Task 2 Unsupervised ML Sparks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Submitted by: Jainil Shah\n",
    "# From the given ‘Iris’ dataset, predict the optimum number of clusters and represent it visually.\n",
    "## Algorithm used :-  K means Clustering\n",
    "## 1. Import Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# working with arrays\n",
    "import numpy as np\n",
    "# data visualization and graphical plotting\n",
    "import matplotlib.pyplot as plt\n",
    "# it offers data structures and operations for manipulating numerical tables and time series\n",
    "import pandas as pd\n",
    "# provides functions for generating a suite of test problems\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Get The dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"D://Machine Learning//Task 2 - Dataset.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Id</th>\n",
       "      <th>SepalLengthCm</th>\n",
       "      <th>SepalWidthCm</th>\n",
       "      <th>PetalLengthCm</th>\n",
       "      <th>PetalWidthCm</th>\n",
       "      <th>Species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\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>2</td>\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>3</td>\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</td>\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</td>\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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Id  SepalLengthCm  SepalWidthCm  PetalLengthCm  PetalWidthCm      Species\n",
       "0   1            5.1           3.5            1.4           0.2  Iris-setosa\n",
       "1   2            4.9           3.0            1.4           0.2  Iris-setosa\n",
       "2   3            4.7           3.2            1.3           0.2  Iris-setosa\n",
       "3   4            4.6           3.1            1.5           0.2  Iris-setosa\n",
       "4   5            5.0           3.6            1.4           0.2  Iris-setosa"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# used to return top n (5 by default) rows of a data frame or series.1\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Finding optimum numbers of clusters for K means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  1. ,   5.1,   3.5,   1.4],\n",
       "       [  2. ,   4.9,   3. ,   1.4],\n",
       "       [  3. ,   4.7,   3.2,   1.3],\n",
       "       [  4. ,   4.6,   3.1,   1.5],\n",
       "       [  5. ,   5. ,   3.6,   1.4],\n",
       "       [  6. ,   5.4,   3.9,   1.7],\n",
       "       [  7. ,   4.6,   3.4,   1.4],\n",
       "       [  8. ,   5. ,   3.4,   1.5],\n",
       "       [  9. ,   4.4,   2.9,   1.4],\n",
       "       [ 10. ,   4.9,   3.1,   1.5],\n",
       "       [ 11. ,   5.4,   3.7,   1.5],\n",
       "       [ 12. ,   4.8,   3.4,   1.6],\n",
       "       [ 13. ,   4.8,   3. ,   1.4],\n",
       "       [ 14. ,   4.3,   3. ,   1.1],\n",
       "       [ 15. ,   5.8,   4. ,   1.2],\n",
       "       [ 16. ,   5.7,   4.4,   1.5],\n",
       "       [ 17. ,   5.4,   3.9,   1.3],\n",
       "       [ 18. ,   5.1,   3.5,   1.4],\n",
       "       [ 19. ,   5.7,   3.8,   1.7],\n",
       "       [ 20. ,   5.1,   3.8,   1.5],\n",
       "       [ 21. ,   5.4,   3.4,   1.7],\n",
       "       [ 22. ,   5.1,   3.7,   1.5],\n",
       "       [ 23. ,   4.6,   3.6,   1. ],\n",
       "       [ 24. ,   5.1,   3.3,   1.7],\n",
       "       [ 25. ,   4.8,   3.4,   1.9],\n",
       "       [ 26. ,   5. ,   3. ,   1.6],\n",
       "       [ 27. ,   5. ,   3.4,   1.6],\n",
       "       [ 28. ,   5.2,   3.5,   1.5],\n",
       "       [ 29. ,   5.2,   3.4,   1.4],\n",
       "       [ 30. ,   4.7,   3.2,   1.6],\n",
       "       [ 31. ,   4.8,   3.1,   1.6],\n",
       "       [ 32. ,   5.4,   3.4,   1.5],\n",
       "       [ 33. ,   5.2,   4.1,   1.5],\n",
       "       [ 34. ,   5.5,   4.2,   1.4],\n",
       "       [ 35. ,   4.9,   3.1,   1.5],\n",
       "       [ 36. ,   5. ,   3.2,   1.2],\n",
       "       [ 37. ,   5.5,   3.5,   1.3],\n",
       "       [ 38. ,   4.9,   3.1,   1.5],\n",
       "       [ 39. ,   4.4,   3. ,   1.3],\n",
       "       [ 40. ,   5.1,   3.4,   1.5],\n",
       "       [ 41. ,   5. ,   3.5,   1.3],\n",
