759dOrUqX7oyBGsyXT27Nn6f8+cnByUUprev+HsGllL\nizoppXjwwQfp378/8+bNa3QbZ9fLmkwtrlUrLtw2KjQ0VN1+++0qOjpaRUdHq0cffVQppVRxcbFK\nTk6u327Lli0qPDxchYSEqLS0NHvH+ImPPvpIBQcHq3bt2qnAwEA1duzYBplOnjypjEajMhqNKioq\nyiUyKeXcOiml1MWLF1VCQoIKCwtTJpNJff/99w1yOatWjX33NWvWqDVr1tRv89hjj6mQkBA1aNCg\nZmc2OSvTa6+9pqKiopTRaFTDhw9Xe/fudWieKVOmqKCgIOXl5aWCg4PVP/7xD81rZE0uZ9dJKaV2\n7dqldDqdMhqN9f1py5YtmtbLmkwtrZVd7igVQgjhGuTJR0II4UakqQshhBuRpi6EEG5EmroQQrgR\naepCCOFGpKkLIYQb+X+DWLBp2mZB9gAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Clustering comes with assumptions**: A clustering algorithm find clusters using specific criterion, that correspond to given assumptions. For K-means clustering, the model is that all clusters have equal, spherical variance. In the case of the iris dataset this assumption does not match the geometry of the classes, and thus the clustering cannot recover the classes.\n",
      "\n",
      "**Gaussian Mixture Models**: we can choose a different set of assumptions using a Gaussian Mixture Model (GMM). The GMM can be used to relax the assumptions of equal variance or of sphericality. However, the less assumptions, the more the problem is ill-posed and hard to learn. The `covariance_type` argument of the GMM controls these assumptions. For the iris dataset, we will use the 'tied' mode, which imposes the same covariance for each classes. This makes the covariance learning problem easier."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sklearn.mixture import GMM\n",
      "gmm = GMM(n_components=3, covariance_type='tied')\n",
      "gmm.fit(X_pca)\n",
      "\n",
      "plot_2D(X_pca, gmm.predict(X_pca), [\"c0\", \"c1\", \"c2\"])\n",
      "plt.title('GMM labels')\n",
      "\n",
      "plot_2D(X_pca, iris.target, iris.target_names)\n",
      "plt.title('True labels')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.text.Text at 0x10ad62fd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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WDIthmFdISEjAwu8XQjNYA/2HemgGabB7325cv37dVOZF0gvA/uU5vB2P5y9e7owUHR2N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\n"
      },
      {
       "output_type": "display_data",
       "png": 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ndyM5p4gLDg5Gp9MRGxvrfC7n//l1q+nu5s+fz/Lly1m3bh1JSUmcPHkSyWr1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\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We see that the label are now much closer to the ground truth.\n",
      "\n",
      "**In general, there is no garanty that structure found by a clustering algorithm has anything to do with latent structures of the data**."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Some Notable Clustering Routines"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The following are two well-known clustering algorithms. Like most unsupervised learning\n",
      "models in the scikit, they expect the data to be clustered to have the shape `(n_samples, n_features)`:\n",
      "\n",
      "- `sklearn.cluster.KMeans`: <br/>\n",
      "    The simplest, yet effective clustering algorithm. Needs to be provided with the\n",
      "    number of clusters in advance, and assumes that the data is normalized as input\n",
      "    (but use a PCA model as preprocessor).\n",
      "- `sklearn.cluster.MeanShift`: <br/>\n",
      "    Can find better looking clusters than KMeans but is not scalable to high number of samples.\n",
      "- `sklearn.cluster.DBSCAN`: <br/>\n",
      "    Can detect irregularly shaped clusters based on density, i.e. sparse regions in\n",
      "    the input space are likely to become inter-cluster boundaries. Can also detect\n",
      "    outliers (samples that are not part of a cluster).\n",
      "\n",
      "Other clustering algorithms do not work with a data array of shape (n_samples, n_features)\n",
      "but directly with a precomputed affinity matrix of shape (n_samples, n_samples):\n",
      "\n",
      "- `sklearn.cluster.AffinityPropagation`: <br/>\n",
      "    Clustering algorithm based on message passing between data points.\n",
      "- `sklearn.cluster.SpectralClustering`: <br/>\n",
      "    KMeans applied to a projection of the normalized graph Laplacian: finds\n",
      "    normalized graph cuts if the affinity matrix is interpreted as an adjacency matrix of a graph.\n",
      "- `sklearn.cluster.Ward`: <br/>\n",
      "    Ward implements hierarchical clustering based on the Ward algorithm,\n",
      "    a variance-minimizing approach. At each step, it minimizes the sum of\n",
      "    squared differences within all clusters (inertia criterion).\n",
      "- `sklearn.cluster.DBSCAN`: <br/>\n",
      "    DBSCAN can work with either an array of samples or an affinity matrix."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Some Applications of Clustering"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here are some common applications of clustering algorithms:\n",
      "\n",
      "- Compression, in a data reduction sens\n",
      "- Can be used as a preprocessing step for recommender systems\n",
      "- Similarly:\n",
      "   - grouping related web news (e.g. Google News) and web search results\n",
      "   - grouping related stock quotes for investment portfolio management\n",
      "   - building customer profiles for market analysis\n",
      "- Building a code book of prototype samples for unsupervised feature extraction for supervised learning algorithms\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Exercise"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Perform the K-Means cluster search again, but this time learn the\n",
      "clusters using the full data matrix ``X``, rather than the projected\n",
      "matrix ``X_pca``.\n",
      "\n",
      "Does this change the results?\n",
      "\n",
      "Plot the results (you can still use X_pca for visualization, but plot\n",
      "the labels derived from the full 4-D set).\n",
      "Do the 4D K-means labels look closer to the true labels?\n",
      "\n",
      "Explore how this changes using GMMs with different covariance types."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    }
   ],
   "metadata": {}
  }
 ]
}