Day_35_Principal_Component_Analysis.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNVRLniFXrz0UDFUqu//B6e"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Principal Component Analysis is a dimensionality-reduction technique used to reduce the dimensionality of large data sets to smaller one, by transforming a large set of variables while preserving the information all along."
      ],
      "metadata": {
        "id": "EAT5Ju4gk_Ng"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "JgrUoC8fkid6"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "plt.style.use(\"ggplot\")\n",
        "plt.rcParams[\"figure.figsize\"] = (15,10)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Load the Data"
      ],
      "metadata": {
        "id": "73LfAcoUlG_X"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "iris = pd.read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data\", header= None)\n",
        "iris.columns = [\"sepal_length\", \"sepal_width\", \"petal_length\", \"petal_width\", \"species\"]\n",
        "iris.info()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pN-qqd16lJVW",
        "outputId": "a24c6ce4-d86a-43c1-dfe7-cf9b63142998"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 150 entries, 0 to 149\n",
            "Data columns (total 5 columns):\n",
            " #   Column        Non-Null Count  Dtype  \n",
            "---  ------        --------------  -----  \n",
            " 0   sepal_length  150 non-null    float64\n",
            " 1   sepal_width   150 non-null    float64\n",
            " 2   petal_length  150 non-null    float64\n",
            " 3   petal_width   150 non-null    float64\n",
            " 4   species       150 non-null    object \n",
            "dtypes: float64(4), object(1)\n",
            "memory usage: 6.0+ KB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Data Visualization"
      ],
      "metadata": {
        "id": "SdpX5ymclNgX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sns.scatterplot(x=iris.sepal_length,y=iris.sepal_width,hue=iris.species,style=iris.species)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 626
        },
        "id": "RZWIu7dmlbe3",
        "outputId": "3ff72918-aec8-48b1-94d6-f848c481e8fc"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7ff20e8f45d0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "VKOc_hZYlNZn"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X = iris.iloc[:,0:4].values\n",
        "y=iris.species.values\n",
        "X= StandardScaler().fit_transform(X)"
      ],
      "metadata": {
        "id": "MKF7h6xqmEyw"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Compute the Eigenvectors and Eigenvalues"
      ],
      "metadata": {
        "id": "v0OHicwzlNTu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "covariance_matrix = np.cov(X.T)\n",
        "eigen_values, eigen_vectors = np.linalg.eig(covariance_matrix)\n",
        "print(\"Eigen Values:\",eigen_values)\n",
        "print(\"Eigen Vectors:\", eigen_vectors)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-0IPycw6mxqL",
        "outputId": "0735a5bf-357f-408b-f03b-c0b321380d0f"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Eigen Values: [2.93035378 0.92740362 0.14834223 0.02074601]\n",
            "Eigen Vectors: [[ 0.52237162 -0.37231836 -0.72101681  0.26199559]\n",
            " [-0.26335492 -0.92555649  0.24203288 -0.12413481]\n",
            " [ 0.58125401 -0.02109478  0.14089226 -0.80115427]\n",
            " [ 0.56561105 -0.06541577  0.6338014   0.52354627]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Singular Value Decomposition (SVD)"
      ],
      "metadata": {
        "id": "E7dioiLDm_BT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "eigen_svd, s, v = np.linalg.svd(X.T)\n",
        "eigen_svd"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sxcmQAIZnCcP",
        "outputId": "7f1bee23-3e9f-40eb-b9f4-e0aab31ec98d"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.52237162, -0.37231836,  0.72101681,  0.26199559],\n",
              "       [ 0.26335492, -0.92555649, -0.24203288, -0.12413481],\n",
              "       [-0.58125401, -0.02109478, -0.14089226, -0.80115427],\n",
              "       [-0.56561105, -0.06541577, -0.6338014 ,  0.52354627]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Principle Components"
      ],
      "metadata": {
        "id": "4gvCy-75m--k"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "var_e = [(i/sum(eigen_values))*100 for i in eigen_values]\n",
        "sns.lineplot(x=[1,2,3,4],y=np.cumsum(var_e))\n",
        "plt.xlabel(\"No of Components\")\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 609
        },
        "id": "u4NxLe6InH84",
        "outputId": "ef3cf849-f20d-42be-8793-5be22396f9f4"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Plot Data"
      ],
      "metadata": {
        "id": "0kERW2_6m-8K"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p_m = (eigen_vectors.T[:][:])[:2].T\n",
        "X_pca = X.dot(p_m)\n",
        "for species in ('Iris-setosa','Iris-versicolor','Iris-virginica'):\n",
        "    sns.scatterplot(X_pca[y==species,0],\n",
        "                   X_pca[y==species,1])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 716
        },
        "id": "K1DVXNj8nTjD",
        "outputId": "f7d20080-ca2a-4bb8-b839-ca87f9fbb6a0"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x720 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}