DimReduction: PCA_digits.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/gulabpatel/ML_Algos/blob/main/DimReduction%3A%20PCA_digits.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gz05V7oB0ixV"
      },
      "source": [
        "<h2 align='center'>Principal Component Analysis Tutorial</h2>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "scrolled": false,
        "id": "_EVzAfKn0ixa",
        "outputId": "cfa97b65-adbf-4be9-9282-2476119d06b6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'images', 'DESCR'])"
            ]
          },
          "metadata": {},
          "execution_count": 1
        }
      ],
      "source": [
        "from sklearn.datasets import load_digits\n",
        "import pandas as pd\n",
        "\n",
        "dataset = load_digits()\n",
        "dataset.keys()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "JAcxbGQS0ixd",
        "outputId": "b1663823-c822-41cc-e7d2-8b3547ddf108",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 64)"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ],
      "source": [
        "dataset.data.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "Iz8_Ik1w0ixe",
        "outputId": "b9c67b18-5139-4372-f487-b73b7da7b094",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.,  0.,  0., 13., 15., 10.,\n",
              "       15.,  5.,  0.,  0.,  3., 15.,  2.,  0., 11.,  8.,  0.,  0.,  4.,\n",
              "       12.,  0.,  0.,  8.,  8.,  0.,  0.,  5.,  8.,  0.,  0.,  9.,  8.,\n",
              "        0.,  0.,  4., 11.,  0.,  1., 12.,  7.,  0.,  0.,  2., 14.,  5.,\n",
              "       10., 12.,  0.,  0.,  0.,  0.,  6., 13., 10.,  0.,  0.,  0.])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ],
      "source": [
        "dataset.data[0]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "UlSFwXm00ixe",
        "outputId": "5c6fb850-5b7b-4579-b808-5bf175da081c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
              "       [ 0.,  0., 13., 15., 10., 15.,  5.,  0.],\n",
              "       [ 0.,  3., 15.,  2.,  0., 11.,  8.,  0.],\n",
              "       [ 0.,  4., 12.,  0.,  0.,  8.,  8.,  0.],\n",
              "       [ 0.,  5.,  8.,  0.,  0.,  9.,  8.,  0.],\n",
              "       [ 0.,  4., 11.,  0.,  1., 12.,  7.,  0.],\n",
              "       [ 0.,  2., 14.,  5., 10., 12.,  0.,  0.],\n",
              "       [ 0.,  0.,  6., 13., 10.,  0.,  0.,  0.]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ],
      "source": [
        "dataset.data[0].reshape(8,8)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "k5GubwUQ0ixf",
        "outputId": "532f929d-b57b-4380-877f-39e384618029",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 310
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f6c3184eb10>"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 0 Axes>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "from matplotlib import pyplot as plt\n",
        "%matplotlib inline\n",
        "plt.gray()\n",
        "plt.matshow(dataset.data[0].reshape(8,8))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "SFYwothN0ixg",
        "outputId": "26353ceb-1505-41e2-b4ea-a30bf25145a2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 292
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7f6c31589f10>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 288x288 with 1 Axes>"
            ],
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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "plt.matshow(dataset.data[9].reshape(8,8))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "Lm8u4GUT0ixi",
        "outputId": "d1d17e5b-de8e-44c6-8dd8-024ed2707c39",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, 3, 4])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "dataset.target[:5]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "uD9KmiL90ixj",
        "outputId": "92f51b1c-00f7-4b0c-cf6b-d7c0b6b54380",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "   pixel_0_6  pixel_0_7  pixel_1_0  pixel_1_1  ...  pixel_6_6  pixel_6_7  \\\n",
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              "   pixel_7_6  pixel_7_7  \n",
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              "          const element = document.querySelector('#df-3cebd548-9c3b-4507-b3e0-e0aa3ee75fb0');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "df = pd.DataFrame(dataset.data, columns=dataset.feature_names)\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "qdKdVV9u0ixm",
        "outputId": "82122af2-9e0f-4e70-b7c1-38635ae19538",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2, ..., 8, 9, 8])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "dataset.target"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "5t9ykBh70ixm",
        "outputId": "93e7a4ab-ed92-431d-c3b8-193883d1c0c4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "       pixel_0_0    pixel_0_1    pixel_0_2    pixel_0_3    pixel_0_4  \\\n",
              "count     1797.0  1797.000000  1797.000000  1797.000000  1797.000000   \n",
              "mean         0.0     0.303840     5.204786    11.835838    11.848080   \n",
              "std          0.0     0.907192     4.754826     4.248842     4.287388   \n",
              "min          0.0     0.000000     0.000000     0.000000     0.000000   \n",
              "25%          0.0     0.000000     1.000000    10.000000    10.000000   \n",
