PCA.ipynb

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    "colab": {
      "name": "PCA.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyOC7GdZIxjWQeXHY+10IYcx"
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      "name": "python3",
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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "### Principal Component Analysis"
      ],
      "metadata": {
        "id": "a6n8zIq5YhC2"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "K3ASVPqPYcmz"
      },
      "outputs": [],
      "source": [
        "#import libraries\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### The Data\n",
        "Let's work with the cancer data set since it had so many features."
      ],
      "metadata": {
        "id": "i2zwube6Y3sc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.datasets import load_breast_cancer\n"
      ],
      "metadata": {
        "id": "Hqz97BUHY0Bt"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "cancer = load_breast_cancer()"
      ],
      "metadata": {
        "id": "OlvxYagNY8Q0"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "cancer.keys()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AlknsGxmY9l7",
        "outputId": "e7edfa4b-0422-4fa6-942b-4cff397129ed"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names', 'filename', 'data_module'])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(cancer['DESCR'])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "g975emUiY_MY",
        "outputId": "3ff4dc26-c448-43ae-8ca0-52c5b83d9fdc"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            ".. _breast_cancer_dataset:\n",
            "\n",
            "Breast cancer wisconsin (diagnostic) dataset\n",
            "--------------------------------------------\n",
            "\n",
            "**Data Set Characteristics:**\n",
            "\n",
            "    :Number of Instances: 569\n",
            "\n",
            "    :Number of Attributes: 30 numeric, predictive attributes and the class\n",
            "\n",
            "    :Attribute Information:\n",
            "        - radius (mean of distances from center to points on the perimeter)\n",
            "        - texture (standard deviation of gray-scale values)\n",
            "        - perimeter\n",
            "        - area\n",
            "        - smoothness (local variation in radius lengths)\n",
            "        - compactness (perimeter^2 / area - 1.0)\n",
            "        - concavity (severity of concave portions of the contour)\n",
            "        - concave points (number of concave portions of the contour)\n",
            "        - symmetry\n",
            "        - fractal dimension (\"coastline approximation\" - 1)\n",
            "\n",
            "        The mean, standard error, and \"worst\" or largest (mean of the three\n",
            "        worst/largest values) of these features were computed for each image,\n",
            "        resulting in 30 features.  For instance, field 0 is Mean Radius, field\n",
            "        10 is Radius SE, field 20 is Worst Radius.\n",
            "\n",
            "        - class:\n",
            "                - WDBC-Malignant\n",
            "                - WDBC-Benign\n",
            "\n",
            "    :Summary Statistics:\n",
            "\n",
            "    ===================================== ====== ======\n",
            "                                           Min    Max\n",
            "    ===================================== ====== ======\n",
            "    radius (mean):                        6.981  28.11\n",
            "    texture (mean):                       9.71   39.28\n",
            "    perimeter (mean):                     43.79  188.5\n",
            "    area (mean):                          143.5  2501.0\n",
            "    smoothness (mean):                    0.053  0.163\n",
            "    compactness (mean):                   0.019  0.345\n",
            "    concavity (mean):                     0.0    0.427\n",
            "    concave points (mean):                0.0    0.201\n",
            "    symmetry (mean):                      0.106  0.304\n",
            "    fractal dimension (mean):             0.05   0.097\n",
            "    radius (standard error):              0.112  2.873\n",
            "    texture (standard error):             0.36   4.885\n",
            "    perimeter (standard error):           0.757  21.98\n",
            "    area (standard error):                6.802  542.2\n",
            "    smoothness (standard error):          0.002  0.031\n",
            "    compactness (standard error):         0.002  0.135\n",
            "    concavity (standard error):           0.0    0.396\n",
            "    concave points (standard error):      0.0    0.053\n",
            "    symmetry (standard error):            0.008  0.079\n",
            "    fractal dimension (standard error):   0.001  0.03\n",
            "    radius (worst):                       7.93   36.04\n",
            "    texture (worst):                      12.02  49.54\n",
            "    perimeter (worst):                    50.41  251.2\n",
            "    area (worst):                         185.2  4254.0\n",
            "    smoothness (worst):                   0.071  0.223\n",
            "    compactness (worst):                  0.027  1.058\n",
            "    concavity (worst):                    0.0    1.252\n",
            "    concave points (worst):               0.0    0.291\n",
            "    symmetry (worst):                     0.156  0.664\n",
            "    fractal dimension (worst):            0.055  0.208\n",
            "    ===================================== ====== ======\n",
            "\n",
            "    :Missing Attribute Values: None\n",
            "\n",
            "    :Class Distribution: 212 - Malignant, 357 - Benign\n",
            "\n",
