370_11_Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SI 370 - Machine Learning I: Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q1: Record your music preferences\n",
    "\n",
    "Fill in your music preferences on https://docs.google.com/spreadsheets/d/1KY8tBiiSeehMDxXc4GU_mOoD8MRnUVkUtinadNJEgrU/edit?usp=sharing\n",
    "\n",
    "Values should range from 1 to 10.  1=no way; 10=the best.  Please fill in a value for each column.\n",
    "\n",
    "We will be downloading the completed sheet to use as data for this class.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide02.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide03.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide01.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide04.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide07.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide09.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide10.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide11.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide12.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide13.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide14.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide15.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide16.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide17.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide18.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide19.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide20.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide21.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide22.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide23.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide24.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide25.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "import scipy.cluster.hierarchy as shc\n",
    "\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "music = pd.read_csv('data/music_w18.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "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>Name</th>\n",
       "      <th>Jazz</th>\n",
       "      <th>Soul</th>\n",
       "      <th>Pop</th>\n",
       "      <th>R&amp;B</th>\n",
       "      <th>Opera</th>\n",
       "      <th>Country</th>\n",
       "      <th>Rock&amp;Roll</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Kai</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Chris</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Michael</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Sonal</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Inayah</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      Name  Jazz  Soul  Pop  R&B  Opera  Country  Rock&Roll\n",
       "0      Kai     8     8   10   10      2        5        6.0\n",
       "1    Chris     4     6    2    7      8        9       10.0\n",
       "2  Michael     7     7    9    8      3        7        7.0\n",
       "3    Sonal     8     7    8    7      3        6        5.0\n",
       "4   Inayah     8     7    9    9      5        6        5.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "music.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "music = music.dropna() # Clustering doesn't like NaNs\n",
    "music_names = music['Name']\n",
    "music_nonames = music.drop('Name',axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0        Kai\n",
       "1      Chris\n",
       "2    Michael\n",
       "3      Sonal\n",
       "4     Inayah\n",
       "Name: Name, dtype: object"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "music_names.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "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>Jazz</th>\n",
       "      <th>Soul</th>\n",
