HW2_Q2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Load the dataset.\n",
    "2. Trim the unwanted columns to perform pca and for clustering.  \n",
    "3. Scale, Fit , Transform the data before PCA.\n",
    "4. Calculate PCA and Variance for n components, here n = (1,2,3,4).\n",
    "5. kmeans is performed over Projected data.\n",
    "6. Silhoutte score is calculated using the parameters : Projected data and Kmeans labels.\n",
    "7. Adjusted Rand index Score is calculated using the parameters: Labels and Kmeans labels.\n",
    "    Note: Labels are given to each group in 'target'.\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "import seaborn\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_score, adjusted_rand_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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>sepal length</th>\n",
       "      <th>sepal width</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>Iris-virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal length  sepal width  petal length  petal width          target\n",
       "0             5.1          3.5           1.4          0.2     Iris-setosa\n",
       "1             4.9          3.0           1.4          0.2     Iris-setosa\n",
       "2             4.7          3.2           1.3          0.2     Iris-setosa\n",
       "3             4.6          3.1           1.5          0.2     Iris-setosa\n",
       "4             5.0          3.6           1.4          0.2     Iris-setosa\n",
       "..            ...          ...           ...          ...             ...\n",
       "145           6.7          3.0           5.2          2.3  Iris-virginica\n",
       "146           6.3          2.5           5.0          1.9  Iris-virginica\n",
       "147           6.5          3.0           5.2          2.0  Iris-virginica\n",
       "148           6.2          3.4           5.4          2.3  Iris-virginica\n",
       "149           5.9          3.0           5.1          1.8  Iris-virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sscore = []\n",
    "ariscore = []\n",
    "df=pd.read_csv('iris.csv')\n",
    "df = pd.read_csv('iris.csv', names=['sepal length','sepal width','petal length','petal width','target'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = df.drop(['target'],axis =1)\n",
    "label = df['target']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA in conjunction with k-means is a powerful method for visualizing high dimensional data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.Reduce Dimensionality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_std = StandardScaler().fit_transform(df1)#scale, fit, transform  the data "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "USING 1 COMPONENT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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S1DiDQJIaZxBIUuMMAklqnEEgSY0zCCSpcQaBJDXOIJCkxhkEktQ4g0CSGmcQSFLjDAJJapxBIEmN6zUIkmxJciTJTJJrR6x/dJI/6NZ/NMn6PuuRJJ2otyBIsgrYDVwJbAKuTrJpXrefAO6rqqcCbwJ+ra96JEmj9XlEsBmYqaqjVfUgsBfYNq/PNuCt3ecbgecnSY81SZLmObfHsdcAdw21Z4FLF+pTVceSfBb4V8A/DndKsgPY0TW/kORILxVL0tew0/w7+ckLregzCEZVXKfQh6raA+w5E0VJkh6uz1NDs8C6ofZa4O6F+iQ5F3gc8Okea5IkzdNnEBwANibZkGQ1sB2YmtdnCnhJ9/mFwPur6oQjAklSf3o7NdSd898J7AdWAW+pqkNJdgHTVTUF/G/g95LMMDgS2N5XPZKk0eIf4DqbJPkK8AkGf+TcDrykqr6Y5JuA3wQuAb4M3AG8uqo+1W33GuD1wBOr6rMLjP1G4PuBfVX18ydZ18XAk6pq3yn9YFKPvLNYZ5sHquriqnoG8CDwsu6S5HcCH6iqp1TVJuAXgCcObXc1g9OZVy0y9k8Bzz7ZEOhczCBExpYB/x9V7/yPTGezm4GnApcBD1XV/zi+oqoOVtXNAEmeApwHvI5BIJwgyRTw9cBHk7woyUSSP0xyoPt6btdvc5L/l+Tj3fend3Nku4AXJTnYbX99kp8bGv+TSdZ3X7cneTPwMWBdku9L8pEkH0vyjiTnddv81ySHk9yW5NfP/D+fWuGpIZ1Vknyhqs7rrkL7Q+BPgUcBG6rqNQts8zoGlzL/KnAU2FxV9yw0dvf5BuDNVfWhJBcB+6vqW5JcAHyxmyO7HHh5Vf1QkmuAyara2W1/PfCFqvr1rv1J4AXdro4C31lVtyS5EPgj4Mqquj/Ja4FHA/8N+AjwzVVVSb6hqj5zmv98alSf9xFIK+HrkhzsPt/M4IKEly2xzXbgqqr6apI/An6YweNRFnM5sGnoBp8LkpzP4BLotybZyOCemEedws9wZ1Xd0n1+DoNHtHy429dqBgHwOeBLwP9K8h7g3aewHwkwCHT2eaCqLh5ekOQQg8uTT5DkmcBG4L1Dv2iPsnQQnAN8R1U9MG+83wFuqqqruocofmCB7Y/x8FOzjxn6fP/wkMB7q+qEU1ZJNgPPZxBkO4HvXaJmaSTnCNSC9wOPTvLS4wuSXJLkeQzmBK6vqvXd15OANUkWvB2/82cMfvkeH+94+DwO+Pvu8zVD/T8PnD/UvgN4drfts4ENC+znFuC5SZ7a9X1skqd18wSP665CejWDyWjplBgEOut1NyleBVyR5G+6I4TrGdzpvp3BFUXD3snS97S8EpjsJmoP8y+nn94AvD7JhxncP3PcTQxOJR1M8iIG8xeP705jvRz41AK1zzEIlN9PchuDYPhmBqHy7m7ZB4GR8x/SOJwslqTGeUQgSY0zCCSpcQaBJDXOIJCkxhkEktQ4g0CSGmcQSFLj/gmhX+S9tNljrwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca1 = PCA(n_components=1)# calculating the pca\n",
    "principalComponents1 = pca1.fit_transform(X_std)# projecting the data \n",
    "features = range(pca1.n_components_)\n",
    "plt.bar([1], pca1.explained_variance_ratio_, color='black')\n",
    "plt.xlabel('PCA features')\n",
    "plt.ylabel('variance %')\n",
    "plt.xticks(features)\n",
    "PCA_components1 = pd.DataFrame(principalComponents1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhoutte score is 0.6754183875905303\n",
      "Adjusted rand index is 0.8015498244339507\n"
     ]
    }
   ],
   "source": [
    "kmeans1 = KMeans(n_clusters=3)\n",
    "#print(kmeans.labels_)\n",
    "kmeans1.fit(PCA_components1)\n",
    "#print(kmeans.labels_)\n",
    "score1 = silhouette_score(PCA_components1,kmeans1.labels_)\n",
    "print('Silhoutte score is', score1)\n",
    "labels1 = pd.factorize(label)[0]\n",
    "len(kmeans1.labels_)\n",
    "ari1 = adjusted_rand_score(labels1,kmeans1.labels_)\n",
    "print('Adjusted rand index is', ari1)\n",
    "#pca 1 component\n",
    "sscore.append(score1)\n",
    "ariscore.append(ari1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "USING 2 COMPONENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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": [
    "pca2 = PCA(n_components=2)\n",
    "principalComponents2 = pca2.fit_transform(X_std)\n",
    "features = range(pca2.n_components_)\n",
    "plt.bar([1,2], pca2.explained_variance_ratio_, color='black')\n",
    "plt.xlabel('PCA features')\n",
    "plt.ylabel('variance %')\n",
    "plt.xticks(features)\n",
    "PCA_components2 = pd.DataFrame(principalComponents2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhoutte score is 0.5113245176460453\n",
      "Adjusted rand index is 0.6011286543750637\n"
     ]
    }
   ],
   "source": [
    "kmeans2 = KMeans(n_clusters=3)\n",
    "kmeans2.fit(PCA_components2)\n",
    "score2 = silhouette_score(PCA_components2,kmeans2.labels_)\n",
    "print('Silhoutte score is', score2)\n",
    "labels2 = pd.factorize(label)[0]\n",
    "len(kmeans2.labels_)\n",
    "ari2 = adjusted_rand_score(labels2, kmeans2.labels_)\n",
    "print('Adjusted rand index is', ari2)\n",
    "#pca 2 components\n",
    "sscore.append(score2)\n",
    "ariscore.append(ari2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "USING 3 COMPONENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    },
    {
     "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": [
    "pca3 = PCA(n_components=3)\n",
    "principalComponents3 = pca3.fit_transform(X_std)\n",
    "features = range(pca3.n_components_)\n",
    "plt.bar([1, 2, 3], pca3.explained_variance_ratio_, color='black')\n",