              "50%          0.0     0.000000     4.000000    13.000000    13.000000   \n",
              "75%          0.0     0.000000     9.000000    15.000000    15.000000   \n",
              "max          0.0     8.000000    16.000000    16.000000    16.000000   \n",
              "\n",
              "         pixel_0_5    pixel_0_6    pixel_0_7    pixel_1_0    pixel_1_1  ...  \\\n",
              "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  ...   \n",
              "mean      5.781859     1.362270     0.129661     0.005565     1.993879  ...   \n",
              "std       5.666418     3.325775     1.037383     0.094222     3.196160  ...   \n",
              "min       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
              "25%       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
              "50%       4.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
              "75%      11.000000     0.000000     0.000000     0.000000     3.000000  ...   \n",
              "max      16.000000    16.000000    15.000000     2.000000    16.000000  ...   \n",
              "\n",
              "         pixel_6_6    pixel_6_7    pixel_7_0    pixel_7_1    pixel_7_2  \\\n",
              "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000   \n",
              "mean      3.725097     0.206455     0.000556     0.279354     5.557596   \n",
              "std       4.919406     0.984401     0.023590     0.934302     5.103019   \n",
              "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
              "25%       0.000000     0.000000     0.000000     0.000000     1.000000   \n",
              "50%       1.000000     0.000000     0.000000     0.000000     4.000000   \n",
              "75%       7.000000     0.000000     0.000000     0.000000    10.000000   \n",
              "max      16.000000    13.000000     1.000000     9.000000    16.000000   \n",
              "\n",
              "         pixel_7_3    pixel_7_4    pixel_7_5    pixel_7_6    pixel_7_7  \n",
              "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  \n",
              "mean     12.089037    11.809126     6.764051     2.067891     0.364496  \n",
              "std       4.374694     4.933947     5.900623     4.090548     1.860122  \n",
              "min       0.000000     0.000000     0.000000     0.000000     0.000000  \n",
              "25%      11.000000    10.000000     0.000000     0.000000     0.000000  \n",
              "50%      13.000000    14.000000     6.000000     0.000000     0.000000  \n",
              "75%      16.000000    16.000000    12.000000     2.000000     0.000000  \n",
              "max      16.000000    16.000000    16.000000    16.000000    16.000000  \n",
              "\n",
              "[8 rows x 64 columns]"
            ],
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              "\n",
              "  <div id=\"df-6b9fdf16-25c7-4a33-8baf-5b0d6f3e9444\">\n",
              "    <div class=\"colab-df-container\">\n",
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              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>pixel_0_0</th>\n",
              "      <th>pixel_0_1</th>\n",
              "      <th>pixel_0_2</th>\n",
              "      <th>pixel_0_3</th>\n",
              "      <th>pixel_0_4</th>\n",
              "      <th>pixel_0_5</th>\n",
              "      <th>pixel_0_6</th>\n",
              "      <th>pixel_0_7</th>\n",
              "      <th>pixel_1_0</th>\n",
              "      <th>pixel_1_1</th>\n",
              "      <th>...</th>\n",
              "      <th>pixel_6_6</th>\n",
              "      <th>pixel_6_7</th>\n",
              "      <th>pixel_7_0</th>\n",
              "      <th>pixel_7_1</th>\n",
              "      <th>pixel_7_2</th>\n",
              "      <th>pixel_7_3</th>\n",
              "      <th>pixel_7_4</th>\n",
              "      <th>pixel_7_5</th>\n",
              "      <th>pixel_7_6</th>\n",
              "      <th>pixel_7_7</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>1797.0</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "      <td>1797.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.303840</td>\n",
              "      <td>5.204786</td>\n",
              "      <td>11.835838</td>\n",
              "      <td>11.848080</td>\n",
              "      <td>5.781859</td>\n",
              "      <td>1.362270</td>\n",
              "      <td>0.129661</td>\n",
              "      <td>0.005565</td>\n",
              "      <td>1.993879</td>\n",
              "      <td>...</td>\n",
              "      <td>3.725097</td>\n",
              "      <td>0.206455</td>\n",
              "      <td>0.000556</td>\n",
              "      <td>0.279354</td>\n",
              "      <td>5.557596</td>\n",
              "      <td>12.089037</td>\n",
              "      <td>11.809126</td>\n",
              "      <td>6.764051</td>\n",
              "      <td>2.067891</td>\n",
              "      <td>0.364496</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.907192</td>\n",
              "      <td>4.754826</td>\n",
              "      <td>4.248842</td>\n",
              "      <td>4.287388</td>\n",
              "      <td>5.666418</td>\n",
              "      <td>3.325775</td>\n",
              "      <td>1.037383</td>\n",
              "      <td>0.094222</td>\n",