       "      <th>Pop</th>\n",
       "      <th>R&amp;B</th>\n",
       "      <th>Opera</th>\n",
       "      <th>Country</th>\n",
       "      <th>Rock&amp;Roll</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Jazz  Soul  Pop  R&B  Opera  Country  Rock&Roll\n",
       "0     8     8   10   10      2        5        6.0\n",
       "1     4     6    2    7      8        9       10.0\n",
       "2     7     7    9    8      3        7        7.0\n",
       "3     8     7    8    7      3        6        5.0\n",
       "4     8     7    9    9      5        6        5.0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "music_nonames.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 0, 2, 0, 1, 0, 1, 2, 1,\n",
       "       1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0,\n",
       "       2, 1, 2, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = AgglomerativeClustering(n_clusters=3) # we can make up the value for clusters\n",
    "model.fit_predict(music_nonames)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEDCAYAAAAlRP8qAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAHtRJREFUeJzt3X+ULHV55/H3xwsK2gREYOACclXQA4bYV+8irolplRj8kYXdVaOjBFbcKye66vFHwB9rWEQPJhH1HIluo+6FE1rAJIgmmmjQiUsU48VpJYoKsgg43OGC/GpQA/rsH/Xte2t6emZ6pqunu6s/r3PmTHd1dfW3q6uffuqpb31LEYGZmY2/Rwy7AWZmVgwHdDOzknBANzMrCQd0M7OScEA3MysJB3Qzs5IYi4Au6XuSaiPQjk2SQtIeSzz+TkmfGORr9PD8syX9VT9tKIqklqQnDrsdRUifyZHDbkdRJL1A0mdXMf82SecOsk3joshtQdKjJP1A0kFFLG/oAV3SzZJO6Jh2mqSr2/cj4qkRMbPujVuliHh/RLx20K8jaVrS9hQwb5f0RUm/XeDy+/pRaYuISkTcVFS72tKP1kOS7k9/P5L0UUmHFP1aJfZ+4Lz2HWXeKOnfJD0g6TZJn5F0bFEvKKkm6bailpdbZki6oGP61ZJOK/K1BiEifgl8CjiziOUNPaAP0loCkqQNg2hLUSS9Bfgw2RdyCng88JfAScNsV16/PwQ9uiwi9gH2B/4zcDBw7TCCepHbTAqsA/1eSvoPwL4RcU1u8keANwFvJFunTwY+C7x4kG1ZjWW2qweAP5K0af1a07/c+2kAp0p6VL/LHIuAns/iJT1C0lmSfizpLkmXS9o/PdbOLE+XdAvwlTT9M5J2SLpX0tckPTW37G2SPibpC5IeAJ4raW9JH5T0k/ScqyXtnWvSqyTdIulOSe/KLWtBuUPSb0v6uqR7JN3azhgkvVjSrKT70vSze1wP+wLnAK+PiL+NiAci4qGI+HxEvL3L/Isyoo51eVzK9O+TNC/p/DTb19L/e9JewLPS/K+RdL2kuyX9o6QjcssNSa+XdANwQ27akbn1fIGkv09Z9TclPSn3/BdI+mFa338p6Z8lrbi3k97/94A/BHYCb80t8yWSmmn9f13Sb3Wsh7dJ+m56zcsk7ZV7/O3K9n7mJL2mYx1222b2lXSxpJ1pu3l3OzBL2pC2pzsl/T9Jb1BuD0jSjKT3SfoX4EHgiZL+W1rX90u6SdLrOj9XSX8i6Y7UzpMlvUjZ3srPJL1zmdX2QuCfc8s7Cng98MqI+EpE/DIiHoyISyLivM4nq2MPOk3Lf9YvkvT91PafpvX8GOCLwMa0TbUkbdQavs9d3ANsA/6024NdvpcL9kDT+j83bSMtSZ+X9DhJl6Tvxre0+MfiRelzuVPSnyv3I7za70lE3AbcDRy/xPvrXUQM9Q+4GTihY9ppwNXd5gHeDFwDHAY8CvjfwKfTY5uAAC4GHgPsnaa/Btgnzf9hoJlb9jbgXuDZZD9wewEXADPAocAG4D+m57aXfyGwN/A04JfA0WlZZwN/lW4/HrgfeCWwJ/A4oJoeqwHHptf7LWAeOLnjPezRZV2dCDzc7bHcPPk21IDbllrfwDeAU9LtCnD8Um0ATgZuBI4G9gDeDXw993gAXybL7vbOTTsyt55/BhyXnn8JcGl67ADgPuC/pMfeBDwEvHal99gx/Rzgm+n204E7gGemz/DU9N4flVsP/wpsTG2+Hjgjt57ngd8k244aXd5L5zZzMXAl2Xa2CfgRcHqa/wzg+2Tb7GOBf8qvX7Jt7Rbgqen970mWGT8JEPC7ZIH+6bnP9WHgPWne/072Y9ZIr/9U4BfAE5dYf58B3p67fwbwkxW+p9uAc7t9P7t81rcDv5NuP7aj3Z3b46q/zx3PrwG3ke2h3Qc8JU2/Gjit2/ZCx/ad1v+NaX3vmz6rHwEnpM/jYuD/dLzXr5JtN49P8752rd+TNP1zwBv7jqf9LqDvBmRfrBbZr2z770GWDujXA8/PPXYI2Zd/j9wH1XVDTvPvl+bZN7ehXpx7/BHAz4GndXlue/mH5ab9K/CKzg0HeAdwRY/r4MPAh7ptbB3zvQrYscKy8m2osXxA/xrwv4ADlnif+YD+RVKAyq2nB4Ejchvq8zqW0xkEP5F77EXAD9LtPwK+kXtMwK2sPqCfAdyQbn8MeG/H4z8Efje3Hl6de+zPgI+n258Czss99uQu7yW/zWwg+2E/JjftdcBMuv0V4HW5x05gcUA5Z4XP9bPAm3Kf68+BDen+Pml5z8zNfy0pSeiyrC+TfrzS/XcB16zw+tvoPaDfkt7/b3TMU2Px9tjv93nXMtNneFm6vdqA/q7c4x8Evpi7/wcsTAIDODF3/4+Bq9b6PUnTLwHes9xn0MvfqJRcTo6I/dp/ZCtoKUcAV6Td6HvINohfkdWT225t30i7u+elXbr7yL7IkGWFi+ZP0/cCfrxMG3bkbj9Ilt12OnypZUh6pqSvpt3ze8kC0QHd5u1wF3CAiqtRn04WrH6Qditfssy8RwAfya33n5EF3kNz89za9Zm7LbXeNuafG9kWvpaDZ4emdrXb+9Z2e1ObD0+vtar2AD/p8lqd28wjO+b7CbvXTefyuq2nBdMkvVDSNal8cg/ZD2B+G7krIn6Vbv88/Z/PPf5zum+XkO3e75NfFlkgLcp/JWvvT5SVzp61zLyr+j6v4APA70t62hra3LnuVlqXndtHe7ta6/dkH7Jkti+jEtBX41bghfkfgIjYKyJ+mpsncrenyQ4YnkC2O7UpTdcS899Jtrv6JPpz6zLLaJDtYh0eEfsCH+9oz1K+kdp2co9teAB4dPuOsoN3B7bvR8QNEfFK4CCyL8Nfp1pndC6I7P