{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering for dataset exploration\n",
    "> A Summary of lecture \"Unsupervised Learning with scikit-learn\", via datacamp\n",
    "\n",
    "- toc: true \n",
    "- badges: true\n",
    "- comments: true\n",
    "- author: Chanseok Kang\n",
    "- categories: [Python, Datacamp, Machine_Learning]\n",
    "- image: images/kmeans-centroid.png"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unsupervised Learning\n",
    "- Unsupervised Learning\n",
    "    - Finds patterns in data (E.g., clustering customers by their purchase)\n",
    "    - Compressing the data using purchase patterns (dimension reduction)\n",
    "- Supervised vs unsupervised learning\n",
    "    - Supervised learning finds patterns for a prediction task \n",
    "    \n",
    "    e.g., classify tumors as benign or cancerous (labels)\n",
    "    - Unsupervised learning finds patterns in data, but without a specific prediction task in mind\n",
    "- K-means clustering\n",
    "    - Finds clusters of samples\n",
    "    - Number of clusters must be specified\n",
    "- Cluster labels for new samples\n",
    "    - New samples can be assigned to existing clusters\n",
    "    - k-means remembers the mean of each cluster (the \"centroids\")\n",
    "    - Finds the nearest centroid to each new sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many clusters?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = np.array([[ 0.06544649, -0.76866376],\n",
    "       [-1.52901547, -0.42953079],\n",
    "       [ 1.70993371,  0.69885253],\n",
    "       [ 1.16779145,  1.01262638],\n",
    "       [-1.80110088, -0.31861296],\n",
    "       [-1.63567888, -0.02859535],\n",
    "       [ 1.21990375,  0.74643463],\n",
    "       [-0.26175155, -0.62492939],\n",
    "       [-1.61925804, -0.47983949],\n",
    "       [-1.84329582, -0.16694431],\n",
    "       [ 1.35999602,  0.94995827],\n",
    "       [ 0.42291856, -0.7349534 ],\n",
    "       [-1.68576139,  0.10686728],\n",
    "       [ 0.90629995,  1.09105162],\n",
    "       [-1.56478322, -0.84675394],\n",
    "       [-0.0257849 , -1.18672539],\n",
    "       [ 0.83027324,  1.14504612],\n",
    "       [ 1.22450432,  1.35066759],\n",
    "       [-0.15394596, -0.71704301],\n",
    "       [ 0.86358809,  1.06824613],\n",
    "       [-1.43386366, -0.2381297 ],\n",
    "       [ 0.03844769, -0.74635022],\n",
    "       [-1.58567922,  0.08499354],\n",
    "       [ 0.6359888 , -0.58477698],\n",
    "       [ 0.24417242, -0.53172465],\n",
    "       [-2.19680359,  0.49473677],\n",
    "       [ 1.0323503 , -0.55688   ],\n",
    "       [-0.28858067, -0.39972528],\n",
    "       [ 0.20597008, -0.80171536],\n",
    "       [-1.2107308 , -0.34924109],\n",
    "       [ 1.33423684,  0.7721489 ],\n",
    "       [ 1.19480152,  1.04788556],\n",
    "       [ 0.9917477 ,  0.89202008],\n",
    "       [-1.8356219 , -0.04839732],\n",
    "       [ 0.08415721, -0.71564326],\n",
    "       [-1.48970175, -0.19299604],\n",
    "       [ 0.38782418, -0.82060119],\n",
    "       [-0.01448044, -0.9779841 ],\n",
    "       [-2.0521341 , -0.02129125],\n",
    "       [ 0.10331194, -0.82162781],\n",
    "       [-0.44189315, -0.65710974],\n",
    "       [ 1.10390926,  1.02481182],\n",
    "       [-1.59227759, -0.17374038],\n",
    "       [-1.47344152, -0.02202853],\n",
    "       [-1.35514704,  0.22971067],\n",
    "       [ 0.0412337 , -1.23776622],\n",
    "       [ 0.4761517 , -1.13672124],\n",
    "       [ 1.04335676,  0.82345905],\n",
    "       [-0.07961882, -0.85677394],\n",
    "       [ 0.87065059,  1.08052841],\n",
    "       [ 1.40267313,  1.07525119],\n",
    "       [ 0.80111157,  1.28342825],\n",
    "       [-0.16527516, -1.23583804],\n",
    "       [-0.33779221, -0.59194323],\n",
    "       [ 0.80610749, -0.73752159],\n",
    "       [-1.43590032, -0.56384446],\n",
    "       [ 0.54868895, -0.95143829],\n",
    "       [ 0.46803131, -0.74973907],\n",
    "       [-1.5137129 , -0.83914323],\n",
    "       [ 0.9138436 ,  1.51126532],\n",
    "       [-1.97233903, -0.41155375],\n",
    "       [ 0.5213406 , -0.88654894],\n",
    "       [ 0.62759494, -1.18590477],\n",
    "       [ 0.94163014,  1.35399335],\n",
    "       [ 0.56994768,  1.07036606],\n",
    "       [-1.87663382,  0.14745773],\n",
    "       [ 0.90612186,  0.91084011],\n",
    "       [-1.37481454,  0.28428395],\n",
    "       [-1.80564029, -0.96710574],\n",
    "       [ 0.34307757, -0.79999275],\n",
    "       [ 0.70380566,  1.00025804],\n",
    "       [-1.68489862, -0.30564595],\n",
    "       [ 1.31473221,  0.98614978],\n",
    "       [ 0.26151216, -0.26069251],\n",
    "       [ 0.9193121 ,  0.82371485],\n",
    "       [-1.21795929, -0.20219674],\n",
    "       [-0.17722723, -1.02665245],\n",
    "       [ 0.64824862, -0.66822881],\n",
    "       [ 0.41206786, -0.28783784],\n",
    "       [ 1.01568202,  1.13481667],\n",
    "       [ 0.67900254, -0.91489502],\n",
    "       [-1.05182747, -0.01062376],\n",
    "       [ 0.61306599,  1.78210384],\n",
    "       [-1.50219748, -0.52308922],\n",
    "       [-1.72717293, -0.46173916],\n",
    "       [-1.60995631, -0.1821007 ],\n",
    "       [-1.09111021, -0.0781398 ],\n",
    "       [-0.01046978, -0.80913034],\n",
