Task #3 - To Explore Unsupervised Machine Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Radhu Ladani"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task #3 - To Explore Unsupervised Machine Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means is a type of unsupervised learning and one of the popular methods of clustering unlabelled data into k clusters. One of the trickier tasks in clustering is identifying the appropriate number of clusters k. In this task, we will provide an overview of how k-means works and discuss how to implement your own clusters. We will also understand how to use the elbow method as a way to estimate the value k."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Importing the libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</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",
       "    </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",
       "    </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",
       "    </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",
       "    </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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
       "0                5.1               3.5                1.4               0.2\n",
       "1                4.9               3.0                1.4               0.2\n",
       "2                4.7               3.2                1.3               0.2\n",
       "3                4.6               3.1                1.5               0.2\n",
       "4                5.0               3.6                1.4               0.2"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Load the iris dataset\n",
    "iris = datasets.load_iris()\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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(150, 4)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_df.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\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 (cm)</th>\n",
       "      <th>sepal width (cm)</th>\n",
       "      <th>petal length (cm)</th>\n",
       "      <th>petal width (cm)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.843333</td>\n",
       "      <td>3.057333</td>\n",
       "      <td>3.758000</td>\n",
       "      <td>1.199333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.828066</td>\n",
       "      <td>0.435866</td>\n",
       "      <td>1.765298</td>\n",
       "      <td>0.762238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.300000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.100000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>1.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.400000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>1.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.900000</td>\n",
       "      <td>4.400000</td>\n",
       "      <td>6.900000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sepal length (cm)  sepal width (cm)  petal length (cm)  \\\n",
       "count         150.000000        150.000000         150.000000   \n",
       "mean            5.843333          3.057333           3.758000   \n",
       "std             0.828066          0.435866           1.765298   \n",
       "min             4.300000          2.000000           1.000000   \n",
       "25%             5.100000          2.800000           1.600000   \n",
       "50%             5.800000          3.000000           4.350000   \n",
       "75%             6.400000          3.300000           5.100000   \n",
       "max             7.900000          4.400000           6.900000   \n",
       "\n",
       "       petal width (cm)  \n",
       "count        150.000000  \n",
       "mean           1.199333  \n",
       "std            0.762238  \n",
       "min            0.100000  \n",
       "25%            0.300000  \n",
       "50%            1.300000  \n",
       "75%            1.800000  \n",
       "max            2.500000  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "categorical_features = ['Species']\n",
    "continuous_features = ['SepalLengthCm','SepalWidthCm','PetalLengthCm','PetalWidthCm']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Finding the optimal number of clusters using the elbow method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Finding the optimum number of clusters for k-means classification\n",
    "x = iris_df.iloc[:, [0, 1, 2, 3]].values\n",
    "from sklearn.cluster import KMeans\n",
    "wcss = []\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",
    "    wcss.append(kmeans.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
    "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": [
    "We can clearly see the elbow in this 'The elbow method graph'. The optimum clusters is where the elbow occurs. This is when the within cluster sum of squares (WCSS) doesn't decrease significantly with every iteration.\n",
    "\n",
    "From this we choose the number of clusters, k value as 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training the K-means algorithm on the training dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Applying kmeans to the dataset\n",
    "kmeans = KMeans(n_clusters = 3, init = 'k-means++',max_iter = 300, n_init = 10, random_state = 0)\n",
    "y_kmeans = kmeans.fit_predict(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing the Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x13c1b7dd8d0>"
      ]
     },
     "execution_count": 13,
     "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], \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",
    "# Plotting the centroids of the clusters\n",
    "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:,1], s = 100, c = 'yellow', label = 'Centroids')\n",
    "plt.legend()"
   ]
  },
  {
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   "source": [
    "The centroids of every cluster is marked seperately in yellow.\n",
    "\n",
    "Thus the Elbow method gives us the best optimized value for k (as 3) for getting a better unsupervised classification accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "r"
   ]
  }
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