Assignment 04 Clustering Cars.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cars Data has Information about 3 brands/make of cars. Namely US, Japan, Europe. Target of the data set to find the brand of a car using the parameters such as horsepower, Cubic inches, Make year, etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "# Importing the dataset\n",
    "dataset = pd.read_csv(\"Data/Unsupervised/cars.csv\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "mpg            float64\n",
       "cylinders        int64\n",
       "cubicinches      int64\n",
       "hp               int64\n",
       "weightlbs        int64\n",
       "time-to-60       int64\n",
       "year             int64\n",
       "dtype: object"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Remove spaces from the Column names\n",
    "dataset.columns = dataset.columns.str.strip()\n",
    "\n",
    "#Check the data types of all columns\n",
    "dataset.dtypes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#feature_col_names = ['mpg', 'cylinders', 'cubicinches', 'hp', 'weightlbs', 'time-to-60', 'year']\n",
    "\n",
    "\n",
    "#X = dataset[feature_col_names].values  \n",
    "X = dataset.iloc[:, :].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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": [
    "# Using the elbow method to find the optimal number of clusters\n",
    "from sklearn.cluster import KMeans\n",
    "wcss = []\n",
    "for i in range(1, 11):\n",
    "    k_means = KMeans(n_clusters = i, init = 'k-means++', random_state = 42)\n",
    "    k_means.fit(X)\n",
    "    wcss.append(k_means.inertia_)\n",
    "plt.plot(range(1, 11), wcss)\n",
    "plt.title('Elbow Method')\n",
    "plt.xlabel('Number of Clusters')\n",
    "plt.ylabel('WCSS')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Applying k-means to the cars dataset\n",
    "model = KMeans(n_clusters = 3, init = 'k-means++', random_state = 42)\n",
    "model_predict = model.fit_predict(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 0 1 0 0 0 2 1 1 1 0 2 0 0 1 2 1 1 1 1 2 0 1 1 1 0 2 1 1 2 1 2 1 2 1\n",
      " 1 0 2 0 0 2 2 2 1 0 1 1 2 0 2 2 1 0 0 2 1 1 0 2 1 2 1 0 2 1 1 1 0 2 1 1 1\n",
      " 1 2 2 1 1 1 0 0 2 1 1 1 2 2 1 1 1 1 0 2 1 0 0 2 0 0 0 0 1 1 1 1 1 1 1 2 1\n",
      " 2 0 1 1 0 2 2 1 0 1 1 0 2 1 1 0 1 1 1 1 1 0 2 0 0 1 2 2 2 1 1 1 1 2 2 2 2\n",
      " 2 2 1 1 0 2 1 2 1 1 1 2 2 0 2 2 1 2 2 1 2 1 1 2 1 1 1 1 0 2 2 1 2 1 0 2 1\n",
      " 2 2 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 2 2 1 0 1 2 0 2 2 2 1 1 2 1 1 0 1 0 2 2\n",
      " 0 0 0 1 0 1 1 2 2 1 1 0 2 1 0 2 1 1 0 2 0 1 0 2 0 1 1 1 1 1 2 0 2 1 0 1 2\n",
      " 2 2]\n"
     ]
    }
   ],
   "source": [
    "print(model_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    "# Visualising the clusters\n",
    "size = 25\n",
    "plt.scatter(X[model_predict == 0, 0], X[model_predict == 0, 1], s = size, c = 'cyan', label = 'Brand 1')\n",
    "plt.scatter(X[model_predict == 1, 0], X[model_predict == 1, 1], s = size, c = 'blue', label = 'Brand 2')\n",
    "plt.scatter(X[model_predict == 2, 0], X[model_predict == 2, 1], s = size, c = 'yellow', label = 'Brand 3')\n",
    "plt.scatter(model.cluster_centers_[:, 0], model.cluster_centers_[:, 1], s = 60, c = 'black', label = 'Centroid')\n",
    "plt.title('Car Brands')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}