2. Unsupervised Learning.ipynb

{
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  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Unsupervised-Learning-on-Wine-Quality-Dataset\" data-toc-modified-id=\"Unsupervised-Learning-on-Wine-Quality-Dataset-1\">Unsupervised Learning on Wine Quality Dataset</a></span><ul class=\"toc-item\"><li><span><a href=\"#K-Means-Cluster\" data-toc-modified-id=\"K-Means-Cluster-1.1\">K Means Cluster</a></span></li><li><span><a href=\"#Hierarchical-Cluster-Analysis\" data-toc-modified-id=\"Hierarchical-Cluster-Analysis-1.2\">Hierarchical Cluster Analysis</a></span></li><li><span><a href=\"#Principal-Component-Analysis\" data-toc-modified-id=\"Principal-Component-Analysis-1.3\">Principal Component Analysis</a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Unsupervised Learning on Wine Quality Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "import seaborn as sns\n",
    "\n",
    "pd.options.display.float_format = '{:,.3f}'.format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# load data\n",
    "\n",
    "red = pd.read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/wine-quality/winequality-red.csv\", \n",
    "                  sep = ';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Preprocess data\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(red)\n",
    "\n",
    "X = pd.DataFrame(scaler.transform(red), index=red.index, columns=red.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "      <th>quality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>7.400</td>\n",
       "      <td>0.700</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1.900</td>\n",
       "      <td>0.076</td>\n",
       "      <td>11.000</td>\n",
       "      <td>34.000</td>\n",
       "      <td>0.998</td>\n",
       "      <td>3.510</td>\n",
       "      <td>0.560</td>\n",
       "      <td>9.400</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7.800</td>\n",
       "      <td>0.880</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2.600</td>\n",
       "      <td>0.098</td>\n",
       "      <td>25.000</td>\n",
       "      <td>67.000</td>\n",
       "      <td>0.997</td>\n",
       "      <td>3.200</td>\n",
       "      <td>0.680</td>\n",
       "      <td>9.800</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
       "0          7.400             0.700        0.000           1.900      0.076   \n",
       "1          7.800             0.880        0.000           2.600      0.098   \n",
       "\n",
       "   free sulfur dioxide  total sulfur dioxide  density    pH  sulphates  \\\n",
       "0               11.000                34.000    0.998 3.510      0.560   \n",
       "1               25.000                67.000    0.997 3.200      0.680   \n",
       "\n",
       "   alcohol  quality  \n",
       "0    9.400        5  \n",
       "1    9.800        5  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Before scaling\n",
    "red.iloc[0:2,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "      <th>quality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.528</td>\n",
       "      <td>0.962</td>\n",
       "      <td>-1.391</td>\n",
       "      <td>-0.453</td>\n",
       "      <td>-0.244</td>\n",
       "      <td>-0.466</td>\n",
       "      <td>-0.379</td>\n",
       "      <td>0.558</td>\n",
       "      <td>1.289</td>\n",
       "      <td>-0.579</td>\n",
       "      <td>-0.960</td>\n",
       "      <td>-0.788</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.299</td>\n",
       "      <td>1.967</td>\n",
       "      <td>-1.391</td>\n",
       "      <td>0.043</td>\n",
       "      <td>0.224</td>\n",
       "      <td>0.873</td>\n",
       "      <td>0.624</td>\n",
       "      <td>0.028</td>\n",
       "      <td>-0.720</td>\n",
       "      <td>0.129</td>\n",
       "      <td>-0.585</td>\n",
       "      <td>-0.788</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   fixed acidity  volatile acidity  citric acid  residual sugar  chlorides  \\\n",
       "0         -0.528             0.962       -1.391          -0.453     -0.244   \n",
       "1         -0.299             1.967       -1.391           0.043      0.224   \n",
       "\n",
       "   free sulfur dioxide  total sulfur dioxide  density     pH  sulphates  \\\n",
       "0               -0.466                -0.379    0.558  1.289     -0.579   \n",
       "1                0.873                 0.624    0.028 -0.720      0.129   \n",
       "\n",
       "   alcohol  quality  \n",
       "0   -0.960   -0.788  \n",
       "1   -0.585   -0.788  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# After scaling\n",
    "X.iloc[0:2,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## K Means Cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use K Means Cluster Analysis to identify cluster(s) of observations that have high and low values of the wine quality. (Assume all variables are continuous.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Elbow curve')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use Elbow curve to help select the number of clusters\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "within_cluster_variance = []\n",