    "       [ 0.32782303, -0.80734754],\n",
    "       [ 1.22038503,  1.1959793 ],\n",
    "       [-1.33328681, -0.30001937],\n",
    "       [ 0.87959517,  1.11566491],\n",
    "       [-1.14829098, -0.30400762],\n",
    "       [-0.58019755, -1.19996018],\n",
    "       [-0.01161159, -0.78468854],\n",
    "       [ 0.17359724, -0.63398145],\n",
    "       [ 1.32738556,  0.67759969],\n",
    "       [-1.93467327,  0.30572472],\n",
    "       [-1.57761893, -0.27726365],\n",
    "       [ 0.47639   ,  1.21422648],\n",
    "       [-1.65237509, -0.6803981 ],\n",
    "       [-0.12609976, -1.04327457],\n",
    "       [-1.89607082, -0.70085502],\n",
    "       [ 0.57466899,  0.74878369],\n",
    "       [-0.16660312, -0.83110295],\n",
    "       [ 0.8013355 ,  1.22244435],\n",
    "       [ 1.18455426,  1.4346467 ],\n",
    "       [ 1.08864428,  0.64667112],\n",
    "       [-1.61158505,  0.22805725],\n",
    "       [-1.57512205, -0.09612576],\n",
    "       [ 0.0721357 , -0.69640328],\n",
    "       [-1.40054298,  0.16390598],\n",
    "       [ 1.09607713,  1.16804691],\n",
    "       [-2.54346204, -0.23089822],\n",
    "       [-1.34544875,  0.25151126],\n",
    "       [-1.35478629, -0.19103317],\n",
    "       [ 0.18368113, -1.15827725],\n",
    "       [-1.31368677, -0.376357  ],\n",
    "       [ 0.09990129,  1.22500491],\n",
    "       [ 1.17225574,  1.30835143],\n",
    "       [ 0.0865397 , -0.79714371],\n",
    "       [-0.21053923, -1.13421511],\n",
    "       [ 0.26496024, -0.94760742],\n",
    "       [-0.2557591 , -1.06266022],\n",
    "       [-0.26039757, -0.74774225],\n",
    "       [-1.91787359,  0.16434571],\n",
    "       [ 0.93021139,  0.49436331],\n",
    "       [ 0.44770467, -0.72877918],\n",
    "       [-1.63802869, -0.58925528],\n",
    "       [-1.95712763, -0.10125137],\n",
    "       [ 0.9270337 ,  0.88251423],\n",
    "       [ 1.25660093,  0.60828073],\n",
    "       [-1.72818632,  0.08416887],\n",
    "       [ 0.3499788 , -0.30490298],\n",
    "       [-1.51696082, -0.50913109],\n",
    "       [ 0.18763605, -0.55424924],\n",
    "       [ 0.89609809,  0.83551508],\n",
    "       [-1.54968857, -0.17114782],\n",
    "       [ 1.2157457 ,  1.23317728],\n",
    "       [ 0.20307745, -1.03784906],\n",
    "       [ 0.84589086,  1.03615273],\n",
    "       [ 0.53237919,  1.47362884],\n",
    "       [-0.05319044, -1.36150553],\n",
    "       [ 1.38819743,  1.11729915],\n",
    "       [ 1.00696304,  1.0367721 ],\n",
    "       [ 0.56681869, -1.09637176],\n",
    "       [ 0.86888296,  1.05248874],\n",
    "       [-1.16286609, -0.55875245],\n",
    "       [ 0.27717768, -0.83844015],\n",
    "       [ 0.16563267, -0.80306607],\n",
    "       [ 0.38263303, -0.42683241],\n",
    "       [ 1.14519807,  0.89659026],\n",
    "       [ 0.81455857,  0.67533667],\n",
    "       [-1.8603152 , -0.09537561],\n",
    "       [ 0.965641  ,  0.90295579],\n",
    "       [-1.49897451, -0.33254044],\n",
    "       [-0.1335489 , -0.80727582],\n",
    "       [ 0.12541527, -1.13354906],\n",
    "       [ 1.06062436,  1.28816358],\n",
    "       [-1.49154578, -0.2024641 ],\n",
    "       [ 1.16189032,  1.28819877],\n",
    "       [ 0.54282033,  0.75203524],\n",
    "       [ 0.89221065,  0.99211624],\n",
    "       [-1.49932011, -0.32430667],\n",
    "       [ 0.3166647 , -1.34482915],\n",
    "       [ 0.13972469, -1.22097448],\n",
    "       [-1.5499724 , -0.10782584],\n",
    "       [ 1.23846858,  1.37668804],\n",
    "       [ 1.25558954,  0.72026098],\n",
    "       [ 0.25558689, -1.28529763],\n",
    "       [ 0.45168933, -0.55952093],\n",
    "       [ 1.06202057,  1.03404604],\n",
    "       [ 0.67451908, -0.54970299],\n",
    "       [ 0.22759676, -1.02729468],\n",
    "       [-1.45835281, -0.04951074],\n",
    "       [ 0.23273501, -0.70849262],\n",
    "       [ 1.59679589,  1.11395076],\n",
    "       [ 0.80476105,  0.544627  ],\n",
    "       [ 1.15492521,  1.04352191],\n",
    "       [ 0.59632776, -1.19142897],\n",
    "       [ 0.02839068, -0.43829366],\n",
    "       [ 1.13451584,  0.5632633 ],\n",
    "       [ 0.21576204, -1.04445753],\n",
    "       [ 1.41048987,  1.02830719],\n",
    "       [ 1.12289302,  0.58029441],\n",
    "       [ 0.25200688, -0.82588436],\n",
    "       [-1.28566081, -0.07390909],\n",
    "       [ 1.52849815,  1.11822469],\n",
    "       [-0.23907858, -0.70541972],\n",
    "       [-0.25792784, -0.81825035],\n",
    "       [ 0.59367818, -0.45239915],\n",
    "       [ 0.07931909, -0.29233213],\n",
    "       [-1.27256815,  0.11630577],\n",
    "       [ 0.66930129,  1.00731481],\n",
    "       [ 0.34791546, -1.20822877],\n",
    "       [-2.11283993, -0.66897935],\n",
    "       [-1.6293824 , -0.32718222],\n",
    "       [-1.53819139, -0.01501972],\n",
    "       [-0.11988545, -0.6036339 ],\n",
    "       [-1.54418956, -0.30389844],\n",
    "       [ 0.30026614, -0.77723173],\n",
    "       [ 0.00935449, -0.53888192],\n",
    "       [-1.33424393, -0.11560431],\n",
    "       [ 0.47504489,  0.78421384],\n",
    "       [ 0.59313264,  1.232239  ],\n",
    "       [ 0.41370369, -1.35205857],\n",
    "       [ 0.55840948,  0.78831053],\n",
    "       [ 0.49855018, -0.789949  ],\n",