28rmO97x0RX8/N0+15vbidbJe73U7l7/ci1TD/APi/ufa+r6O9j46IT/fYnsNz9x/fZZ7ObeYhsi9z/jntbXLB++tY9qLlKTs49jfAXwBTKcn5Ar1tI734LtkPedtVwGGStvT4/M7t6uD8gxHxrYg4iWy7+ixwefuhLsta7fd5SRFxF9ne7nuXay9ZeaZfndvHXLq91u/J0cB3+m3UOAb0jwPvax9okHSgpOV6eOxDtjt8F9mH+v7lFh4Rvybb5T4/HbTZIOlZWv0R6EuAEyS9XNIe6SBLNdemn0XELyQdR/ajs6KIuJesbnpBOgj2aEl7pmzuz7o85UfAXsoOwu5JVs/b9T4kvVrSgek9t7ODX5HVY38N5PuQfxx4h9IBZWUHAV/W47pYyd8Dx6b3tAfZAbqevnTp/R8NfDo9p31g90LgjLQ3JEmPSethnyUXttvlwGmSjpH0aJY42NaWMuXLybbLfdK2+RagfSDucuBNkg6VtB8rd1F7JNnntBN4WNILgRf00O5efYGsLt9u/w1kPaU+reyA6yMl7SXpFZLO6vL87wBPlVRVdiD57PYD6bmvkrRvRDxEVtdu70nMA49TdnC/bbXf55WcT3bM6+jctCbwHEmPT6/9jj6W3/Z2SY+VdDjZMZ/L0vRVf08kHUpWU79mufl6MY4B/SNk2e2XJN1PthKeucz8F5PtEv2U7GBHLyvtbcB1wLfIdpk+wCrXVUTcQrbb+da0jCbZQVTISkrnpPa/h90ZTC/LPZ8sWLyb7At/K/AGskyoc95702t9guz9P8DCUsaJwPcktcjW6ysi4hcR8SDwPuBf0q7j8RFxBdl6uDSVrv6NrLdE3yLiTuBlZDXQu4BjgO1kP8RL+cPU7nvItoe7gGdExFxa5nayg4UfJSsx3EhW++2lPV8ky/S+kp63VO+KvP9Btn5vIqvfNsgSA8h+XL5ElhnPkgXUh9kd6Dpf/36y7oOXp7ZPp/dYiIj4NnCvpPz35o1k6+oCsnX6Y7LuoJ/v8vwfkR2A/ieynhpXd8xyCnBz2k7OAF6dnvcDsh/em9J2tZHVf59Xem/3kW1H++emfZks4H6X7NjC3611+TlXpmU1yRKST6bXWsv3ZBq4KLI+6X1RKsibjYxUPrkNeFVEfHXY7Slayrg/HhFHrDjz4NrwAuCPI6LX8p0NQNrz/w7wnIi4o+/lOaDbKJD0+8A3yQ5AvZ2s7PLEiPj5sk8cA8rOYXguWZY+RVYfvyYi3jzUhlnpjGPJxcrpWWS7+XeSHdw8uQzBPBFZ99C7yUou15OV2swK5QzdzKwknKGbmZXEegyitMsBBxwQmzZtWs+XNDMbe9dee+2dEXHgSvOta0DftGkT27dvX8+XNDMbe5K6na28iEsuZmYl4YBuZlYSDuhmZiXhgG5mVhIO6GZmJeGAbmZWEg7oZmYl4YBuZlYS63pikS2vXodGY9itMCve9DRs3TrsVpSfM/QR0mhAsznsVpgVq9l0orJenKGPmGoVZmaG3Qqz4tRqw27B5HBANyupUSnhtfc6RyGwl73045KLWUmNSgmvWs3+hm0SSj/O0M1KzCW83UZhD2HQnKGbmZVEaTL0UakX9mOUao1rVfYapdkoK02GPir1wn6MSq1xrSahRmk2ykqToYPrhcM2znsWZmVQmgzdzGzSlSpDN7PxtB7HwNbjGNWwjyE5QzezoVuPY2CDPkY1CseQnKGb2UgY92Ngo3AMyRm6mVlJOEMfc6PU/37U+tEPu55ptt6coY+5Uep/P0r96Eehnmm23pyhl8C41x4HYVT2EszWkwO62RhZTYltLSUwl6nGm0suZmNkNSW21ZbAXKYafz1l6JJuBu4HfgU8HBFbJO0PXAZsAm4GXh4Rdw+mmWbWNqgSm8tU4281GfpzI6IaEVvS/bOAqyLiKOCqdN/MzIaknxr6SUAt3b4ImAHO7LM9ZmYjY9yOWfSaoQfwJUnXSmq//FRE3A6Q/h/U7YmStkraLmn7zp07+2+xmdk6GbdjFr1m6M+OiDlJBwFflvSDXl8gIupAHWDLli2xhjaamQ3NOB2z6ClDj4i59P8O4ArgOGBe0iEA6f8dxTfPzMx6tWKGLukxwCMi4v50+wXAOcDngFOB89L/KwfZUDMbP73WoFdTf3Zf+aX1UnKZAq6Q1J6/ERH/IOlbwOWSTgduAV42uGaa2Thq16BXqi33WntuB34H9O5WDOgRcRPwtC7T7wKeP4hGmVl5FFmDdl/55fnUf7MJ1K0UslTZwyWO8eFT/80mULfueN263Xk4gPHiDN1sQvVSCnGJY7w4QzczKwln6DZyirgKUxFXT3Lt2MaNM3QbOUVchanfqye5dmzjyBm6jaRhX4XJtWMbR87QzcxKwhm62YhyX3FbLWfoZiPKfcVttZyhm40w9xW31XBAN7OR0Et31V67o05qCcolFzMbCb10V+2lO+okl6CcoZvZyCiiu+okl6CcoZuZlYQz9CEo4tT2tiJOce80qfVHs3HnDH0Iiji1va3fU9w7TXL90WzcOUMfkmGf2r6USa4/mo07Z+hmZiXhDN3MbMB6Hcah3+NXztDNzAasl2Ecijh+5QzdzGwdrHTcrIjjVw7oZmaUY3RLl1zMzCjH6JbO0M3MknEf3dIZuplZSThDt4m00vALvQypMKp1VJtcztBtIq00/MJKQyqMch3VJlfPGbqkDcB24KcR8RJJTwAuBfYHvg2cEhH/PphmmhWvn+EXRrmOapNrNRn6m4Drc/c/AHwoIo4C7gZOL7JhZma2Oj1l6JIOA14MvA94iyQBzwOm0ywXAWcDHxtAG83MFlnqOMi49R0vUq8Z+oeBPwF+ne4/DrgnIh5O928DDu32RElbJW2XtH3nzp19NdbMrG2p4yDj1ne8SCtm6JJeAtwREddKqrUnd5k1uj0/IupAHWDLli1d5zEzW4tej4NMyjGPXkouzwb+k6QXAXsBv0GWse8naY+UpR8GzA2umWZmtpIVA3pEvAN4B0DK0N8WEa+S9BngpWQ9XU4FriyyYfVr6zSu630fqbnjwwDUtr15Va8zfew0W59R8sKamU2Efk4sOhO4VNK5wCzwyWKalGlc16C5o0n14N6ur1Y9a3WBHKC5IyvAOaCbWRmsKqBHxAwwk27fBBxXfJN2qx5cZea0mYEtv7atNrBlm5mtN5/6b7aEubk68/Pdy36tVlbim53tvmc4NTXNxo3e87P15YButoT5+QatVpNKZXHZ78ILly7xtVpZKc8B3dabA7rZMiqVKps3z6zqObOztYG0xWwlHpzLzKwknKHbupirzzHfmO9p3lbzSABmazf2NP/U9BQbt25cc9vMysIB3dbFfGOeVrNFpVpZcd4Lq70FcoBWswXggG6GA7qto0q1wuaZzYUuc7Y2W+jyzMaZa+hmZiXhDN3MbBn1ep1GbqjGZjMNM1Jb2HV1enqarUMen9cB3cxsGY1Gg2azSTWNyVutLj4HoZnG8XVANzMbcdVqlZllxumtjcj4vA7oE6w+N0djfmFXwmYr6zJYm13Y02R6aoqtG92TxGyUOaBPsMb8PM1Wi2pld1fC6oWLuww2W1nXQAd0s9HmgD7hqpUKM5uX70pYm3XXQLNx4G6LZmYl4QzdxsJSQwe0zxTtdoKRhwSwSeMM3cZCe+iATpVqpetwAq1mq+exY8zKwhm6jY3VDB3gIQFsEjlDNzMriYnJ0OvX1mlct/ByYu2LRHdeW3T62GlfONrMxs7EZOiN6xq7Anhb9eAq1YMXXl6suaO5KPCbmY2DicnQIQvgM6fNLDtPZ7ZuZjYuJiqgm9nyOkuTzR1pZMFtuwekcklydDmgm