    "\n",
    "for k in range(2, 20):\n",
    "    kmeans = KMeans(n_clusters=k, random_state = 0)\n",
    "    kmeans.fit(X)\n",
    "    within_cluster_variance.append(kmeans.inertia_)\n",
    "\n",
    "fig = plt.figure(figsize=(14, 4))\n",
    "plt.plot(range(2, 20), within_cluster_variance, marker='o')\n",
    "plt.grid(True)\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Reduction in within cluster variation')\n",
    "plt.xticks(np.arange(2, 20, step=1))\n",
    "plt.title('Elbow curve')  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(algorithm='auto', copy_x=True, init='k-means++', max_iter=300,\n",
       "    n_clusters=7, n_init=20, n_jobs=1, precompute_distances='auto',\n",
       "    random_state=10, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "km7 = KMeans(n_clusters=7, n_init=20, random_state=10)\n",
    "km7.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "scrolled": false
   },
   "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>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quality</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.034</th>\n",
       "      <td>0.269</td>\n",
       "      <td>-0.994</td>\n",
       "      <td>0.760</td>\n",
       "      <td>-0.100</td>\n",
       "      <td>-0.239</td>\n",
       "      <td>-0.341</td>\n",
       "      <td>-0.537</td>\n",
       "      <td>-0.505</td>\n",
       "      <td>-0.257</td>\n",
       "      <td>0.463</td>\n",
       "      <td>1.016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.501</th>\n",
       "      <td>-1.082</td>\n",
       "      <td>0.340</td>\n",
       "      <td>-0.903</td>\n",
       "      <td>-0.271</td>\n",
       "      <td>-0.414</td>\n",
       "      <td>0.276</td>\n",
       "      <td>-0.162</td>\n",
       "      <td>-1.330</td>\n",
       "      <td>1.148</td>\n",
       "      <td>-0.125</td>\n",
       "      <td>1.174</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.090</th>\n",
       "      <td>1.671</td>\n",
       "      <td>-0.553</td>\n",
       "      <td>1.219</td>\n",
       "      <td>0.119</td>\n",
       "      <td>0.052</td>\n",
       "      <td>-0.487</td>\n",
       "      <td>-0.432</td>\n",
       "      <td>1.205</td>\n",
       "      <td>-0.990</td>\n",
       "      <td>0.223</td>\n",
       "      <td>-0.141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.023</th>\n",
       "      <td>-0.086</td>\n",
       "      <td>-0.035</td>\n",
       "      <td>0.415</td>\n",
       "      <td>4.962</td>\n",
       "      <td>0.296</td>\n",
       "      <td>1.750</td>\n",
       "      <td>1.696</td>\n",
       "      <td>1.225</td>\n",
       "      <td>-0.325</td>\n",
       "      <td>-0.024</td>\n",
       "      <td>-0.364</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.361</th>\n",
       "      <td>0.082</td>\n",
       "      <td>0.018</td>\n",
       "      <td>1.144</td>\n",
       "      <td>-0.399</td>\n",
       "      <td>5.605</td>\n",
       "      <td>-0.070</td>\n",
       "      <td>0.474</td>\n",
       "      <td>0.186</td>\n",
       "      <td>-1.687</td>\n",
       "      <td>3.721</td>\n",
       "      <td>-0.883</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.425</th>\n",
       "      <td>-0.129</td>\n",
       "      <td>0.024</td>\n",
       "      <td>0.059</td>\n",
       "      <td>-0.021</td>\n",
       "      <td>-0.039</td>\n",
       "      <td>1.000</td>\n",
       "      <td>1.233</td>\n",
       "      <td>0.199</td>\n",
       "      <td>-0.094</td>\n",
       "      <td>-0.171</td>\n",
       "      <td>-0.573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.510</th>\n",
       "      <td>-0.429</td>\n",
       "      <td>0.668</td>\n",
       "      <td>-0.783</td>\n",
       "      <td>-0.198</td>\n",
       "      <td>-0.049</td>\n",
       "      <td>-0.486</td>\n",
       "      <td>-0.413</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.342</td>\n",
       "      <td>-0.417</td>\n",
       "      <td>-0.507</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         fixed acidity  volatile acidity  citric acid  residual sugar  \\\n",
       "quality                                                                 \n",
       "1.034            0.269            -0.994        0.760          -0.100   \n",
       "0.501           -1.082             0.340       -0.903          -0.271   \n",
       "0.090            1.671            -0.553        1.219           0.119   \n",
       "-0.023          -0.086            -0.035        0.415           4.962   \n",
       "-0.361           0.082             0.018        1.144          -0.399   \n",
       "-0.425          -0.129             0.024        0.059          -0.021   \n",