    "       [ 0.35675809, -0.81038693],\n",
    "       [-1.86197825, -0.59071305],\n",
    "       [-1.61977671, -0.16076687],\n",
    "       [ 0.80779295, -0.73311294],\n",
    "       [ 1.62745775,  0.62787163],\n",
    "       [-1.56993593, -0.08467567],\n",
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    "       [ 1.23130242,  1.00262186],\n",
    "       [-1.9651013 , -0.15886289],\n",
    "       [ 0.42795032, -0.70384432],\n",
    "       [-1.58306818, -0.19431923],\n",
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    "       [ 1.28619721,  1.28128821],\n",
    "       [ 0.85850596,  0.95541481],\n",
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    "       [-1.90280976, -0.1638976 ],\n",
    "       [-0.22440081, -0.75454248],\n",
    "       [ 0.59559412,  0.92414553],\n",
    "       [ 1.21930773,  1.08175284],\n",
    "       [-1.99427535, -0.37587799],\n",
    "       [-1.27818474, -0.52454551],\n",
    "       [ 0.62352689, -1.01430108],\n",
    "       [ 0.14024251, -0.428266  ],\n",
    "       [-0.16145713, -1.16359731],\n",
    "       [-1.74795865, -0.06033101],\n",
    "       [-1.16659791,  0.0902393 ],\n",
    "       [ 0.41110408, -0.8084249 ],\n",
    "       [ 1.14757168,  0.77804528],\n",
    "       [-1.65590748, -0.40105446],\n",
    "       [-1.15306865,  0.00858699],\n",
    "       [ 0.60892121,  0.68974833],\n",
    "       [-0.08434138, -0.97615256],\n",
    "       [ 0.19170053, -0.42331438],\n",
    "       [ 0.29663162, -1.13357399],\n",
    "       [-1.36893628, -0.25052124],\n",
    "       [-0.08037807, -0.56784155],\n",
    "       [ 0.35695011, -1.15064408],\n",
    "       [ 0.02482179, -0.63594828],\n",
    "       [-1.49075558, -0.2482507 ],\n",
    "       [-1.408588  ,  0.25635431],\n",
    "       [-1.98274626, -0.54584475]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f9ecb1e03d0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = points[:, 0]\n",
    "ys = points[:, 1]\n",
    "\n",
    "plt.scatter(xs, ys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering 2D points\n",
    "From the scatter plot of the previous exercise, you saw that the points seem to separate into 3 clusters. You'll now create a KMeans model to find 3 clusters, and fit it to the data points from the previous exercise. After the model has been fit, you'll obtain the cluster labels for some new points using the ```.predict()``` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_points = np.array([[ 4.00233332e-01, -1.26544471e+00],\n",
    "       [ 8.03230370e-01,  1.28260167e+00],\n",
    "       [-1.39507552e+00,  5.57292921e-02],\n",
    "       [-3.41192677e-01, -1.07661994e+00],\n",
    "       [ 1.54781747e+00,  1.40250049e+00],\n",
    "       [ 2.45032018e-01, -4.83442328e-01],\n",
    "       [ 1.20706886e+00,  8.88752605e-01],\n",
    "       [ 1.25132628e+00,  1.15555395e+00],\n",
    "       [ 1.81004415e+00,  9.65530731e-01],\n",
    "       [-1.66963401e+00, -3.08103509e-01],\n",
    "       [-7.17482105e-02, -9.37939700e-01],\n",
    "       [ 6.82631927e-01,  1.10258160e+00],\n",
    "       [ 1.09039598e+00,  1.43899529e+00],\n",
    "       [-1.67645414e+00, -5.04557049e-01],\n",
    "       [-1.84447804e+00,  4.52539544e-02],\n",
    "       [ 1.24234851e+00,  1.02088661e+00],\n",
    "       [-1.86147041e+00,  6.38645811e-03],\n",
    "       [-1.46044943e+00,  1.53252383e-01],\n",
    "       [ 4.98981817e-01,  8.98006058e-01],\n",
    "       [ 9.83962244e-01,  1.04369375e+00],\n",
    "       [-1.83136742e+00, -1.63632835e-01],\n",
    "       [ 1.30622617e+00,  1.07658717e+00],\n",
    "       [ 3.53420328e-01, -7.51320218e-01],\n",
    "       [ 1.13957970e+00,  1.54503860e+00],\n",
    "       [ 2.93995694e-01, -1.26135005e+00],\n",
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    "       [ 8.65050554e-01,  9.57714887e-01],\n",
    "       [ 3.98717766e-01, -1.24273147e+00],\n",
    "       [ 8.62234892e-01,  1.10955561e+00],\n",
    "       [-1.35999430e+00,  2.49942654e-02],\n",
    "       [-1.19178505e+00, -3.82946323e-02],\n",
    "       [ 1.29392424e+00,  1.10320509e+00],\n",
    "       [ 1.25679630e+00, -7.79857582e-01],\n",
    "       [ 9.38040302e-02, -5.53247258e-01],\n",
    "       [-1.73512175e+00, -9.76271667e-02],\n",
    "       [ 2.23153587e-01, -9.43474351e-01],\n",
    "       [ 4.01989100e-01, -1.10963051e+00],\n",
    "       [-1.42244158e+00,  1.81914703e-01],\n",
    "       [ 3.92476267e-01, -8.78426277e-01],\n",
    "       [ 1.25181875e+00,  6.93614996e-01],\n",
    "       [ 1.77481317e-02, -7.20304235e-01],\n",
    "       [-1.87752521e+00, -2.63870424e-01],\n",
    "       [-1.58063602e+00, -5.50456344e-01],\n",
    "       [-1.59589493e+00, -1.53932892e-01],\n",
    "       [-1.01829770e+00,  3.88542370e-02],\n",
    "       [ 1.24819659e+00,  6.60041803e-01],\n",
    "       [-1.25551377e+00, -2.96172009e-02],\n",
    "       [-1.41864559e+00, -3.58230179e-01],\n",
    "       [ 5.25758326e-01,  8.70500543e-01],\n",
    "       [ 5.55599988e-01,  1.18765072e+00],\n",
    "       [ 2.81344439e-02, -6.99111314e-01]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 0 1 0 1 1 1 2 0 1 1 2 2 1 2 2 1 1 2 1 0 1 0 2 1 2 2 0 0 1 1 1 2 0 1\n",
      " 1 0 1 2 0 0 2 0 1 2 2 1 1 1 1 2 2 0 0 2 2 2 0 0 1 1 1 0 1 2 1 0 2 0 0 0 1\n",