              "      <td>3.196160</td>\n",
              "      <td>...</td>\n",
              "      <td>4.919406</td>\n",
              "      <td>0.984401</td>\n",
              "      <td>0.023590</td>\n",
              "      <td>0.934302</td>\n",
              "      <td>5.103019</td>\n",
              "      <td>4.374694</td>\n",
              "      <td>4.933947</td>\n",
              "      <td>5.900623</td>\n",
              "      <td>4.090548</td>\n",
              "      <td>1.860122</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>10.000000</td>\n",
              "      <td>10.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>11.000000</td>\n",
              "      <td>10.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>13.000000</td>\n",
              "      <td>13.000000</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>4.000000</td>\n",
              "      <td>13.000000</td>\n",
              "      <td>14.000000</td>\n",
              "      <td>6.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>0.0</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>9.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>11.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>10.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>12.000000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>0.0</td>\n",
              "      <td>8.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>...</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>13.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>9.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "      <td>16.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>8 rows × 64 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-6b9fdf16-25c7-4a33-8baf-5b0d6f3e9444')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
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              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-6b9fdf16-25c7-4a33-8baf-5b0d6f3e9444 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-6b9fdf16-25c7-4a33-8baf-5b0d6f3e9444');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "df.describe()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "FSmnPIXv0ixn"
      },
      "outputs": [],
      "source": [
        "X = df\n",
        "y = dataset.target"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "ACr4xu_q0ixn",
        "outputId": "8bad532a-9b5e-4f72-9352-f041e6b9d2ba",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.        , -0.33501649, -0.04308102, ..., -1.14664746,\n",
              "        -0.5056698 , -0.19600752],\n",
              "       [ 0.        , -0.33501649, -1.09493684, ...,  0.54856067,\n",
              "        -0.5056698 , -0.19600752],\n",
              "       [ 0.        , -0.33501649, -1.09493684, ...,  1.56568555,\n",
              "         1.6951369 , -0.19600752],\n",
              "       ...,\n",
              "       [ 0.        , -0.33501649, -0.88456568, ..., -0.12952258,\n",
              "        -0.5056698 , -0.19600752],\n",
              "       [ 0.        , -0.33501649, -0.67419451, ...,  0.8876023 ,\n",
              "        -0.5056698 , -0.19600752],\n",
              "       [ 0.        , -0.33501649,  1.00877481, ...,  0.8876023 ,\n",
              "        -0.26113572, -0.19600752]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ],
      "source": [
        "from sklearn.preprocessing import StandardScaler\n",
        "scaler = StandardScaler()\n",
        "X_scaled = scaler.fit_transform(X)\n",
        "X_scaled"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "id": "N26oOoR-0ixo"
      },
      "outputs": [],
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.2, random_state=30)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "id": "sYtUJsvU0ixp",
        "outputId": "ac9e4ee5-5783-4d2e-8bb1-7fe6dc3005bd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9722222222222222"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "model = LogisticRegression()\n",
        "model.fit(X_train, y_train)\n",
        "model.score(X_test, y_test)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ds0s8ArF0ixp"
      },
      "source": [
        "<h3>Use PCA to reduce dimensions</h3>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "id": "oeuR7EOd0ixp",
        "outputId": "13dc1fe6-5237-4e8e-c783-cb8978373309",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 488
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "X"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YtRGpLHK0ixq"
      },
      "source": [
        "<h4>Use components such that 95% of variance is retained</h4>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "scrolled": false,
        "id": "rXCERRFq0ixq",
        "outputId": "512f147d-0a33-41fd-b2b7-ad3d135f1961",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 29)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "from sklearn.decomposition import PCA\n",
        "\n",
        "pca = PCA(0.95)\n",
        "X_pca = pca.fit_transform(X)\n",
        "X_pca.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "aiQZeVhO0ixq",
        "outputId": "2e4befb9-5ebd-4bb2-e39f-5665d8e4fd53",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.14890594, 0.13618771, 0.11794594, 0.08409979, 0.05782415,\n",
              "       0.0491691 , 0.04315987, 0.03661373, 0.03353248, 0.03078806,\n",