       "-0.510          -0.429             0.668       -0.783          -0.198   \n",
       "\n",
       "         chlorides  free sulfur dioxide  total sulfur dioxide  density     pH  \\\n",
       "quality                                                                         \n",
       "1.034       -0.239               -0.341                -0.537   -0.505 -0.257   \n",
       "0.501       -0.414                0.276                -0.162   -1.330  1.148   \n",
       "0.090        0.052               -0.487                -0.432    1.205 -0.990   \n",
       "-0.023       0.296                1.750                 1.696    1.225 -0.325   \n",
       "-0.361       5.605               -0.070                 0.474    0.186 -1.687   \n",
       "-0.425      -0.039                1.000                 1.233    0.199 -0.094   \n",
       "-0.510      -0.049               -0.486                -0.413    0.008  0.342   \n",
       "\n",
       "         sulphates  alcohol  \n",
       "quality                      \n",
       "1.034        0.463    1.016  \n",
       "0.501       -0.125    1.174  \n",
       "0.090        0.223   -0.141  \n",
       "-0.023      -0.024   -0.364  \n",
       "-0.361       3.721   -0.883  \n",
       "-0.425      -0.171   -0.573  \n",
       "-0.510      -0.417   -0.507  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X['cluster7'] = km7.labels_\n",
    "\n",
    "display(X.groupby('cluster7').mean().sort_values(['quality'], ascending = False).set_index('quality'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">quality</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster7</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.023</td>\n",
       "      <td>34.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.510</td>\n",
       "      <td>491.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.501</td>\n",
       "      <td>199.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.361</td>\n",
       "      <td>29.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.034</td>\n",
       "      <td>274.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.090</td>\n",
       "      <td>237.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.425</td>\n",
       "      <td>335.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         quality        \n",
       "            mean    size\n",
       "cluster7                \n",
       "0         -0.023  34.000\n",
       "1         -0.510 491.000\n",
       "2          0.501 199.000\n",
       "3         -0.361  29.000\n",
       "4          1.034 274.000\n",
       "5          0.090 237.000\n",
       "6         -0.425 335.000"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.loc[:,['cluster7', 'quality']].groupby(['cluster7']).aggregate([np.mean, np.size])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variables that cluster with higher values of wine quality.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Low density and high alchol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variables that cluster with lower values of wine quality.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "high density and low alcohol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Characteristics that are most important according to this analysis?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Density and alcohol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Hierarchical Cluster Analysis "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use complete linkage and the same number of groups (clusters) that you found to be the most meaningful in question 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = pd.DataFrame(scaler.transform(red), index=red.index, columns=red.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    " # Import the dendrogram function and the ward clustering function from SciPy\n",
    "from scipy.cluster.hierarchy import dendrogram, complete\n",
    "\n",
    "# Apply the ward clustering to the data array X\n",
    "# The SciPy ward function returns an array that specifies the distances \n",
    "# bridged when performing agglomerative clustering\n",
    "linkage_array = complete(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Cluster distance')"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1728x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now we plot the dendrogram for the linkage_array containing the distances # between clusters\n",
    "fig = plt.figure(figsize=(24, 10))\n",
    "dendrogram(linkage_array)\n",
    "# Mark the cuts in the tree that signify two or three clusters\n",
    "ax = plt.gca()\n",
    "bounds = ax.get_xbound()\n",
    "\n",
    "ax.plot(bounds, [12.45, 12.45], '--', c='k')\n",
    "ax.plot(bounds, [11.05, 11.05], '--', c='k')\n",
    "\n",
    "ax.text(bounds[1], 12.45, ' Three clusters', va='center', fontdict={'size': 15})\n",
    "ax.text(bounds[1], 11.05, ' seven clusters', va='center', fontdict={'size': 15})\n",