      " 0 2 2 0 1 2 0 2 0 1 2 1 2 0 1 1 1 0 1 1 0 2 2 2 2 0 1 0 2 2 0 0 1 0 2 2 0\n",
      " 2 2 2 1 1 1 1 2 2 1 0 1 2 1 0 2 1 2 2 1 2 1 2 0 1 0 0 1 2 0 1 0 0 2 1 1 0\n",
      " 2 0 2 1 0 2 2 0 2 1 1 2 1 2 2 1 1 0 1 1 2 0 2 0 0 1 0 1 1 0 0 2 0 0 0 2 1\n",
      " 1 0 2 0 2 2 1 1 1 0 1 1 1 2 2 0 1 0 0 0 2 1 1 1 1 1 1 2 2 1 2 2 2 2 1 2 2\n",
      " 1 1 0 2 0 0 2 0 2 0 2 1 1 2 1 1 1 2 0 0 2 1 1 2 1 2 2 1 2 2 0 2 0 0 0 1 2\n",
      " 2 2 0 1 0 2 0 2 2 1 0 0 0 2 1 1 1 0 1 2 2 1 0 0 2 0 0 2 0 1 0 2 2 2 2 1 2\n",
      " 2 1 1 0]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# Create a KMeans instance with 3 clusters: model\n",
    "model = KMeans(n_clusters=3)\n",
    "\n",
    "# Fit model to points\n",
    "model.fit(points)\n",
    "\n",
    "# Determine the cluster labels of new_points: labels\n",
    "labels = model.predict(new_points)\n",
    "\n",
    "# Print cluster labels of new_points\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inspect your clustering\n",
    "Let's now inspect the clustering you performed in the previous exercise!\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Assign the columns of new_points: xs and ys\n",
    "xs = new_points[:, 0]\n",
    "ys = new_points[:, 1]\n",
    "\n",
    "# Make a scatter plot of xs and ys, using labels to define the colors\n",
    "plt.scatter(xs, ys, c=labels, alpha=0.5)\n",
    "\n",
    "# Assign the cluster centers: centroids\n",
    "centroids = model.cluster_centers_\n",
    "\n",
    "# Assign the columns of centroids: centroids_x, centroids_y\n",
    "centroids_x = centroids[:, 0]\n",
    "centroids_y = centroids[:, 1]\n",
    "\n",
    "# Make a scatter plot of centroids_x and centroids_y\n",
    "plt.scatter(centroids_x, centroids_y, marker='D', s=50, color='red')\n",
    "plt.savefig('../images/kmeans-centroid.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Evaluating a clustering\n",
    "- Evaluating a clustering\n",
    "    - Can check correspondence with e.g. iris species, but what if there are no species to check against?\n",
    "    - Measure quality of a clustering\n",
    "    - Informs choice of how many clusters to look for\n",
    "- Cross-tabulation with pandas\n",
    "    - Clusters vs species is a \"cross-tabulation\"\n",
    "- Measuring clustering quality\n",
    "    - Using only samples and their cluster labels\n",
    "    - A good clustering has tight clusters\n",
    "    - Samples in each cluster bunched together\n",
    "- Inertia measures clustering quality\n",
    "    - Measures how spread out the clusters are (lower is better)\n",
    "    - Distance from each sample to centroid of its cluster\n",
    "    - k-means attempts to minimize the inertia when choosing clusters\n",
    "- How many clusters to choose?\n",
    "    - Choose an \"elbow\" in the inertia plot\n",
    "    - Where inertia begins to decrease more slowly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many clusters of grain?\n",
    "In the video, you learned how to choose a good number of clusters for a dataset using the k-means inertia graph. You are given an array ```samples``` containing the measurements (such as area, perimeter, length, and several others) of samples of grain. What's a good number of clusters in this case?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15.26</td>\n",
       "      <td>14.84</td>\n",
       "      <td>0.8710</td>\n",
       "      <td>5.763</td>\n",
       "      <td>3.312</td>\n",
       "      <td>2.221</td>\n",
       "      <td>5.220</td>\n",
       "      <td>Kama wheat</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.88</td>\n",
       "      <td>14.57</td>\n",
       "      <td>0.8811</td>\n",
       "      <td>5.554</td>\n",
       "      <td>3.333</td>\n",
       "      <td>1.018</td>\n",
       "      <td>4.956</td>\n",
       "      <td>Kama wheat</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>14.29</td>\n",
       "      <td>14.09</td>\n",
       "      <td>0.9050</td>\n",
       "      <td>5.291</td>\n",
       "      <td>3.337</td>\n",
       "      <td>2.699</td>\n",
       "      <td>4.825</td>\n",
       "      <td>Kama wheat</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>13.84</td>\n",
       "      <td>13.94</td>\n",
       "      <td>0.8955</td>\n",
       "      <td>5.324</td>\n",
       "      <td>3.379</td>\n",
       "      <td>2.259</td>\n",
       "      <td>4.805</td>\n",
       "      <td>Kama wheat</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>16.14</td>\n",
       "      <td>14.99</td>\n",
       "      <td>0.9034</td>\n",
       "      <td>5.658</td>\n",
       "      <td>3.562</td>\n",
       "      <td>1.355</td>\n",
       "      <td>5.175</td>\n",
       "      <td>Kama wheat</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       0      1       2      3      4      5      6           7\n",
       "0  15.26  14.84  0.8710  5.763  3.312  2.221  5.220  Kama wheat\n",
       "1  14.88  14.57  0.8811  5.554  3.333  1.018  4.956  Kama wheat\n",
       "2  14.29  14.09  0.9050  5.291  3.337  2.699  4.825  Kama wheat\n",
       "3  13.84  13.94  0.8955  5.324  3.379  2.259  4.805  Kama wheat\n",
       "4  16.14  14.99  0.9034  5.658  3.562  1.355  5.175  Kama wheat"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./dataset/seeds.csv', header=None)\n",