9ku7dJkuxRZPWvhyILtsqUD+mhyQDezBZYrTbokOdom5qComVnZOUMvWr0OjRV6yaQrnlBbPFD+AtPTMOQB881sfDigF63RgGYTqtUlZ5npcsWTRdIVUBzQzaxXKwZ0SXsBXwMeleb/64j4U0lPAC4F9ge+DZwSEf8+yMaOjWoVlrm6SU9G5AooZjY+eqmh/xJ4XkQ8DagCJ0o6HvgA8KGIOAq4Gzh9cM00M7OVrJihR0QA7WHu9kx/ATwPmE7TLwLOBj5WfBPNepMfYrdzWF0PpWuToKdeLpI2SGoCdwBfBn4M3BMRD6dZbgMOXeK5WyVtl7R9586dRbTZrKv8ELv5YXU9lK5Nip4OikbEr4CqpP2AK4Cju822xHPrQB1gy5YtXecxK0q3IXY9lK5NilX1Q4+Ie4AZ4HhgP0ntH4TDgLlim2ZmZqvRSy+XA4GHIuIeSXsDJ5AdEP0q8FKyni6nAlcOsqFmlqnX6zRy5zo003kNtdx5DdPT02x1l9eJ00vJ5RDgIkkbyDL6yyPi7yR9H7hU0rnALPDJAbbTzJJGo0Gz2aSaznWodpzX0EznMDigT55eerl8F1h03a+IuAk4bhCNMrPlVatVZpY416Hmcxgmls8UNSuBfBmmnaG3A7vLL5PDg3OZlUC7DANZ9t4uxzSbzQX1dis3Z+hmJdGtDOPyy2Rxhm5mVhLO0G2R+twcjfndZ1Y2W9nZl7XZ3SfoTE9NsXWjT6U3GyXO0G2Rxvz8riAOUK1UqFYqu+43W60FAd/MRoMzdOuqWqkws3lRb1VgYaZuZqPDGbqZWUk4Q7eByA9lC4uHs23zsLZmxXGGbgORH8oWFg5n2+Zhbc2K5QzdBqbbULZ5HtbWrFgO6GY2NPkuss3WkQDUZm8E3DV2LRzQzWxo2l1kq5UK1Qtv3DW93W3WAX11HNDNbKi6dZF119i18UFRM7OScIZuZsWq16E9wmO6mhLtqylNT4OH8h0YB3QzK1ajAc0mVKvM5K+mlIb3dUAfHAd0MytetQqdV1TyUL4D5xq6mVlJDD1Dr19bp3Hd4iuqNHeky2htq3V93vSx02x9hnfdzMzahp6hN65r7AreedWDq1QPrnZ9TnNHs+uPgJnZJBt6hg5Z8J45babn+ZfK2s3MJtlIBHQzs0mULzk3d2RdPGvbsp5BaykrO6CbmQ1Ju+RcPbhK9azdXTzbZWgHdDOzMdKt5LzWsvLQD4qamVkxnKGbWWnNzdWZn2/QamX16dnZrKwxNTXNxo3l6/bsgG5mpZUF8yYXXri7Pt1qZfXpiQzokg4HLgYOBn4N1CPiI5L2By4DNgE3Ay+PiLsH11Qzs9WrVKps3jyz6/7sbG1obRm0XmroDwNvjYijgeOB10s6BjgLuCoijgKuSvfNzGxIVszQI+J24PZ0+35J1wOHAicBtTTbRcAMcOZAWmk2oto12rz2Ln1nJljWuq2NjlX1cpG0CdgMfBOYSsG+HfQPWuI5WyVtl7R9586d/bXWbMS0a7R5lUqVSmXhsBWtVnNR4DcrWs8HRSVVgL8B3hwR90nq6XkRUQfqAFu2bIm1NNJslHXWaLspc93WRkdPGbqkPcmC+SUR8bdp8rykQ9LjhwB3DKaJZmbWi156uQj4JHB9RJyfe+hzwKnAeen/lQNpodk6ytfEO2vhroHbqOul5PJs4BTgOkntYuE7yQL55ZJOB24BXjaYJpqtn3ZNvLMOXua+y1YevfRyuRpYqmD+/GKbYzZ83WriroHbOJjoM0W7XS2p25WSfHUkMxsHEz04V7erJXVeKclXRzKzcTHRGTqsfLUkXx3JzMbFRGfoZmZl4oBuZrYG9XqdWq1GrVaj2WzSbDap1WrU6/WhtckB3cxsDRqNBs1mdgyuWq1SrVZpNps0GsM75jbxNXQzs7WqVqvMzMzsul+r1YbWFnCGbmZWGiOfobuvuJlZb0Y+Q3dfcTOz3ox8hg7uK25m1ouxCOg2mebqc8w35gFoNVsAzNZmAZianmLj1o1Da5vZKBr5kotNrvnG/K5AXqlWqFQrQBbc24HezHZzhm4jrVKtsHlm84Jp7SzdzBZyhm5mVhLO0M1sWfmuw51dht1deLQ4QzezZeW7Due7DLu78Ohxhm5mK+rWddjdhUePM3Qzs5Jwhm5WsLm5OvPzC0sR7YtM569NOjU17YtOW6GcoZsVbH6+sSuAt1UqVSqV3cNVtFrNRUHfrF/O0M0GoFKpsnnzzJKP5zN1s6I4oA9TvQ5LDYafBs5nqfGVp6dhq3fXzWw3l1yGqdHYHbg7VavZXzfN5tI/BGY2sZyhD1u1CrkrnvRkyFdFMbPR5AzdzKwkhpKhL3UqsU8jNjNbu6Fk6N1OJfZpxGZm/VkxQ5f0KeAlwB0R8Ztp2v7AZcAm4Gbg5RFx92peuPNUYp9GbGbWn14y9G3AiR3TzgKuioijgKvSfTMzG6IVM/SI+JqkTR2TTwJq6fZFwAxwZoHtGioPF2pm42itNfSpiLgdIP0/aKkZJW2VtF3S9p07d67x5daXhws1s3E08F4uEVEH6gBbtmyJQb9eUTxcqJmNm7Vm6POSDgFI/+8orklmZrYWa83QPwecCpyX/l9ZWItsJNXn5mjMzwPQbLUAqM1mF2uenppi68aNQ2ubmWVWzNAlfRr4BvAUSbdJOp0skP+epBuA30v3rcQa8/O7Anm1UqFaqQBZcG8HejMbrl56ubxyiYeeX3BbbMRVKxVmNm9eMK2dpZvZ8HkslyLU69mAWbVaNhJis5ndrteH3DAzmyQO6EXID4PbHvbWQ9ya2Trz8LlF6RwG10Pcmtk6c4ZuZlYSztBHXbfL1C11eTpfls5sojlDH3XdLlPX7fJ0rtmbTTxn6OOgl8vUuWZvNvGcoZuZlYQzdDMbG3P1OeYb2ZnJreaRAMzWbgRganqKjVsnewgKB3QzGxvzjXlazRaVaoULqzfumt5qZsNSOKCbmY2RSrXC5pmFQ1DM1jwEBTig2zpbuMucZVWztVnvLpsVwAdFbV21d5khy7Qq1QqtZmtXkDeztXOGbuuuc5fZu8tmxXCGbmZWEs7Qx1XnkADdhgPwUABmE8UZ+rjqHBKgczgADwVgNnGcoY+z5YYE8FAAZhPHGbqZWUk4Q19v+dp3Z93bNW8z64Mz9PXW7XJ14Jq3mfXNGfowdKt9u+ZtZn1yQDdbJ3Nzdebns72wVivbS5udrQEwNTXNxo0ut1l/XHIxWyfz841dgbxSqVKpZOW2Vqu5K9Cb9cMZutk6qlSqbN48s2BaO0s365czdDOzknCGXibuEmk20Zyhl4m7RJpNtL4ydEknAh8BNgCfiIjzCmmVrZ27RJpNrDVn6JI2ABcALwSOAV4p6ZiiGmZmZqvTT4Z+HHBjRNwEIOlS4CTg+0U0rBe1bTUAmjuaC+7PnDazXk0wMxsZioi1PVF6KXBiRLw23T8FeGZEvKFjvq1A+2jcU4Afrr25ZmYT6YiIOHClmfrJ0NVl2qJfh4ioA/U+XsfMzHrQTy+X24DDc/cPA+b6a46Zma1VPwH9W8BRkp4g6ZHAK4DPFdMsMzNbrTWXXCLiYUlvAP6RrNvipyLie4W1zMzMVmXNB0XNzGy0+ExRM7OScEA3MyuLiFjXP+DpwLnA+cBjipzuZY/Ga/r9FLLs3wHOBC4C9i9y+iCXnaY/GdgGnLzctEFPH9dlLzd9xfi6mpmL+AP+nOxg7HM6VlDf073s0XhNv5/+l517zv8EnjiI6QNedq3z/XSbNujp47rs5aYv9zeskkt0/C9yupc9Gq/p99PnsiVNAzdFGl6jyOmDXLYN0WqifxF/wDOA9wIfBCpFTveyR+M1/X4KWfbLgH8A3kx22ndh0we57DT9YOCjwCdzr7lo2qCnj+uyl5u+0p+7LZqZlYR7uZiZlYQDuplZSTigm5mVhAO6mVlJOKCbmZWEA7qZWUn8f34h43ZXTMk2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Authors: Mathew Kallada & Chris Teplovs\n",