    "\n",
    "plt.xlabel(\"Sample index\")\n",
    "plt.ylabel(\"Cluster distance\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AgglomerativeClustering(affinity='euclidean', compute_full_tree='auto',\n",
       "            connectivity=None, linkage='complete', memory=None,\n",
       "            n_clusters=7, pooling_func=<function mean at 0x10e4a5950>)"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "hc7 = AgglomerativeClustering(n_clusters=7,\n",
    "                             affinity='euclidean', \n",
    "                             linkage='complete')\n",
    "hc7.fit(X) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "scrolled": true
   },
   "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>fixed acidity</th>\n",
       "      <th>volatile acidity</th>\n",
       "      <th>citric acid</th>\n",
       "      <th>residual sugar</th>\n",
       "      <th>chlorides</th>\n",
       "      <th>free sulfur dioxide</th>\n",
       "      <th>total sulfur dioxide</th>\n",
       "      <th>density</th>\n",
       "      <th>pH</th>\n",
       "      <th>sulphates</th>\n",
       "      <th>alcohol</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>quality</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1.277</th>\n",
       "      <td>-0.624</td>\n",
       "      <td>-1.291</td>\n",
       "      <td>1.364</td>\n",
       "      <td>5.294</td>\n",
       "      <td>-0.676</td>\n",
       "      <td>3.168</td>\n",
       "      <td>5.956</td>\n",
       "      <td>-1.185</td>\n",
       "      <td>-1.260</td>\n",
       "      <td>-0.815</td>\n",
       "      <td>1.136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.669</th>\n",
       "      <td>2.483</td>\n",
       "      <td>-0.657</td>\n",
       "      <td>1.593</td>\n",
       "      <td>0.193</td>\n",
       "      <td>-0.056</td>\n",
       "      <td>-0.472</td>\n",
       "      <td>-0.452</td>\n",
       "      <td>1.468</td>\n",
       "      <td>-1.626</td>\n",
       "      <td>0.646</td>\n",
       "      <td>0.131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.165</th>\n",
       "      <td>-1.098</td>\n",
       "      <td>0.431</td>\n",
       "      <td>-0.722</td>\n",
       "      <td>-0.284</td>\n",
       "      <td>-0.402</td>\n",
       "      <td>-0.181</td>\n",
       "      <td>-0.186</td>\n",
       "      <td>-1.592</td>\n",
       "      <td>1.127</td>\n",
       "      <td>-0.297</td>\n",
       "      <td>1.529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.070</th>\n",
       "      <td>0.285</td>\n",
       "      <td>-0.598</td>\n",
       "      <td>0.631</td>\n",
       "      <td>6.833</td>\n",
       "      <td>0.639</td>\n",
       "      <td>0.983</td>\n",
       "      <td>0.505</td>\n",
       "      <td>1.903</td>\n",
       "      <td>-0.501</td>\n",
       "      <td>0.115</td>\n",
       "      <td>-0.599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.027</th>\n",
       "      <td>0.010</td>\n",
       "      <td>-0.003</td>\n",
       "      <td>-0.029</td>\n",
       "      <td>-0.043</td>\n",
       "      <td>-0.108</td>\n",
       "      <td>0.023</td>\n",
       "      <td>-0.004</td>\n",
       "      <td>0.070</td>\n",
       "      <td>0.012</td>\n",
       "      <td>-0.125</td>\n",
       "      <td>-0.115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-0.336</th>\n",
       "      <td>0.012</td>\n",
       "      <td>-0.101</td>\n",
       "      <td>0.528</td>\n",
       "      <td>-0.328</td>\n",
       "      <td>2.707</td>\n",
       "      <td>-0.106</td>\n",
       "      <td>0.430</td>\n",
       "      <td>0.260</td>\n",
       "      <td>-1.022</td>\n",
       "      <td>2.585</td>\n",
       "      <td>-0.725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>-1.407</th>\n",
       "      <td>0.075</td>\n",
       "      <td>-0.351</td>\n",
       "      <td>3.127</td>\n",
       "      <td>0.043</td>\n",
       "      <td>11.116</td>\n",
       "      <td>0.394</td>\n",
       "      <td>0.320</td>\n",
       "      <td>0.770</td>\n",
       "      <td>-2.664</td>\n",
       "      <td>5.735</td>\n",
       "      <td>-0.960</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         fixed acidity  volatile acidity  citric acid  residual sugar  \\\n",
       "quality                                                                 \n",
       "1.277           -0.624            -1.291        1.364           5.294   \n",
       "0.669            2.483            -0.657        1.593           0.193   \n",
       "0.165           -1.098             0.431       -0.722          -0.284   \n",
       "0.070            0.285            -0.598        0.631           6.833   \n",
       "-0.027           0.010            -0.003       -0.029          -0.043   \n",
       "-0.336           0.012            -0.101        0.528          -0.328   \n",
       "-1.407           0.075            -0.351        3.127           0.043   \n",
