PCA_iris.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0ab19915",
   "metadata": {},
   "source": [
    "## PCA - applied to the IRIS data set"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb50611e",
   "metadata": {},
   "source": [
    "### Preparing environment - loading packages and data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "478d73d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn import metrics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1edbf4fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 4) (150,)\n"
     ]
    }
   ],
   "source": [
    "url = \"https://raw.githubusercontent.com/Jacob-Gernay/SCP8082660/main/data/Iris.csv\"\n",
    "iris = pd.read_csv(url)\n",
    "iris.head()\n",
    "\n",
    "X, y = iris.iloc[:,1:5].values, iris.loc[:,'Species'].values\n",
    "print(X.shape, y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0029447c",
   "metadata": {},
   "source": [
    "### Standardizing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bcb46441",
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler.fit_transform(X);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3bd3664",
   "metadata": {},
   "source": [
    "### Applying PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4e9f392f",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=4)\n",
    "pca.fit_transform(X);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8915e96",
   "metadata": {},
   "source": [
    "### Analyzing results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0290be59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of explained variance:\n",
      "   prop_var  cumulative\n",
      "0  0.924616    0.924616\n",
      "1  0.053016    0.977632\n",
      "2  0.017185    0.994817\n",
      "3  0.005183    1.000000\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": [
    "prop_var = pca.explained_variance_ratio_\n",
    "pca_var_tab = pd.DataFrame(prop_var, columns = ['prop_var'])\n",
    "pca_var_tab['cumulative'] = pca_var_tab['prop_var'].cumsum(axis = 0)\n",
    "print('Proportion of explained variance:')\n",
    "print(pca_var_tab)\n",
    "\n",
    "PC_values = np.arange(pca.n_components_) + 1\n",
    "plt.plot(PC_values, pca.explained_variance_ratio_, 'o-', linewidth=2, color='red')\n",
    "plt.title('Scree Plot')\n",
    "plt.xlabel('Principal Component')\n",
    "plt.ylabel('Variance Explained')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96cab47a",
   "metadata": {},
   "source": [
    "Scree plot suggest 2 PC's are enough, 2 components explain 97.76% of the variance in the original data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ca74819",
   "metadata": {},
   "source": [
    "## Classification: raw data vs. 2 components"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "551f8c21",
   "metadata": {},
   "source": [
    "### preparing data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e0d01723",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3, random_state = 0)\n",
    "\n",
    "pca2 = PCA(n_components = 2)\n",
    "X_train_pc = pca2.fit_transform(X_train)\n",
    "X_test_pc = pca2.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e806125",
   "metadata": {},
   "source": [
    "### classifying"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b696c91a",
   "metadata": {},
   "outputs": [],
   "source": [
    "classifier = LogisticRegression(multi_class = 'multinomial')\n",
    "classifier_pc = LogisticRegression(multi_class = 'multinomial')\n",
    "\n",
    "classifier.fit(X_train, y_train)\n",
    "classifier_pc.fit(X_train_pc, y_train)\n",
    "\n",
    "y_pred = classifier.predict(X_test)\n",
    "y_pred_pc = classifier_pc.predict(X_test_pc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8d9f439",
   "metadata": {},
   "source": [
    "### Evaluation of the classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "da133f9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[16  0  0]\n",
      " [ 0 17  1]\n",
      " [ 0  0 11]]\n",
      "accuracy raw data: 97.78\n",
      "[[16  0  0]\n",
      " [ 0 17  1]\n",
      " [ 0  0 11]]\n",
      "accuracy principal components: 97.78\n"
     ]
    }
   ],
   "source": [
    "cm = confusion_matrix(y_test, y_pred)\n",
    "cm_pc = confusion_matrix(y_test, y_pred_pc)\n",
    "\n",
    "acc_raw = round(metrics.accuracy_score(y_test, y_pred)*100,2)\n",
    "acc_pc = round(metrics.accuracy_score(y_test, y_pred_pc)*100,2)\n",
    "\n",
    "print(cm)\n",
    "print(\"accuracy raw data:\", acc_raw)\n",
    "\n",
    "print(cm_pc)\n",
    "print(\"accuracy principal components:\", acc_pc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebdb1385",
   "metadata": {},
   "source": [
    "the classification on the 2 principal components is as good as the classification based on the original data."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}