    "# License: BSD 3 clause\n",
    "\"\"\"\n",
    "=========================================\n",
    "Plot Hierarachical Clustering Dendrogram \n",
    "=========================================\n",
    "This example plots the corresponding dendrogram of a hierarchical clustering\n",
    "using AgglomerativeClustering and the dendrogram method available in scipy.\n",
    "\"\"\"\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "def plot_dendrogram(model, **kwargs):\n",
    "\n",
    "    # Children of hierarchical clustering\n",
    "    children = model.children_\n",
    "\n",
    "    # Distances between each pair of children\n",
    "    # Since we don't have this information, we can use a uniform one for plotting\n",
    "    distance = np.arange(children.shape[0])\n",
    "\n",
    "    # The number of observations contained in each cluster level\n",
    "    no_of_observations = np.arange(2, children.shape[0]+2)\n",
    "\n",
    "    # Create linkage matrix and then plot the dendrogram\n",
    "    linkage_matrix = np.column_stack([children, distance, no_of_observations]).astype(float)\n",
    "\n",
    "    # Plot the corresponding dendrogram\n",
    "    dendrogram(linkage_matrix, **kwargs)\n",
    "\n",
    "\n",
    "model = AgglomerativeClustering(n_clusters=3)\n",
    "model = model.fit(music_nonames)\n",
    "\n",
    "plt.title('Hierarchical Clustering Dendrogram (People)')\n",
    "\n",
    "plot_dendrogram(model,labels=music_names.values)\n",
    "plt.xticks(rotation=90)\n",
    "plt.show()\n",
    "\n",
    "plt.title('Hierarchical Clustering Dendrogram (Cluster Number)')\n",
    "plot_dendrogram(model,labels=model.labels_)\n",
    "plt.xticks(rotation=0)\n",
    "plt.show()\n",
    "\n",
    "plt.title('Hierarchical Clustering Dendrogram (Row Number)')\n",
    "plot_dendrogram(model)\n",
    "plt.xticks(rotation=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q2: What's the \"best\" choice for the number of clusters?  What are your options? How would you choose? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Insert your answer here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide26.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide27.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide28.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide31.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide32.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide33.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide34.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide36.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](resources/clustering/Slide37.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.cluster import KMeans\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Labels:\n",
      "[0 0 0 0 0 2 0 2 1 0 2 1 0 2 0 1 2 1 2 0 1 1 1 0 2 2 2 0 1 0 0 2 0 2 0 0 0\n",
      " 0 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 1 2 0 0 0]\n"
     ]
    }
   ],
   "source": [
    "kmeans = KMeans(n_clusters=3) # start with 2 clusters\n",
    "kmeans.fit(music_nonames)\n",
    "print(\"Labels:\")\n",
    "print(kmeans.labels_)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's join the labels with the original dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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>Name</th>\n",
       "      <th>Jazz</th>\n",
       "      <th>Soul</th>\n",
       "      <th>Pop</th>\n",
       "      <th>R&amp;B</th>\n",
       "      <th>Opera</th>\n",
       "      <th>Country</th>\n",