       "\n",
       "         chlorides  free sulfur dioxide  total sulfur dioxide  density     pH  \\\n",
       "quality                                                                         \n",
       "1.277       -0.676                3.168                 5.956   -1.185 -1.260   \n",
       "0.669       -0.056               -0.472                -0.452    1.468 -1.626   \n",
       "0.165       -0.402               -0.181                -0.186   -1.592  1.127   \n",
       "0.070        0.639                0.983                 0.505    1.903 -0.501   \n",
       "-0.027      -0.108                0.023                -0.004    0.070  0.012   \n",
       "-0.336       2.707               -0.106                 0.430    0.260 -1.022   \n",
       "-1.407      11.116                0.394                 0.320    0.770 -2.664   \n",
       "\n",
       "         sulphates  alcohol  \n",
       "quality                      \n",
       "1.277       -0.815    1.136  \n",
       "0.669        0.646    0.131  \n",
       "0.165       -0.297    1.529  \n",
       "0.070        0.115   -0.599  \n",
       "-0.027      -0.125   -0.115  \n",
       "-0.336       2.585   -0.725  \n",
       "-1.407       5.735   -0.960  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X['hc7'] = hc7.labels_\n",
    "\n",
    "\n",
    "\n",
    "display(X.groupby('hc7').mean().sort_values(['quality'], ascending = False).set_index('quality'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"2\" halign=\"left\">quality</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hc7</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.165</td>\n",
       "      <td>130.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.070</td>\n",
       "      <td>13.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.336</td>\n",
       "      <td>63.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.407</td>\n",
       "      <td>2.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.669</td>\n",
       "      <td>51.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.277</td>\n",
       "      <td>3.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.027</td>\n",
       "      <td>1,337.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    quality          \n",
       "       mean      size\n",
       "hc7                  \n",
       "0     0.165   130.000\n",
       "1     0.070    13.000\n",
       "2    -0.336    63.000\n",
       "3    -1.407     2.000\n",
       "4     0.669    51.000\n",
       "5     1.277     3.000\n",
       "6    -0.027 1,337.000"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.loc[:,['hc7', 'quality']].groupby(['hc7']).aggregate([np.mean, np.size])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variables that cluster with higher values of wine quality.**\n",
    "\n",
    "High alcohol, low or high fixed acidity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Variables that cluster with lower values of wine quality.**\n",
    "\n",
    "Low alcohol, medium fixed acidity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Characteristics that are most important according to this analysis?** \n",
    "\n",
    "Alcohol, fixed acidity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Compare Hierarchical clustering with k-means clustering?**\n",
    "\n",
    "Heierarchical do not differentiate density, but fixed acidity. Alcohol remains the most clear sign of quality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principal Component Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use Principal Components Analysis to reduce the dimensions of your data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "# How many PCA returns\n",
    "pca = PCA(n_components=2)\n",
    "X = pd.DataFrame(scaler.transform(red), index=red.index, columns=red.columns)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How much of the variation in your data is explained by the first two principal components. **\n",
    "\n",
    "About 45%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.26009731 0.1868235 ]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_ratio_) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How I use the first two components to do supervised learning on some other variable tied to wine (e.g. - wine price)?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA can reduce the dimensions of the originial data, give us a simpler representation of the training data. \n",
    "\n",
    "Use the first two components we can reduce the data to 2 dimension, which in convenient for visualization, though only contains 45% variance.\n",
    "\n",
    "Use the simpler data to learn other variable can reduce the computational cost and learning time.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create X data with single pca vector\n",
    "X_pca = pca.transform(X) "
   ]
  }
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