    "df[7] = df[7].map({1:'Kama wheat', 2:'Rosa wheat', 3:'Canadian wheat'})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = df.iloc[:, :-1].values\n",
    "varieties = df.iloc[:, -1].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x7f045f7bf090>,\n",
       "  <matplotlib.axis.XTick at 0x7f045f8c3990>,\n",
       "  <matplotlib.axis.XTick at 0x7f045f8c3dd0>,\n",
       "  <matplotlib.axis.XTick at 0x7f045f083b50>,\n",
       "  <matplotlib.axis.XTick at 0x7f045f8bad90>],\n",
       " <a list of 5 Text xticklabel objects>)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ks = range(1,6)\n",
    "inertias = []\n",
    "\n",
    "for k in ks:\n",
    "    # Create a KMeans instance with k clusters: model\n",
    "    model = KMeans(n_clusters=k)\n",
    "    \n",
    "    # Fit model to samples\n",
    "    model.fit(samples)\n",
    "    \n",
    "    # Append the inertia to the list of inertias\n",
    "    inertias.append(model.inertia_)\n",
    "    \n",
    "# Plot ks vs inertias\n",
    "plt.plot(ks, inertias, '-o')\n",
    "plt.xlabel('number of clusters, k')\n",
    "plt.ylabel('inertia')\n",
    "plt.xticks(ks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluating the grain clustering\n",
    "In the previous exercise, you observed from the inertia plot that 3 is a good number of clusters for the grain data. In fact, the grain samples come from a mix of 3 different grain varieties: \"Kama\", \"Rosa\" and \"Canadian\". In this exercise, cluster the grain samples into three clusters, and compare the clusters to the grain varieties using a cross-tabulation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  Canadian wheat  Kama wheat  Rosa wheat\n",
      "labels                                           \n",
      "0                       2          60          10\n",
      "1                       0           1          60\n",
      "2                      68           9           0\n"
     ]
    }
   ],
   "source": [
    "# Create a KMeans model with 3 clusters: model\n",
    "model = KMeans(n_clusters=3)\n",
    "\n",
    "# Use fit_predict to fit model and obtain cluster labels: labels\n",
    "labels = model.fit_predict(samples)\n",
    "\n",
    "# Create a DataFrame with labels and varieties as columns: df\n",
    "df = pd.DataFrame({'labels': labels, 'varieties': varieties})\n",
    "\n",
    "# Create crosstab: ct\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "\n",
    "# Display ct\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Transforming features for better clusterings\n",
    "- StandardScaler\n",
    "    - In kmeans, feature variance = feature influence\n",
    "    - ```StandardScaler``` transforms each feature to have mean 0 and variance 1\n",
    "    - Features are said to be \"standardized\"\n",
    "- StandardScaler, then KMeans\n",
    "    - Need to perform two steps: ```StandardScaler```, then ```KMeans```\n",
    "    - Use ```sklearn``` pipeline to combine multiple steps\n",
    "    - Data flows from one step into the next"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling fish data for clustering\n",
    "You are given an array ```samples``` giving measurements of fish. Each row represents an individual fish. The measurements, such as weight in grams, length in centimeters, and the percentage ratio of height to length, have very different scales. In order to cluster this data effectively, you'll need to standardize these features first. In this exercise, you'll build a pipeline to standardize and cluster the data.\n",
    "\n",
    "These fish measurement data were sourced from the [Journal of Statistics Education](http://ww2.amstat.org/publications/jse/jse_data_archive.htm)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Bream</td>\n",
       "      <td>242.0</td>\n",
       "      <td>23.2</td>\n",
       "      <td>25.4</td>\n",
       "      <td>30.0</td>\n",
       "      <td>38.4</td>\n",
       "      <td>13.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bream</td>\n",
       "      <td>290.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>26.3</td>\n",
       "      <td>31.2</td>\n",
       "      <td>40.0</td>\n",
       "      <td>13.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Bream</td>\n",
       "      <td>340.0</td>\n",
       "      <td>23.9</td>\n",
       "      <td>26.5</td>\n",
       "      <td>31.1</td>\n",
       "      <td>39.8</td>\n",
       "      <td>15.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Bream</td>\n",
       "      <td>363.0</td>\n",
       "      <td>26.3</td>\n",
       "      <td>29.0</td>\n",
       "      <td>33.5</td>\n",
       "      <td>38.0</td>\n",
       "      <td>13.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Bream</td>\n",
       "      <td>430.0</td>\n",
       "      <td>26.5</td>\n",
       "      <td>29.0</td>\n",
       "      <td>34.0</td>\n",
       "      <td>36.6</td>\n",
       "      <td>15.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       0      1     2     3     4     5     6\n",
       "0  Bream  242.0  23.2  25.4  30.0  38.4  13.4\n",
       "1  Bream  290.0  24.0  26.3  31.2  40.0  13.8\n",
       "2  Bream  340.0  23.9  26.5  31.1  39.8  15.1\n",