       "      <th>Rock&amp;Roll</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>Kai</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>Chris</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>Michael</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>Sonal</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>Inayah</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2</td>\n",
       "      <td>Adam</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>Huan</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2</td>\n",
       "      <td>Zoe</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1</td>\n",
       "      <td>Yi</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>PJ</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>2</td>\n",
       "      <td>Luke</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1</td>\n",
       "      <td>EJ</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0</td>\n",
       "      <td>Yifan</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>2</td>\n",
       "      <td>Rap</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0</td>\n",
       "      <td>Arwen</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>10</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1</td>\n",
       "      <td>Shen</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>10</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>2</td>\n",
       "      <td>Johan</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1</td>\n",
       "      <td>Phil</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>2</td>\n",
       "      <td>Koki</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0</td>\n",
       "      <td>Jinghui</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1</td>\n",
       "      <td>Anthony</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1</td>\n",
       "      <td>Stella</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1</td>\n",
       "      <td>Aaron</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0</td>\n",
       "      <td>Anna</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>10</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>2</td>\n",
       "      <td>ChrisB</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>2</td>\n",
       "      <td>Weiran</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>2</td>\n",
       "      <td>Haowen</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0</td>\n",
       "      <td>Luke</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>1</td>\n",
       "      <td>Sunghun</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0</td>\n",
       "      <td>YL</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0</td>\n",
       "      <td>Rugved</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>2</td>\n",
       "      <td>Paul</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>6</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>0</td>\n",
       "      <td>Ang</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>2</td>\n",
       "      <td>Christina</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>0</td>\n",
       "      <td>Chengyi</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>0</td>\n",
       "      <td>Liam</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0</td>\n",
       "      <td>Lauren S</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>0</td>\n",
       "      <td>PinChia</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>1</td>\n",
       "      <td>Lai</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>0</td>\n",
       "      <td>Yuheng Cai</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>0</td>\n",
       "      <td>Sec</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>9.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>1</td>\n",
       "      <td>Chuyao</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>0</td>\n",