       "       [ 42. ,   4.5,   2.3,   1.3],\n",
       "       [ 43. ,   4.4,   3.2,   1.3],\n",
       "       [ 44. ,   5. ,   3.5,   1.6],\n",
       "       [ 45. ,   5.1,   3.8,   1.9],\n",
       "       [ 46. ,   4.8,   3. ,   1.4],\n",
       "       [ 47. ,   5.1,   3.8,   1.6],\n",
       "       [ 48. ,   4.6,   3.2,   1.4],\n",
       "       [ 49. ,   5.3,   3.7,   1.5],\n",
       "       [ 50. ,   5. ,   3.3,   1.4],\n",
       "       [ 51. ,   7. ,   3.2,   4.7],\n",
       "       [ 52. ,   6.4,   3.2,   4.5],\n",
       "       [ 53. ,   6.9,   3.1,   4.9],\n",
       "       [ 54. ,   5.5,   2.3,   4. ],\n",
       "       [ 55. ,   6.5,   2.8,   4.6],\n",
       "       [ 56. ,   5.7,   2.8,   4.5],\n",
       "       [ 57. ,   6.3,   3.3,   4.7],\n",
       "       [ 58. ,   4.9,   2.4,   3.3],\n",
       "       [ 59. ,   6.6,   2.9,   4.6],\n",
       "       [ 60. ,   5.2,   2.7,   3.9],\n",
       "       [ 61. ,   5. ,   2. ,   3.5],\n",
       "       [ 62. ,   5.9,   3. ,   4.2],\n",
       "       [ 63. ,   6. ,   2.2,   4. ],\n",
       "       [ 64. ,   6.1,   2.9,   4.7],\n",
       "       [ 65. ,   5.6,   2.9,   3.6],\n",
       "       [ 66. ,   6.7,   3.1,   4.4],\n",
       "       [ 67. ,   5.6,   3. ,   4.5],\n",
       "       [ 68. ,   5.8,   2.7,   4.1],\n",
       "       [ 69. ,   6.2,   2.2,   4.5],\n",
       "       [ 70. ,   5.6,   2.5,   3.9],\n",
       "       [ 71. ,   5.9,   3.2,   4.8],\n",
       "       [ 72. ,   6.1,   2.8,   4. ],\n",
       "       [ 73. ,   6.3,   2.5,   4.9],\n",
       "       [ 74. ,   6.1,   2.8,   4.7],\n",
       "       [ 75. ,   6.4,   2.9,   4.3],\n",
       "       [ 76. ,   6.6,   3. ,   4.4],\n",
       "       [ 77. ,   6.8,   2.8,   4.8],\n",
       "       [ 78. ,   6.7,   3. ,   5. ],\n",
       "       [ 79. ,   6. ,   2.9,   4.5],\n",
       "       [ 80. ,   5.7,   2.6,   3.5],\n",
       "       [ 81. ,   5.5,   2.4,   3.8],\n",
       "       [ 82. ,   5.5,   2.4,   3.7],\n",
       "       [ 83. ,   5.8,   2.7,   3.9],\n",
       "       [ 84. ,   6. ,   2.7,   5.1],\n",
       "       [ 85. ,   5.4,   3. ,   4.5],\n",
       "       [ 86. ,   6. ,   3.4,   4.5],\n",
       "       [ 87. ,   6.7,   3.1,   4.7],\n",
       "       [ 88. ,   6.3,   2.3,   4.4],\n",
       "       [ 89. ,   5.6,   3. ,   4.1],\n",
       "       [ 90. ,   5.5,   2.5,   4. ],\n",
       "       [ 91. ,   5.5,   2.6,   4.4],\n",
       "       [ 92. ,   6.1,   3. ,   4.6],\n",
       "       [ 93. ,   5.8,   2.6,   4. ],\n",
       "       [ 94. ,   5. ,   2.3,   3.3],\n",
       "       [ 95. ,   5.6,   2.7,   4.2],\n",
       "       [ 96. ,   5.7,   3. ,   4.2],\n",
       "       [ 97. ,   5.7,   2.9,   4.2],\n",
       "       [ 98. ,   6.2,   2.9,   4.3],\n",
       "       [ 99. ,   5.1,   2.5,   3. ],\n",
       "       [100. ,   5.7,   2.8,   4.1],\n",
       "       [101. ,   6.3,   3.3,   6. ],\n",
       "       [102. ,   5.8,   2.7,   5.1],\n",
       "       [103. ,   7.1,   3. ,   5.9],\n",
       "       [104. ,   6.3,   2.9,   5.6],\n",
       "       [105. ,   6.5,   3. ,   5.8],\n",
       "       [106. ,   7.6,   3. ,   6.6],\n",
       "       [107. ,   4.9,   2.5,   4.5],\n",
       "       [108. ,   7.3,   2.9,   6.3],\n",
       "       [109. ,   6.7,   2.5,   5.8],\n",
       "       [110. ,   7.2,   3.6,   6.1],\n",
       "       [111. ,   6.5,   3.2,   5.1],\n",
       "       [112. ,   6.4,   2.7,   5.3],\n",
       "       [113. ,   6.8,   3. ,   5.5],\n",
       "       [114. ,   5.7,   2.5,   5. ],\n",
       "       [115. ,   5.8,   2.8,   5.1],\n",
       "       [116. ,   6.4,   3.2,   5.3],\n",
       "       [117. ,   6.5,   3. ,   5.5],\n",
       "       [118. ,   7.7,   3.8,   6.7],\n",
       "       [119. ,   7.7,   2.6,   6.9],\n",
       "       [120. ,   6. ,   2.2,   5. ],\n",
       "       [121. ,   6.9,   3.2,   5.7],\n",
       "       [122. ,   5.6,   2.8,   4.9],\n",
       "       [123. ,   7.7,   2.8,   6.7],\n",
       "       [124. ,   6.3,   2.7,   4.9],\n",
       "       [125. ,   6.7,   3.3,   5.7],\n",
       "       [126. ,   7.2,   3.2,   6. ],\n",
       "       [127. ,   6.2,   2.8,   4.8],\n",