            "    :Creator:  Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian\n",
            "\n",
            "    :Donor: Nick Street\n",
            "\n",
            "    :Date: November, 1995\n",
            "\n",
            "This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.\n",
            "https://goo.gl/U2Uwz2\n",
            "\n",
            "Features are computed from a digitized image of a fine needle\n",
            "aspirate (FNA) of a breast mass.  They describe\n",
            "characteristics of the cell nuclei present in the image.\n",
            "\n",
            "Separating plane described above was obtained using\n",
            "Multisurface Method-Tree (MSM-T) [K. P. Bennett, \"Decision Tree\n",
            "Construction Via Linear Programming.\" Proceedings of the 4th\n",
            "Midwest Artificial Intelligence and Cognitive Science Society,\n",
            "pp. 97-101, 1992], a classification method which uses linear\n",
            "programming to construct a decision tree.  Relevant features\n",
            "were selected using an exhaustive search in the space of 1-4\n",
            "features and 1-3 separating planes.\n",
            "\n",
            "The actual linear program used to obtain the separating plane\n",
            "in the 3-dimensional space is that described in:\n",
            "[K. P. Bennett and O. L. Mangasarian: \"Robust Linear\n",
            "Programming Discrimination of Two Linearly Inseparable Sets\",\n",
            "Optimization Methods and Software 1, 1992, 23-34].\n",
            "\n",
            "This database is also available through the UW CS ftp server:\n",
            "\n",
            "ftp ftp.cs.wisc.edu\n",
            "cd math-prog/cpo-dataset/machine-learn/WDBC/\n",
            "\n",
            ".. topic:: References\n",
            "\n",
            "   - W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction \n",
            "     for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on \n",
            "     Electronic Imaging: Science and Technology, volume 1905, pages 861-870,\n",
            "     San Jose, CA, 1993.\n",
            "   - O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and \n",
            "     prognosis via linear programming. Operations Research, 43(4), pages 570-577, \n",
            "     July-August 1995.\n",
            "   - W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques\n",
            "     to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994) \n",
            "     163-171.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.DataFrame(cancer['data'],columns=cancer['feature_names'])\n",
        "#(['DESCR', 'data', 'feature_names', 'target_names', 'target'])"
      ],
      "metadata": {
        "id": "3AnmWcJlZB23"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.head()"
      ],
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        },
        "id": "r37dcKPqZJh6",
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      },
      "execution_count": 7,
      "outputs": [
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          "data": {
            "text/plain": [
              "   mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
              "0        17.99         10.38          122.80     1001.0          0.11840   \n",
              "1        20.57         17.77          132.90     1326.0          0.08474   \n",
              "2        19.69         21.25          130.00     1203.0          0.10960   \n",
              "3        11.42         20.38           77.58      386.1          0.14250   \n",
              "4        20.29         14.34          135.10     1297.0          0.10030   \n",
              "\n",
              "   mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
              "0           0.27760          0.3001              0.14710         0.2419   \n",
              "1           0.07864          0.0869              0.07017         0.1812   \n",
              "2           0.15990          0.1974              0.12790         0.2069   \n",
              "3           0.28390          0.2414              0.10520         0.2597   \n",
              "4           0.13280          0.1980              0.10430         0.1809   \n",
              "\n",
              "   mean fractal dimension  ...  worst radius  worst texture  worst perimeter  \\\n",
              "0                 0.07871  ...         25.38          17.33           184.60   \n",
              "1                 0.05667  ...         24.99          23.41           158.80   \n",
              "2                 0.05999  ...         23.57          25.53           152.50   \n",
              "3                 0.09744  ...         14.91          26.50            98.87   \n",
              "4                 0.05883  ...         22.54          16.67           152.20   \n",
              "\n",
              "   worst area  worst smoothness  worst compactness  worst concavity  \\\n",
              "0      2019.0            0.1622             0.6656           0.7119   \n",
              "1      1956.0            0.1238             0.1866           0.2416   \n",
              "2      1709.0            0.1444             0.4245           0.4504   \n",
              "3       567.7            0.2098             0.8663           0.6869   \n",
              "4      1575.0            0.1374             0.2050           0.4000   \n",
              "\n",
              "   worst concave points  worst symmetry  worst fractal dimension  \n",
              "0                0.2654          0.4601                  0.11890  \n",
              "1                0.1860          0.2750                  0.08902  \n",
              "2                0.2430          0.3613                  0.08758  \n",
              "3                0.2575          0.6638                  0.17300  \n",
              "4                0.1625          0.2364                  0.07678  \n",