       "      <td>Yuanting</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>7.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>0</td>\n",
       "      <td>Jing Wang</td>\n",
       "      <td>8</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>0</td>\n",
       "      <td>Eric Kim</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>1</td>\n",
       "      <td>Akio</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>1</td>\n",
       "      <td>Anant</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>6</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>0</td>\n",
       "      <td>Shanmeng</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>1</td>\n",
       "      <td>js</td>\n",
       "      <td>7</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>0</td>\n",
       "      <td>Chen</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>1</td>\n",
       "      <td>Ping</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51</th>\n",
       "      <td>0</td>\n",
       "      <td>Mengying</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52</th>\n",
       "      <td>1</td>\n",
       "      <td>Innocent</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53</th>\n",
       "      <td>1</td>\n",
       "      <td>Dong</td>\n",
       "      <td>10</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>2</td>\n",
       "      <td>Ethan</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0</td>\n",
       "      <td>PJC</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "      <td>6</td>\n",
       "      <td>6.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0</td>\n",
       "      <td>Albert</td>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>10</td>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>57</th>\n",
       "      <td>0</td>\n",
       "      <td>Yen</td>\n",
       "      <td>9</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>8.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    0        Name  Jazz  Soul  Pop  R&B  Opera  Country  Rock&Roll\n",
       "0   0         Kai     8     8   10   10      2        5        6.0\n",
       "1   0       Chris     4     6    2    7      8        9       10.0\n",
       "2   0     Michael     7     7    9    8      3        7        7.0\n",
       "3   0       Sonal     8     7    8    7      3        6        5.0\n",
       "4   0      Inayah     8     7    9    9      5        6        5.0\n",
       "5   2        Adam     8     7   10    8      1        2        9.0\n",
       "6   0        Huan     7     8    9    8      5        5        9.0\n",
       "7   2         Zoe     4     9    8   10      2        1        8.0\n",
       "8   1          Yi     6     3    7    2      6        3        5.0\n",
       "9   0          PJ     4    10    7    3      1        6        6.0\n",
       "10  2        Luke     5     3    4    2      2        1       10.0\n",
       "11  1          EJ     9     8    6    4      4        2        5.0\n",
       "12  0       Yifan     3     3    8    7      4        7       10.0\n",
       "13  2         Rap     8     5    7    6      2        2        8.0\n",
       "14  0       Arwen     7     8    8    5      2       10        8.0\n",
       "15  1        Shen     7     8    7    3      4       10        1.0\n",
       "16  2       Johan     4     6    7    9      1        2        7.0\n",
       "17  1        Phil     8     7    4    4      9        1        8.0\n",
       "18  2        Koki     7     5    3    9      1        1        8.0\n",
       "19  0     Jinghui     8     6    6    4      4        7        9.0\n",
       "20  1     Anthony     6     6    4    4      0        8        2.0\n",
       "21  1      Stella     6     4    9    7      2        1        1.0\n",