       "3  Bream  363.0  26.3  29.0  33.5  38.0  13.3\n",
       "4  Bream  430.0  26.5  29.0  34.0  36.6  15.1"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./dataset/fish.csv', header=None)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = df.iloc[:, 1:].values\n",
    "species = df.iloc[:, 0].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# Create scaler: scaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# Create KMeans instance: kmeans\n",
    "kmeans = KMeans(n_clusters=4)\n",
    "\n",
    "# Create pipeline: pipeline\n",
    "pipeline = make_pipeline(scaler, kmeans)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering the fish data\n",
    "You'll now use your standardization and clustering pipeline from the previous exercise to cluster the fish by their measurements, and then create a cross-tabulation to compare the cluster labels with the fish species."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "species  Bream  Pike  Roach  Smelt\n",
      "labels                            \n",
      "0           33     0      1      0\n",
      "1            0    17      0      0\n",
      "2            0     0      0     13\n",
      "3            1     0     19      1\n"
     ]
    }
   ],
   "source": [
    "# Fit the pipeline to samples\n",
    "pipeline.fit(samples)\n",
    "\n",
    "# Calculate the cluster labels: labels\n",
    "labels = pipeline.predict(samples)\n",
    "\n",
    "# Create a DataFrame with labels and species as columns: df\n",
    "df = pd.DataFrame({'labels': labels, 'species': species})\n",
    "\n",
    "# Create crosstab: ct\n",
    "ct = pd.crosstab(df['labels'], df['species'])\n",
    "\n",
    "# Display ct\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Clustering stocks using KMeans\n",
    "In this exercise, you'll cluster companies using their daily stock price movements (i.e. the dollar difference between the closing and opening prices for each trading day). You are given a NumPy array ```movements``` of daily price movements from 2010 to 2015 (obtained from Yahoo! Finance), where each row corresponds to a company, and each column corresponds to a trading day.\n",
    "\n",
    "Some stocks are more expensive than others. To account for this, include a ```Normalizer``` at the beginning of your pipeline. The Normalizer will separately transform each company's stock price to a relative scale before the clustering begins.\n",
    "\n",
    "Note that ```Normalizer()``` is different to ```StandardScaler()```, which you used in the previous exercise. While ```StandardScaler()``` standardizes features (such as the features of the fish data from the previous exercise) by removing the mean and scaling to unit variance, ```Normalizer()``` rescales each sample - here, each company's stock price - independently of the other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Preprocess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2010-01-04</th>\n",
       "      <th>2010-01-05</th>\n",
       "      <th>2010-01-06</th>\n",
       "      <th>2010-01-07</th>\n",
       "      <th>2010-01-08</th>\n",
       "      <th>2010-01-11</th>\n",
       "      <th>2010-01-12</th>\n",
       "      <th>2010-01-13</th>\n",
       "      <th>2010-01-14</th>\n",
       "      <th>2010-01-15</th>\n",
       "      <th>...</th>\n",
       "      <th>2013-10-16</th>\n",
       "      <th>2013-10-17</th>\n",
       "      <th>2013-10-18</th>\n",
       "      <th>2013-10-21</th>\n",
       "      <th>2013-10-22</th>\n",
       "      <th>2013-10-23</th>\n",
       "      <th>2013-10-24</th>\n",
       "      <th>2013-10-25</th>\n",
       "      <th>2013-10-28</th>\n",
       "      <th>2013-10-29</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Apple</th>\n",
       "      <td>0.580000</td>\n",
       "      <td>-0.220005</td>\n",
       "      <td>-3.409998</td>\n",
       "      <td>-1.170000</td>\n",
       "      <td>1.680011</td>\n",
       "      <td>-2.689994</td>\n",
       "      <td>-1.469994</td>\n",
       "      <td>2.779997</td>\n",
       "      <td>-0.680003</td>\n",
       "      <td>-4.999995</td>\n",
       "      <td>...</td>\n",
       "      <td>0.320008</td>\n",
       "      <td>4.519997</td>\n",
       "      <td>2.899987</td>\n",
       "      <td>9.590019</td>\n",
       "      <td>-6.540016</td>\n",
       "      <td>5.959976</td>\n",
       "      <td>6.910011</td>\n",
       "      <td>-5.359962</td>\n",
       "      <td>0.840019</td>\n",
       "      <td>-19.589981</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AIG</th>\n",
       "      <td>-0.640002</td>\n",
       "      <td>-0.650000</td>\n",
       "      <td>-0.210001</td>\n",
       "      <td>-0.420000</td>\n",
       "      <td>0.710001</td>\n",
       "      <td>-0.200001</td>\n",
       "      <td>-1.130001</td>\n",
       "      <td>0.069999</td>\n",
       "      <td>-0.119999</td>\n",
       "      <td>-0.500000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.919998</td>\n",
       "      <td>0.709999</td>\n",
       "      <td>0.119999</td>\n",
       "      <td>-0.480000</td>\n",
       "      <td>0.010002</td>\n",
       "      <td>-0.279998</td>\n",
       "      <td>-0.190003</td>\n",
       "      <td>-0.040001</td>\n",
       "      <td>-0.400002</td>\n",