              "       0.02372341, 0.02272697, 0.01821863, 0.01773855, 0.01467101,\n",
              "       0.01409716, 0.01318589, 0.01248138, 0.01017718, 0.00905617,\n",
              "       0.00889538, 0.00797123, 0.00767493, 0.00722904, 0.00695889,\n",
              "       0.00596081, 0.00575615, 0.00515158, 0.0048954 ])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "pca.explained_variance_ratio_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "6vB05l9-0ixr",
        "outputId": "2f0837db-365b-4548-f139-6eb085e11d34",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "29"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "pca.n_components_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UCT5Ci5h0ixr"
      },
      "source": [
        "**PCA created 29 components out of 64 original columns**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "igObB-7Y0ixr",
        "outputId": "691cc831-9a15-4f3a-c62f-04cc5bf7c315",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ -1.25946645,  21.27488348,  -9.46305462, ...,   3.67072108,\n",
              "         -0.9436689 ,  -1.13250195],\n",
              "       [  7.9576113 , -20.76869896,   4.43950604, ...,   2.18261819,\n",
              "         -0.51022719,   2.31354911],\n",
              "       [  6.99192297,  -9.95598641,   2.95855808, ...,   4.22882114,\n",
              "          2.1576573 ,   0.8379578 ],\n",
              "       ...,\n",
              "       [ 10.8012837 ,  -6.96025223,   5.59955453, ...,  -3.56866194,\n",
              "          1.82444444,   3.53885886],\n",
              "       [ -4.87210009,  12.42395362, -10.17086635, ...,   3.25330054,\n",
              "          0.95484174,  -0.93895602],\n",
              "       [ -0.34438963,   6.36554919,  10.77370849, ...,  -3.01636722,\n",
              "          1.29752723,   2.58810313]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "X_pca"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "7M4w5u3-0ixs"
      },
      "outputs": [],
      "source": [
        "X_train_pca, X_test_pca, y_train, y_test = train_test_split(X_pca, y, test_size=0.2, random_state=30)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "id": "64_6iCUL0ixt",
        "outputId": "3fc84d79-c1a6-4f59-f4a6-da085bb7041a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9694444444444444"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "model = LogisticRegression(max_iter=1000)\n",
        "model.fit(X_train_pca, y_train)\n",
        "model.score(X_test_pca, y_test)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "raeYHXs90ixt"
      },
      "source": [
        "**Let's now select only two components**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "YKofGzQz0ixu",
        "outputId": "8d51846d-169f-4b1f-961b-a31473b4efe8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1797, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ],
      "source": [
        "pca = PCA(n_components=2)\n",
        "X_pca = pca.fit_transform(X)\n",
        "X_pca.shape"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "id": "yRSv9DyN0ixu",
        "outputId": "ea3567c1-bdc1-497b-a73c-4ac0f68ca376",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ -1.25946684,  21.27488293],\n",
              "       [  7.95761014, -20.76869843],\n",
              "       [  6.991924  ,  -9.95598599],\n",
              "       ...,\n",
              "       [ 10.80128462,  -6.96025298],\n",
              "       [ -4.87210055,  12.42395505],\n",
              "       [ -0.34438793,   6.36554823]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ],
      "source": [
        "X_pca"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 24,
      "metadata": {
        "id": "yRtP6DTu0ixu",
        "outputId": "ebb96f8d-d144-4a0f-a946-47895568eb6d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.14890594, 0.13618771])"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ],
      "source": [
        "pca.explained_variance_ratio_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0Bmp6vvF0ixv"
      },
      "source": [
        "**You can see that both combined retains 0.14+0.13=0.27 or 27% of important feature information**"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "-1L_XV5R0ixv",
        "outputId": "193295ff-5f7a-420c-ca8c-0f546f90dc21",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.6083333333333333"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ],
      "source": [
        "X_train_pca, X_test_pca, y_train, y_test = train_test_split(X_pca, y, test_size=0.2, random_state=30)\n",
        "\n",
        "model = LogisticRegression(max_iter=1000)\n",
        "model.fit(X_train_pca, y_train)\n",
        "model.score(X_test_pca, y_test)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7X6CQAoG0ixv"
      },
      "source": [
        "We get less accuancy (~60%) as using only 2 components did not retain much of the feature information. However in real life you will find many cases where using 2 or few PCA components can still give you a pretty good accuracy"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
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      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
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    },
    "colab": {
      "name": "DimReduction: PCA_digits.ipynb",
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