              "\n",
              "[5 rows x 30 columns]"
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              "      <th></th>\n",
              "      <th>mean radius</th>\n",
              "      <th>mean texture</th>\n",
              "      <th>mean perimeter</th>\n",
              "      <th>mean area</th>\n",
              "      <th>mean smoothness</th>\n",
              "      <th>mean compactness</th>\n",
              "      <th>mean concavity</th>\n",
              "      <th>mean concave points</th>\n",
              "      <th>mean symmetry</th>\n",
              "      <th>mean fractal dimension</th>\n",
              "      <th>...</th>\n",
              "      <th>worst radius</th>\n",
              "      <th>worst texture</th>\n",
              "      <th>worst perimeter</th>\n",
              "      <th>worst area</th>\n",
              "      <th>worst smoothness</th>\n",
              "      <th>worst compactness</th>\n",
              "      <th>worst concavity</th>\n",
              "      <th>worst concave points</th>\n",
              "      <th>worst symmetry</th>\n",
              "      <th>worst fractal dimension</th>\n",
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              "      <th>0</th>\n",
              "      <td>17.99</td>\n",
              "      <td>10.38</td>\n",
              "      <td>122.80</td>\n",
              "      <td>1001.0</td>\n",
              "      <td>0.11840</td>\n",
              "      <td>0.27760</td>\n",
              "      <td>0.3001</td>\n",
              "      <td>0.14710</td>\n",
              "      <td>0.2419</td>\n",
              "      <td>0.07871</td>\n",
              "      <td>...</td>\n",
              "      <td>25.38</td>\n",
              "      <td>17.33</td>\n",
              "      <td>184.60</td>\n",
              "      <td>2019.0</td>\n",
              "      <td>0.1622</td>\n",
              "      <td>0.6656</td>\n",
              "      <td>0.7119</td>\n",
              "      <td>0.2654</td>\n",
              "      <td>0.4601</td>\n",
              "      <td>0.11890</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>20.57</td>\n",
              "      <td>17.77</td>\n",
              "      <td>132.90</td>\n",
              "      <td>1326.0</td>\n",
              "      <td>0.08474</td>\n",
              "      <td>0.07864</td>\n",
              "      <td>0.0869</td>\n",
              "      <td>0.07017</td>\n",
              "      <td>0.1812</td>\n",
              "      <td>0.05667</td>\n",
              "      <td>...</td>\n",
              "      <td>24.99</td>\n",
              "      <td>23.41</td>\n",
              "      <td>158.80</td>\n",
              "      <td>1956.0</td>\n",
              "      <td>0.1238</td>\n",
              "      <td>0.1866</td>\n",
              "      <td>0.2416</td>\n",
              "      <td>0.1860</td>\n",
              "      <td>0.2750</td>\n",
              "      <td>0.08902</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>19.69</td>\n",
              "      <td>21.25</td>\n",
              "      <td>130.00</td>\n",
              "      <td>1203.0</td>\n",
              "      <td>0.10960</td>\n",
              "      <td>0.15990</td>\n",
              "      <td>0.1974</td>\n",
              "      <td>0.12790</td>\n",
              "      <td>0.2069</td>\n",
              "      <td>0.05999</td>\n",
              "      <td>...</td>\n",
              "      <td>23.57</td>\n",
              "      <td>25.53</td>\n",
              "      <td>152.50</td>\n",
              "      <td>1709.0</td>\n",
              "      <td>0.1444</td>\n",
              "      <td>0.4245</td>\n",
              "      <td>0.4504</td>\n",
              "      <td>0.2430</td>\n",
              "      <td>0.3613</td>\n",
              "      <td>0.08758</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>11.42</td>\n",
              "      <td>20.38</td>\n",
              "      <td>77.58</td>\n",
              "      <td>386.1</td>\n",
              "      <td>0.14250</td>\n",
              "      <td>0.28390</td>\n",
              "      <td>0.2414</td>\n",
              "      <td>0.10520</td>\n",
              "      <td>0.2597</td>\n",
              "      <td>0.09744</td>\n",
              "      <td>...</td>\n",
              "      <td>14.91</td>\n",
              "      <td>26.50</td>\n",
              "      <td>98.87</td>\n",
              "      <td>567.7</td>\n",
              "      <td>0.2098</td>\n",
              "      <td>0.8663</td>\n",
              "      <td>0.6869</td>\n",
              "      <td>0.2575</td>\n",
              "      <td>0.6638</td>\n",
              "      <td>0.17300</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>20.29</td>\n",
              "      <td>14.34</td>\n",
              "      <td>135.10</td>\n",
              "      <td>1297.0</td>\n",
              "      <td>0.10030</td>\n",
              "      <td>0.13280</td>\n",
              "      <td>0.1980</td>\n",
              "      <td>0.10430</td>\n",
              "      <td>0.1809</td>\n",
              "      <td>0.05883</td>\n",
              "      <td>...</td>\n",
              "      <td>22.54</td>\n",
              "      <td>16.67</td>\n",
              "      <td>152.20</td>\n",
              "      <td>1575.0</td>\n",
              "      <td>0.1374</td>\n",
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              "            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": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###PCA Visualization\n",
        "As we've noticed before it is difficult to visualize high dimensional data, we can use PCA to find the first two principal components, and visualize the data in this new, two-dimensional space, with a single scatter-plot. Before we do this though, we'll need to scale our data so that each feature has a single unit variance."