       "      <td>0.660000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Amazon</th>\n",
       "      <td>-2.350006</td>\n",
       "      <td>1.260009</td>\n",
       "      <td>-2.350006</td>\n",
       "      <td>-2.009995</td>\n",
       "      <td>2.960006</td>\n",
       "      <td>-2.309997</td>\n",
       "      <td>-1.640007</td>\n",
       "      <td>1.209999</td>\n",
       "      <td>-1.790001</td>\n",
       "      <td>-2.039994</td>\n",
       "      <td>...</td>\n",
       "      <td>2.109985</td>\n",
       "      <td>3.699982</td>\n",
       "      <td>9.570008</td>\n",
       "      <td>-3.450013</td>\n",
       "      <td>4.820008</td>\n",
       "      <td>-4.079986</td>\n",
       "      <td>2.579986</td>\n",
       "      <td>4.790009</td>\n",
       "      <td>-1.760009</td>\n",
       "      <td>3.740021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>American express</th>\n",
       "      <td>0.109997</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.260002</td>\n",
       "      <td>0.720002</td>\n",
       "      <td>0.190003</td>\n",
       "      <td>-0.270001</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.300004</td>\n",
       "      <td>0.639999</td>\n",
       "      <td>-0.130001</td>\n",
       "      <td>...</td>\n",
       "      <td>0.680001</td>\n",
       "      <td>2.290001</td>\n",
       "      <td>0.409996</td>\n",
       "      <td>-0.069999</td>\n",
       "      <td>0.100006</td>\n",
       "      <td>0.069999</td>\n",
       "      <td>0.130005</td>\n",
       "      <td>1.849999</td>\n",
       "      <td>0.040001</td>\n",
       "      <td>0.540001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Boeing</th>\n",
       "      <td>0.459999</td>\n",
       "      <td>1.770000</td>\n",
       "      <td>1.549999</td>\n",
       "      <td>2.690003</td>\n",
       "      <td>0.059997</td>\n",
       "      <td>-1.080002</td>\n",
       "      <td>0.360000</td>\n",
       "      <td>0.549999</td>\n",
       "      <td>0.530002</td>\n",
       "      <td>-0.709999</td>\n",
       "      <td>...</td>\n",
       "      <td>1.559997</td>\n",
       "      <td>2.480003</td>\n",
       "      <td>0.019997</td>\n",
       "      <td>-1.220001</td>\n",
       "      <td>0.480003</td>\n",
       "      <td>3.020004</td>\n",
       "      <td>-0.029999</td>\n",
       "      <td>1.940002</td>\n",
       "      <td>1.130005</td>\n",
       "      <td>0.309998</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 963 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  2010-01-04  2010-01-05  2010-01-06  2010-01-07  2010-01-08  \\\n",
       "Apple               0.580000   -0.220005   -3.409998   -1.170000    1.680011   \n",
       "AIG                -0.640002   -0.650000   -0.210001   -0.420000    0.710001   \n",
       "Amazon             -2.350006    1.260009   -2.350006   -2.009995    2.960006   \n",
       "American express    0.109997    0.000000    0.260002    0.720002    0.190003   \n",
       "Boeing              0.459999    1.770000    1.549999    2.690003    0.059997   \n",
       "\n",
       "                  2010-01-11  2010-01-12  2010-01-13  2010-01-14  2010-01-15  \\\n",
       "Apple              -2.689994   -1.469994    2.779997   -0.680003   -4.999995   \n",
       "AIG                -0.200001   -1.130001    0.069999   -0.119999   -0.500000   \n",
       "Amazon             -2.309997   -1.640007    1.209999   -1.790001   -2.039994   \n",
       "American express   -0.270001    0.750000    0.300004    0.639999   -0.130001   \n",
       "Boeing             -1.080002    0.360000    0.549999    0.530002   -0.709999   \n",
       "\n",
       "                  ...  2013-10-16  2013-10-17  2013-10-18  2013-10-21  \\\n",
       "Apple             ...    0.320008    4.519997    2.899987    9.590019   \n",
       "AIG               ...    0.919998    0.709999    0.119999   -0.480000   \n",
       "Amazon            ...    2.109985    3.699982    9.570008   -3.450013   \n",
       "American express  ...    0.680001    2.290001    0.409996   -0.069999   \n",
       "Boeing            ...    1.559997    2.480003    0.019997   -1.220001   \n",
       "\n",
       "                  2013-10-22  2013-10-23  2013-10-24  2013-10-25  2013-10-28  \\\n",
       "Apple              -6.540016    5.959976    6.910011   -5.359962    0.840019   \n",
       "AIG                 0.010002   -0.279998   -0.190003   -0.040001   -0.400002   \n",
       "Amazon              4.820008   -4.079986    2.579986    4.790009   -1.760009   \n",
       "American express    0.100006    0.069999    0.130005    1.849999    0.040001   \n",
       "Boeing              0.480003    3.020004   -0.029999    1.940002    1.130005   \n",
       "\n",
       "                  2013-10-29  \n",
       "Apple             -19.589981  \n",
       "AIG                 0.660000  \n",
       "Amazon              3.740021  \n",
       "American express    0.540001  \n",
       "Boeing              0.309998  \n",
       "\n",
       "[5 rows x 963 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('./dataset/company-stock-movements-2010-2015-incl.csv', index_col=0)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "movements = df.values\n",