    "plt.xlabel('PCA features')\n",
    "plt.ylabel('variance %')\n",
    "plt.xticks(features)\n",
    "PCA_components3 = pd.DataFrame(principalComponents3)\n",
    "print(type(principalComponents3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhoutte score is 0.46613062910381436\n",
      "Adjusted rand index is 0.6201351808870379\n"
     ]
    }
   ],
   "source": [
    "\n",
    "kmeans3 = KMeans(n_clusters=3)\n",
    "kmeans3.fit(PCA_components3)\n",
    "score3 = silhouette_score(PCA_components3,kmeans3.labels_)\n",
    "\n",
    "print('Silhoutte score is', score3)\n",
    "labels3 = pd.factorize(label)[0]\n",
    "ari3 = adjusted_rand_score(labels3, kmeans3.labels_)\n",
    "print('Adjusted rand index is', ari3)\n",
    "#pca 3 components\n",
    "sscore.append(score3)\n",
    "ariscore.append(ari3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "USING 4 COMPONENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "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": [
    "pca4 = PCA(n_components=4)\n",
    "principalComponents4 = pca4.fit_transform(X_std)\n",
    "features = range(pca4.n_components_)\n",
    "plt.bar([1, 2, 3, 4], pca4.explained_variance_ratio_, color='black')\n",
    "plt.xlabel('PCA features')\n",
    "plt.ylabel('variance %')\n",
    "plt.xticks(features)\n",
    "PCA_components4 = pd.DataFrame(principalComponents4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhoutte score is 0.45937792074496625\n",
      "Adjusted rand index is 0.6100728505285608\n"
     ]
    }
   ],
   "source": [
    "\n",
    "kmeans4 = KMeans(n_clusters=3)\n",
    "kmeans4.fit(PCA_components4)\n",
    "score4 = silhouette_score(X_std, kmeans4.labels_)\n",
    "print('Silhoutte score is', score4)\n",
    "labels4 = pd.factorize(label)[0]\n",
    "len(kmeans4.labels_)\n",
    "ari4 = adjusted_rand_score(labels4, kmeans4.labels_)\n",
    "print('Adjusted rand index is', ari4)\n",
    "#PCA 4 components\n",
    "sscore.append(score4)\n",
    "ariscore.append(ari4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Silhoutte scores:\n",
      " [0.6754183875905303, 0.5113245176460453, 0.46613062910381436, 0.45937792074496625]\n"
     ]
    }
   ],
   "source": [
    "print(\"Silhoutte scores:\\n\",sscore)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjusted rand index score:\n",
      " [0.8015498244339507, 0.6011286543750637, 0.6201351808870379, 0.6100728505285608]\n"
     ]
    }
   ],
   "source": [
    "print(\"Adjusted rand index score:\\n\",ariscore)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x23144079fc8>"
      ]
     },
     "execution_count": 31,
     "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": [
    "import numpy as np\n",
    "plt.xlabel('Number of components')\n",
    "plt.xticks(np.arange(1, 5)) #change from 0-based array index to 1-based human-readable label\n",
    "plt.ylabel('score')\n",
    "plt.plot([1, 2, 3, 4],sscore,label ='sil score')\n",
    "plt.plot([1, 2, 3, 4],ariscore,label = 'ari')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comments: Silhoutte score is decreasing with the number of components linearly,The best number of components is 1 with respect to Silhoutte score calculated for different components.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comments: ARI is high for less number of components, Therefore since Rand index is related to the accuracy, The best number of components is 1 with respect to adjusted rand index."
   ]
  },
  {
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}