PCA analysis in ML programs

PCA.ipynb

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  "cells": [
    {
      "cell_type": "code",
      "execution_count": 30,
      "metadata": {
        "id": "Tyv7Jx-W9xsa"
      },
      "outputs": [],
      "source": [
        "# Import libraries\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from sklearn.datasets import load_iris\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.decomposition import PCA, KernelPCA\n",
        "from sklearn.model_selection import GridSearchCV\n",
        "from sklearn.pipeline import Pipeline\n",
        "from sklearn.svm import SVC\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 31,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "ItVs4aT2-ou6",
        "outputId": "47da9a6b-e6ac-4abc-d19d-65b6346cf95f"
      },
      "outputs": [
        {
          "data": {
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              "<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",
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            ],
            "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": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Obtain data\n",
        "df = pd.DataFrame(data=load_iris().data, columns=load_iris().feature_names)\n",
        "df.head()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 32,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fX7h9rBz-zI1",
        "outputId": "eba4a0d7-204f-4056-d2ff-67f3bbb4b83d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 150 entries, 0 to 149\n",
            "Data columns (total 4 columns):\n",
            " #   Column             Non-Null Count  Dtype  \n",
            "---  ------             --------------  -----  \n",
            " 0   sepal length (cm)  150 non-null    float64\n",
            " 1   sepal width (cm)   150 non-null    float64\n",
            " 2   petal length (cm)  150 non-null    float64\n",
            " 3   petal width (cm)   150 non-null    float64\n",
            "dtypes: float64(4)\n",
            "memory usage: 4.8 KB\n"
          ]
        }
      ],
      "source": [
        "df.info()  # Data summary\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 33,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_4tjjgUP-2y4",
        "outputId": "165eaef1-45c0-4b6b-ffae-28baf7dcb9c0"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "sepal length (cm)    0\n",
              "sepal width (cm)     0\n",
              "petal length (cm)    0\n",
              "petal width (cm)     0\n",
              "dtype: int64"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df.isnull().sum()  # Check for missing values\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 34,
      "metadata": {
        "id": "EIieIqid_JOz"
      },
      "outputs": [],
      "source": [
        "# Preprocessing, normalize the data\n",
        "x = StandardScaler().fit_transform(df)\n",
        "y = load_iris().target\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "ElFQOVqs_Utp"
      },
      "outputs": [],
      "source": [
        "# Instantiate PCA object and set the output dimensions to 2\n",
        "pca = PCA(n_components=2)\n",
        "\n",
        "# Use the PCA object to transform the data\n",
        "principalComponents = pca.fit_transform(x)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "k-HIMPum_jwq",
        "outputId": "d0c2ea9d-245d-4632-8d73-7aaa43110a97"
      },
      "outputs": [
        {
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>PC1</th>\n",
              "      <th>PC2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-2.264703</td>\n",
              "      <td>0.480027</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-2.080961</td>\n",
              "      <td>-0.674134</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-2.364229</td>\n",
              "      <td>-0.341908</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-2.299384</td>\n",
              "      <td>-0.597395</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-2.389842</td>\n",
              "      <td>0.646835</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        PC1       PC2\n",
              "0 -2.264703  0.480027\n",
              "1 -2.080961 -0.674134\n",
              "2 -2.364229 -0.341908\n",
              "3 -2.299384 -0.597395\n",
              "4 -2.389842  0.646835"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Create DataFrame for visualization\n",
        "principalComponents = pd.DataFrame(data=principalComponents, columns=[\"PC1\", \"PC2\"])\n",
        "principalComponents.head()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 37,
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      "outputs": [
        {
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",
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# 2D Visualization\n",
        "# Create figure and axes for the plot\n",
        "fig = plt.figure(figsize=(8, 8))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "ax.set_xlabel(\"Principal Component 1\", fontsize=15)\n",
        "ax.set_ylabel(\"Principal Component 2\", fontsize=15)\n",
        "ax.set_title(\"2 component PCA\", fontsize=20)\n",
        "\n",
        "targets = np.unique(y)  # Get all label names\n",