       "       [128. ,   6.1,   3. ,   4.9],\n",
       "       [129. ,   6.4,   2.8,   5.6],\n",
       "       [130. ,   7.2,   3. ,   5.8],\n",
       "       [131. ,   7.4,   2.8,   6.1],\n",
       "       [132. ,   7.9,   3.8,   6.4],\n",
       "       [133. ,   6.4,   2.8,   5.6],\n",
       "       [134. ,   6.3,   2.8,   5.1],\n",
       "       [135. ,   6.1,   2.6,   5.6],\n",
       "       [136. ,   7.7,   3. ,   6.1],\n",
       "       [137. ,   6.3,   3.4,   5.6],\n",
       "       [138. ,   6.4,   3.1,   5.5],\n",
       "       [139. ,   6. ,   3. ,   4.8],\n",
       "       [140. ,   6.9,   3.1,   5.4],\n",
       "       [141. ,   6.7,   3.1,   5.6],\n",
       "       [142. ,   6.9,   3.1,   5.1],\n",
       "       [143. ,   5.8,   2.7,   5.1],\n",
       "       [144. ,   6.8,   3.2,   5.9],\n",
       "       [145. ,   6.7,   3.3,   5.7],\n",
       "       [146. ,   6.7,   3. ,   5.2],\n",
       "       [147. ,   6.3,   2.5,   5. ],\n",
       "       [148. ,   6.5,   3. ,   5.2],\n",
       "       [149. ,   6.2,   3.4,   5.4],\n",
       "       [150. ,   5.9,   3. ,   5.1]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# First 4 columns are printed\n",
    "x = df.iloc[:, [0, 1, 2, 3]].values\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# unsupervised machine learning algorithms that forms clusters of data based on the similarity between data instances\n",
    "# number of clusters has to be defined beforehand\n",
    "# K in the K-means refers to the number of clusters.\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# within cluster sum of squares\n",
    "# For each value of K, we are calculating WCSS ( Within-Cluster Sum of Square )\n",
    "# WCSS is the sum of squared distance between each point and the centroid in a cluster\n",
    "#  When we plot the WCSS with the K value, the plot looks like an Elbow\n",
    "# number of clusters increases, the WCSS value will start to decrease\n",
    "wcss = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# To get the values used in the graph, we train multiple models using a different number of clusters \n",
    "# and storing the value of the intertia_ property (WCSS) every time.\n",
    "# k-means++ ensures that you get don’t fall into the random initialization trap.\n",
    "for i in range(1, 11):\n",
    "    kmeans = KMeans(n_clusters = i, init = 'k-means++', max_iter = 300, n_init = 10, random_state = 0)\n",
    "    kmeans.fit(x)\n",
    "    wcss.append(kmeans.inertia_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting the results onto a line graph, \n",
    "# allowing us to observe 'The elbow'\n",
    "# number of clusters increases, the WCSS value will start to decrease\n",
    "plt.plot(range(1, 11), wcss)\n",
    "plt.title('The Elbow method')\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('WCSS') # Within cluster sum of squares\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimum number of clusters: 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# categorize the data using the optimum number of clusters (3) we determined in the last step\n",
    "kmeans = KMeans(n_clusters = 3, init = 'k-means++',max_iter = 300, n_init = 10, random_state = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# it finds the centroids and assigns the labels to the dataset\n",
    "y_kmeans = kmeans.fit_predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x19ebea82cd0>"
      ]
     },
     "execution_count": 11,
     "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": [
    "# Visualising the clusters - On the first two columns\n",
    "plt.scatter(x[y_kmeans == 0, 0], x[y_kmeans == 0, 1], s = 100, c = 'black', label = 'Iris-setosa')\n",
    "plt.scatter(x[y_kmeans == 1, 0], x[y_kmeans == 1, 1], s = 100, c = 'orange', label = 'Iris-versicolour')\n",
    "plt.scatter(x[y_kmeans == 2, 0], x[y_kmeans == 2, 1],s = 100, c = 'green', label = 'Iris-virginica')\n",
    "# Plotting the centroids of the clusters:\n",
    "# cluster_centers: Predict the closest cluster each sample in X belongs to\n",
    "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:,1], s = 100, c = 'red', label = 'Centroids')\n",
    "\n",
    "plt.legend()"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}