      ],
      "metadata": {
        "id": "Mj7nFB_4ZN-a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import StandardScaler\n"
      ],
      "metadata": {
        "id": "f75IeLAsZLGS"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "scaler = StandardScaler()\n",
        "scaler.fit(df)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VUcift94ZUTl",
        "outputId": "4d2993e5-6aca-4512-e606-9d48e53dfcaf"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "StandardScaler()"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "scaled_data = scaler.transform(df)\n"
      ],
      "metadata": {
        "id": "DitI4VVbZVy8"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "PCA with Scikit Learn uses a very similar process to other preprocessing functions that come with SciKit Learn. We instantiate a PCA object, find the principal components using the fit method, then apply the rotation and dimensionality reduction by calling transform().\n",
        "\n",
        "We can also specify how many components we want to keep when creating the PCA object."
      ],
      "metadata": {
        "id": "A5Ar8ltcZdlk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.decomposition import PCA\n"
      ],
      "metadata": {
        "id": "9ET_HBFvZXUf"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "pca = PCA(n_components=2)\n",
        "pca.fit(scaled_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yBsxGmavZgL6",
        "outputId": "b7a5ce29-49e0-49ef-c8ae-16b296e2902a"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(n_components=2)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Now we can transform this data to its first 2 principal components.\n",
        "\n",
        "x_pca = pca.transform(scaled_data)"
      ],
      "metadata": {
        "id": "7yY0LLGyZhxb"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "scaled_data.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4LqrGdcQZnGi",
        "outputId": "34668450-3904-4903-f326-94123e8d989b"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(569, 30)"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_pca.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jH_henHMZ1aF",
        "outputId": "2c273be6-71dc-4b85-8d64-1a0e3b59d696"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(569, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Great! We've reduced 30 dimensions to just 2! Let's plot these two dimensions out!\n",
        "\n"
      ],
      "metadata": {
        "id": "Y-2aqVMdZ6oA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(8,6))\n",
        "plt.scatter(x_pca[:,0],x_pca[:,1],c=cancer['target'],cmap='plasma')\n",
        "plt.xlabel('First principal component')\n",
        "plt.ylabel('Second Principal Component')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 405
        },
        "id": "Pqx5tCZ4Z3q0",
        "outputId": "acd37d7a-f3b4-4087-916a-266ff04cd6c4"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Second Principal Component')"
            ]
          },
          "metadata": {},
          "execution_count": 21
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Clearly by using these two components we can easily separate these two classes.\n",
        "\n"
      ],
      "metadata": {
        "id": "d1Sz6-HzaB3L"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Interpreting the components\n",
        "Unfortunately, with this great power of dimensionality reduction, comes the cost of being able to easily understand what these components represent.\n",
        "\n",
        "The components correspond to combinations of the original features, the components themselves are stored as an attribute of the fitted PCA object:"
      ],
      "metadata": {
        "id": "OoYqkwNpaLAg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "pca.components_\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_ZcjGyQ1Z-vr",
        "outputId": "d1d86281-658a-4846-ae9c-7eebf9f125d7"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.21890244,  0.10372458,  0.22753729,  0.22099499,  0.14258969,\n",
              "         0.23928535,  0.25840048,  0.26085376,  0.13816696,  0.06436335,\n",
              "         0.20597878,  0.01742803,  0.21132592,  0.20286964,  0.01453145,\n",
              "         0.17039345,  0.15358979,  0.1834174 ,  0.04249842,  0.10256832,\n",
              "         0.22799663,  0.10446933,  0.23663968,  0.22487053,  0.12795256,\n",
              "         0.21009588,  0.22876753,  0.25088597,  0.12290456,  0.13178394],\n",
              "       [-0.23385713, -0.05970609, -0.21518136, -0.23107671,  0.18611302,\n",
              "         0.15189161,  0.06016536, -0.0347675 ,  0.19034877,  0.36657547,\n",
              "        -0.10555215,  0.08997968, -0.08945723, -0.15229263,  0.20443045,\n",
              "         0.2327159 ,  0.19720728,  0.13032156,  0.183848  ,  0.28009203,\n",
              "        -0.21986638, -0.0454673 , -0.19987843, -0.21935186,  0.17230435,\n",
              "         0.14359317,  0.09796411, -0.00825724,  0.14188335,  0.27533947]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this numpy matrix array, each row represents a principal component, and each column relates back to the original features. we can visualize this relationship with a heatmap:"
      ],
      "metadata": {
        "id": "YcixJFdcaTg1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "kF_7yy5zaNuS"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}