    "companies = df.index.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "         steps=[('normalizer', Normalizer(copy=True, norm='l2')),\n",
       "                ('kmeans',\n",
       "                 KMeans(algorithm='auto', copy_x=True, init='k-means++',\n",
       "                        max_iter=300, n_clusters=10, n_init=10, n_jobs=None,\n",
       "                        precompute_distances='auto', random_state=None,\n",
       "                        tol=0.0001, verbose=0))],\n",
       "         verbose=False)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import Normalizer\n",
    "\n",
    "# Create a normalizer: normalizer\n",
    "normalizer = Normalizer()\n",
    "\n",
    "# Create a KMeans model with 10 clusters: kmeans\n",
    "kmeans = KMeans(n_clusters=10)\n",
    "\n",
    "# Make a pipeline chaining normalizer and kmeans: pipeline\n",
    "pipeline = make_pipeline(normalizer, kmeans)\n",
    "\n",
    "# Fit pipeline to the daily price movements\n",
    "pipeline.fit(movements)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Which stocks move together?\n",
    "In the previous exercise, you clustered companies by their daily stock price movements. So which company have stock prices that tend to change in the same way? You'll now inspect the cluster labels from your clustering to find out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    labels                           companies\n",
      "42       0                   Royal Dutch Shell\n",
      "39       0                              Pfizer\n",
      "52       0                            Unilever\n",
      "37       0                            Novartis\n",
      "6        0            British American Tobacco\n",
      "46       0                      Sanofi-Aventis\n",
      "49       0                               Total\n",
      "19       0                     GlaxoSmithKline\n",
      "22       1                                  HP\n",
      "14       1                                Dell\n",
      "34       2                          Mitsubishi\n",
      "45       2                                Sony\n",
      "48       2                              Toyota\n",
      "15       2                                Ford\n",
      "21       2                               Honda\n",
      "7        2                               Canon\n",
      "55       3                         Wells Fargo\n",
      "26       3                      JPMorgan Chase\n",
      "3        3                    American express\n",
      "5        3                     Bank of America\n",
      "18       3                       Goldman Sachs\n",
      "16       3                   General Electrics\n",
      "1        3                                 AIG\n",
      "10       4                      ConocoPhillips\n",
      "35       4                            Navistar\n",
      "8        4                         Caterpillar\n",
      "53       4                       Valero Energy\n",
      "57       4                               Exxon\n",
      "44       4                        Schlumberger\n",
      "12       4                             Chevron\n",
      "38       5                               Pepsi\n",
      "40       5                      Procter Gamble\n",
      "28       5                           Coca Cola\n",
      "9        5                   Colgate-Palmolive\n",
      "41       5                       Philip Morris\n",
      "56       5                            Wal-Mart\n",
      "27       5                      Kimberly-Clark\n",
      "33       6                           Microsoft\n",
      "24       6                               Intel\n",
      "11       6                               Cisco\n",
      "51       7                   Texas instruments\n",
      "50       7  Taiwan Semiconductor Manufacturing\n",
      "47       7                            Symantec\n",
      "59       7                               Yahoo\n",
      "32       7                                  3M\n",
      "31       7                           McDonalds\n",
      "30       7                          MasterCard\n",
      "58       7                               Xerox\n",
      "25       7                   Johnson & Johnson\n",
      "23       7                                 IBM\n",
      "20       7                          Home Depot\n",
      "13       7                   DuPont de Nemours\n",
      "2        7                              Amazon\n",
      "43       7                                 SAP\n",
      "54       7                            Walgreen\n",
      "0        8                               Apple\n",
      "17       8                     Google/Alphabet\n",
      "4        9                              Boeing\n",
      "36       9                    Northrop Grumman\n",
      "29       9                     Lookheed Martin\n"
     ]
    }
   ],
   "source": [
    "# Predict the cluster labels: labels\n",
    "labels = pipeline.predict(movements)\n",
    "\n",
    "# Create a DataFrame aligning labels and companies: df\n",
    "df = pd.DataFrame({'labels': labels, 'companies': companies})\n",
    "\n",
    "# Display df sorted by cluster label\n",
    "print(df.sort_values('labels'))"
   ]
  }
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