Task2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "# THE SPARKS FOUNDATION\n",
    "## Task-2 Prediction using Unsupervised ML\n",
    "## Predicting the optimum number of clusters and representing it visually\n",
    "## Author: Goutham Pasumarthy\n",
    "## Algorithm used: K-Means Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Importing the libraries**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "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>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": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn import datasets\n",
    "#URL which contains the file\n",
    "url = \"https://drive.google.com/file/d/11Iq7YvbWZbt8VXjfm06brx66b10YiwK-/\"\n",
    "# Fetching the file from google drive\n",
    "url2 ='https://drive.google.com/uc?id=' + url.split('/')[-2]\n",
    "#Loading the data\n",
    "iris_df = pd.read_csv(url2)\n",
    "#iris_df = pd.DataFrame(iris.data, columns = iris.feature_names)\n",
    "iris_df.head() # See the first 5 rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Dropping the id\n",
    "iris_df.drop(\"Id\",axis = 1,inplace =True)\n",
    "#iris_df.columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['SepalLengthCm', 'SepalWidthCm', 'PetalLengthCm', 'PetalWidthCm',\n",
       "       'Species'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_df.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Finding the value of k / Determining the number of clusters**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Converting the values in the dataset to an array removing the class label\n",
    "x = iris_df.iloc[:, [0, 1, 2, 3]].values\n",
    "from sklearn.cluster import KMeans\n",
    "#wccs is the sum of squares\n",
    "wcss = []\n",
    "\n",
    "# Now we are incrementing the value of k and\n",
    "#calculating the sum of squares of the data for each iteration and adding it to wcss variable\n",
    "for i in range(1, 11):\n",
    "    kmeans = KMeans(n_clusters = i, init = 'k-means++', \n",
    "                    max_iter = 300, n_init = 10, random_state = 0)\n",
    "    kmeans.fit(x)\n",
    "    #kmeans.inertia returns the wcss value of the clustered data\n",
    "    wcss.append(kmeans.inertia_)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Plotting the data obtained above**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "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": [
    "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": [
    "## Elbow Method\n",
    "#### The elbow method is used in determining the number of clusters in a data set. The method consists of plotting the explained variation as a function of the number of clusters, and picking the elbow of the curve as the number of clusters to use.\n",
    "\n",
    "#### We can observe that the graph is similar to the shape of an elbow. The optimum number of clusters is where the graph bends.\n",
    "#### This is when the within cluster sum of squares (WCSS) doesn't decrease significantly with every iteration.\n",
    "\n",
    "#### So from this graph , lets choose of the k to be 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0,\n",
       "       0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0,\n",
       "       0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#K is 3 and we are applying the KMeans model to the data\n",
    "kmeans = KMeans(n_clusters = 3, init = 'k-means++',\n",
    "                max_iter = 300, n_init = 10, random_state = 0)\n",
    "y_kmeans = kmeans.fit_predict(x)\n",
    "\n",
    "#Observe the values clustered by the Kmeans\n",
    "y_kmeans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visual Representation Of Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "#plotting the ouput using Matplotlib\n",
    "plt.scatter(x[y_kmeans == 0, 0], x[y_kmeans == 0, 1], \n",
    "            s = 100, c = 'red', label = 'Iris-setosa')\n",
    "plt.scatter(x[y_kmeans == 1, 0], x[y_kmeans == 1, 1], \n",
    "            s = 100, c = 'blue', label = 'Iris-versicolour')\n",
    "plt.scatter(x[y_kmeans == 2, 0], x[y_kmeans == 2, 1],\n",
    "            s = 100, c = 'green', label = 'Iris-virginica')\n",
    "\n",
    "# Plotting the centroids of the clusters\n",
    "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:,1], \n",
    "            s = 100, c = 'yellow', label = 'Centroids')\n",
    "#plt.grid(True)\n",
    "plt.title('Clusters of Iris')\n",
    "out = plt.legend()"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}