        "colors = [\n",
        "    \"magenta\",\n",
        "    \"cyan\",\n",
        "    \"yellow\",\n",
        "]  # Create a list of colors to assign to each label\n",
        "\n",
        "# Iterate through the data set and color each label with the corresponding color\n",
        "# Create a scatter plot to visualize the 2 dimensions of the new dataset\n",
        "for target, color in zip(targets, colors):\n",
        "    indicesToKeep = y == target\n",
        "    ax.scatter(\n",
        "        principalComponents.loc[indicesToKeep, \"PC1\"],\n",
        "        principalComponents.loc[indicesToKeep, \"PC2\"],\n",
        "        c=color,\n",
        "        s=50,\n",
        "    )\n",
        "\n",
        "ax.legend(targets)\n",
        "ax.grid()\n",
        "\n",
        "# # Plot the data points\n",
        "# ax.scatter(principalComponents[\"PC1\"], principalComponents[\"PC2\"], c=y)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 38,
      "metadata": {
        "id": "syLx_5OUBFeG"
      },
      "outputs": [],
      "source": [
        "# Create kpca instance\n",
        "kpca = KernelPCA(n_components=2, kernel=\"rbf\")\n",
        "\n",
        "# Build a pipeline with PCA and SVC\n",
        "pipeline = Pipeline([(\"kpca\", kpca), (\"svc\", SVC())])\n",
        "\n",
        "# Select parameter range for kpca\n",
        "# Select all values from 0.03 to 0.05 incremented by 0.001\n",
        "kpca_params = [{\"kpca__gamma\": np.arange(0.03, 0.05, 0.001)}]\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 39,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w6PMP_ZKCPSs",
        "outputId": "4c9baa90-f81e-46d0-94da-baa99ae0a353"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'kpca__gamma': 0.047000000000000014}"
            ]
          },
          "execution_count": 39,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Tuning gamma\n",
        "kpca_tune = GridSearchCV(pipeline, kpca_params, cv=5)\n",
        "kpca_tune.fit(x, y)\n",
        "kpca_tune.best_params_\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 40,
      "metadata": {
        "id": "wj9HqNwlCo-b"
      },
      "outputs": [],
      "source": [
        "# Initialize kpca model with best gamma value\n",
        "kpca = KernelPCA(n_components=2, kernel=\"rbf\", gamma=0.047)\n",
        "# Use the pca object to transform the data\n",
        "principalComponents = kpca.fit_transform(x)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 41,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "JBOAwtb9C5ao",
        "outputId": "c3b4d83e-f6ca-4150-9e65-a865cef15ec3"
      },
      "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>PC1</th>\n",
              "      <th>PC2</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.583591</td>\n",
              "      <td>-0.123095</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.520770</td>\n",
              "      <td>0.156202</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.585235</td>\n",
              "      <td>0.059063</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.563369</td>\n",
              "      <td>0.120939</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.603853</td>\n",
              "      <td>-0.166604</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        PC1       PC2\n",
              "0  0.583591 -0.123095\n",
              "1  0.520770  0.156202\n",
              "2  0.585235  0.059063\n",
              "3  0.563369  0.120939\n",
              "4  0.603853 -0.166604"
            ]
          },
          "execution_count": 41,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Use DataFrame for data visualization\n",
        "principalComponents = pd.DataFrame(data=principalComponents, columns=[\"PC1\", \"PC2\"])\n",
        "principalComponents.head()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 750
        },
        "id": "T4Tm0EVPDHhm",
        "outputId": "6817c6b9-d42d-46b8-91f1-9fd1060aed47"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Plot 2D Visualization\n",
        "# Create figure and axes for the plot\n",
        "fig = plt.figure(figsize=(8, 8))\n",
        "ax = fig.add_subplot(1, 1, 1)\n",
        "ax.set_xlabel(\"Principal Component 1\", fontsize=15)\n",
        "ax.set_ylabel(\"Principal Component 2\", fontsize=15)\n",
        "ax.set_title(\"2 component PCA\", fontsize=20)\n",
        "\n",
        "targets = np.unique(y)  # Get all label names\n",
        "colors = [\"red\", \"green\", \"blue\"]  # Create a list of colors to assign to each label\n",
        "\n",
        "# Iterate through the data set and color each label with the corresponding color\n",
        "# Create a scatter plot to visualize the 2 dimensions of the new dataset\n",
        "for target, color in zip(targets, colors):\n",
        "    indicesToKeep = y == target\n",
        "    ax.scatter(\n",
        "        principalComponents.loc[indicesToKeep, \"PC1\"],\n",
        "        principalComponents.loc[indicesToKeep, \"PC2\"],\n",
        "        c=color,\n",
        "        s=50,\n",
        "    )\n",
        "\n",
        "ax.legend(targets)\n",
        "ax.grid()\n"
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.11.9"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}