       "22  1       Aaron     8     3    2    5      8        1        9.0\n",
       "23  0        Anna     7     7   10    6      2        9        9.0\n",
       "24  2      ChrisB     7     3    8    9      2        1        7.0\n",
       "25  2      Weiran     8     5    8    7      2        2        9.0\n",
       "26  2      Haowen     7     5   10    8      4        1        8.0\n",
       "27  0        Luke     6     4    8    6      2        6        7.0\n",
       "28  1     Sunghun     8     8    7    5      3        4        5.0\n",
       "29  0          YL     9     8    9    8      3        7        5.0\n",
       "30  0      Rugved     6     7    5    9      2        7       10.0\n",
       "31  2        Paul     2     2    8    8      0        6        9.0\n",
       "32  0         Ang     6     4    8    6      6        5        8.0\n",
       "33  2   Christina     7     8    8   10      3        3        5.0\n",
       "34  0     Chengyi     7     3    9   10      8        8        7.0\n",
       "35  0        Liam     5     6   10    9      0        8        7.0\n",
       "36  0    Lauren S     5     3   10    1      2        8        6.0\n",
       "37  0     PinChia     5     5    8    7      3        7        8.0\n",
       "38  1         Lai     8     3    1    5      6        7        5.0\n",
       "39  0  Yuheng Cai     8     2    8    8      2        9        9.0\n",
       "40  0         Sec     3     7    7    3      5       10        9.0\n",
       "41  1      Chuyao     9     5    5    2      7        7        7.0\n",
       "42  0    Yuanting    10     5    8    8      2        9        7.0\n",
       "43  0   Jing Wang     8     7    9    7      4        5        6.0\n",
       "44  0    Eric Kim     3     8    9    9     10       10        4.0\n",
       "45  1        Akio     7     4    5    5      8        3        3.0\n",
       "46  1       Anant     9    10    5    5      2        6        2.0\n",
       "47  0    Shanmeng     8     5   10    5      5        8       10.0\n",
       "48  1          js     7     5   10    9      6        3        2.0\n",
       "49  0        Chen     7     6    9    8      5        8        5.0\n",
       "50  1        Ping     2     2    4    4      5        8        2.0\n",
       "51  0    Mengying     2     9    7    4      4        9        6.0\n",
       "52  1    Innocent    10     8    5    9      5        3        3.0\n",
       "53  1        Dong    10     7    3   10      9        5        3.0\n",
       "54  2       Ethan     6     7    7    9      3        3       10.0\n",
       "55  0         PJC     5     7    9    6      4        6        6.0\n",
       "56  0      Albert     9     8   10   10      5       10       10.0\n",
       "57  0         Yen     9     6    9    9      5        7        8.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([pd.DataFrame(kmeans.labels_).reset_index(),music.reset_index()],axis=1).drop('index',axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a number of different evaluation metrics available, but one of the most common is called the \"silhouette score\", which range between -1 and 1.  Higher values indicate a better model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16923750699186288"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "metrics.silhouette_score(music_nonames,kmeans.labels_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Q3: Repeat the k-means clustering with 3,4,5...n clusters. \n",
    "Which of these is best based on the silhouette scores?  Can you create a plot of silhouette scores vs. k?\n",
    "\n",
    "NOTE: We'll return to visualization of k-means after we talk about dimension reduction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Insert your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}