python/PCA_analysis.ipynb

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    "colab": {
      "name": "PCA-analysis.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_dhYUDq9u6lY",
        "colab_type": "text"
      },
      "source": [
        "# **Machine Learning in Python: Performing Principal Component Analysis (PCA)**\n",
        "\n",
        "Chanin Nantasenamat\n",
        "\n",
        "<i>Data Professor YouTube channel, http://youtube.com/dataprofessor </i>\n",
        "\n",
        "In this Jupyter notebook, we will be performing Principal Component Analysis (PCA) using the Iris data set as an example."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "06FKTxWKxhS3",
        "colab_type": "text"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "993wzT_Qu6ld",
        "colab_type": "text"
      },
      "source": [
        "## **1. Iris data set**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JAoNQBkGxS4k",
        "colab_type": "text"
      },
      "source": [
        "### Load library"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J46-WhoNwu1M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn import datasets"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KOezq3OoxXOt",
        "colab_type": "text"
      },
      "source": [
        "### Load dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i7tA2pJru6le",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "iris = datasets.load_iris()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kkfLzx63u6li",
        "colab_type": "text"
      },
      "source": [
        "### Input features"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "dsNpvJrau6li",
        "colab_type": "code",
        "outputId": "c5017eda-020d-4fd1-f3f4-8fc968d0cfef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(iris.feature_names)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZP_yudc_u6lm",
        "colab_type": "text"
      },
      "source": [
        "### Output features"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6drPiuLJu6lm",
        "colab_type": "code",
        "outputId": "362a4109-d3bc-4386-e939-42cb591db072",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(iris.target_names)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['setosa' 'versicolor' 'virginica']\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ok1mrQKBu6ly",
        "colab_type": "text"
      },
      "source": [
        "### Assigning Input (X) and Output (Y) variables\n",
        "Let's assign the 4 input variables to X and the output variable (class label) to Y"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4dRDJdZju6ly",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = iris.data\n",
        "Y = iris.target"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SITDccCXu6l1",
        "colab_type": "text"
      },
      "source": [
        "### Let's examine the data dimension"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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        "colab_type": "code",
        "outputId": "d970f43c-517c-4ec6-9c8d-2dc8295a6dba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "X.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(150, 4)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hGST4G-vu6l5",
        "colab_type": "code",
        "outputId": "ad084e22-0a73-4bf2-9f72-699cd9cd98ea",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "Y.shape"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(150,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I8v0oQWxwlY9",
        "colab_type": "text"
      },
      "source": [
        "---"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zIEVV6ilwmd-",
        "colab_type": "text"
      },
      "source": [
        "## **2. PCA analysis**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZKTWaerqP9Fn",
        "colab_type": "text"
      },
      "source": [
        "### 2.1. Load library"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VsYGSVAqyEfd",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.preprocessing import scale # Data scaling\n",
        "from sklearn import decomposition #PCA\n",
        "import pandas as pd # pandas"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-NgIE0Vaaw80",
        "colab_type": "text"
      },
      "source": [
        "### 2.2. Data scaling"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gwG7MVqWazvO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X = scale(X)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e459eMWpQA5Y",
        "colab_type": "text"
      },
      "source": [
        "### 2.3. Perform PCA analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ljxH8Hclbhpv",
        "colab_type": "text"
      },
      "source": [
        "Here we define the number of PC to use as 3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xc4axaaBQJVh",
        "colab_type": "code",
        "outputId": "b98c8a79-5577-4982-fdf1-1672da43359a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "pca = decomposition.PCA(n_components=3)\n",
        "pca.fit(X)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=3, random_state=None,\n",
              "    svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b6-MMWHVbmoW",
        "colab_type": "text"
      },
      "source": [
        "#### 2.4. Compute and retrieve the **scores** values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CvXA9dWbbecf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "scores = pca.transform(X)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LECV1kDAQcdG",
        "colab_type": "code",
        "outputId": "751b7451-f56e-4541-d143-038d9b5cbef9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        }
      },
      "source": [
        "scores_df = pd.DataFrame(scores, columns=['PC1', 'PC2', 'PC3'])\n",
        "scores_df"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "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",
              "      <th>PC3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-2.264703</td>\n",
              "      <td>0.480027</td>\n",
              "      <td>-0.127706</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-2.080961</td>\n",
              "      <td>-0.674134</td>\n",
              "      <td>-0.234609</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-2.364229</td>\n",
              "      <td>-0.341908</td>\n",
              "      <td>0.044201</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-2.299384</td>\n",
              "      <td>-0.597395</td>\n",
              "      <td>0.091290</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-2.389842</td>\n",
              "      <td>0.646835</td>\n",
              "      <td>0.015738</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145</th>\n",
              "      <td>1.870503</td>\n",
              "      <td>0.386966</td>\n",
              "      <td>0.256274</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>146</th>\n",
              "      <td>1.564580</td>\n",
              "      <td>-0.896687</td>\n",
              "      <td>-0.026371</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>147</th>\n",
              "      <td>1.521170</td>\n",
              "      <td>0.269069</td>\n",
              "      <td>0.180178</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>148</th>\n",
              "      <td>1.372788</td>\n",
              "      <td>1.011254</td>\n",
              "      <td>0.933395</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>149</th>\n",
              "      <td>0.960656</td>\n",
              "      <td>-0.024332</td>\n",
              "      <td>0.528249</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>150 rows × 3 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "          PC1       PC2       PC3\n",
              "0   -2.264703  0.480027 -0.127706\n",
              "1   -2.080961 -0.674134 -0.234609\n",
              "2   -2.364229 -0.341908  0.044201\n",
              "3   -2.299384 -0.597395  0.091290\n",
              "4   -2.389842  0.646835  0.015738\n",
              "..        ...       ...       ...\n",
              "145  1.870503  0.386966  0.256274\n",
              "146  1.564580 -0.896687 -0.026371\n",
              "147  1.521170  0.269069  0.180178\n",
              "148  1.372788  1.011254  0.933395\n",
              "149  0.960656 -0.024332  0.528249\n",
              "\n",
              "[150 rows x 3 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7eFmcxcPQWgI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Y_label = []\n",
        "\n",
        "for i in Y:\n",
        "  if i == 0:\n",
        "    Y_label.append('Setosa')\n",
        "  elif i == 1:\n",
        "    Y_label.append('Versicolor')\n",
        "  else:\n",
        "    Y_label.append('Virginica')\n",
        "\n",
        "Species = pd.DataFrame(Y_label, columns=['Species'])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z7NGBibTSdP2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df_scores = pd.concat([scores_df, Species], axis=1)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hI6HiOUgbrbn",
        "colab_type": "text"
      },
      "source": [
        "#### 2.5. Retrieve the **loadings** values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rmm75irIbdlD",
        "colab_type": "code",
        "outputId": "c077889c-0678-4767-dbd8-f8a9edbb2572",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "source": [
        "loadings = pca.components_.T\n",
        "df_loadings = pd.DataFrame(loadings, columns=['PC1', 'PC2','PC3'], index=iris.feature_names)\n",
        "df_loadings"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "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",
              "      <th>PC3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <td>0.521066</td>\n",
              "      <td>0.377418</td>\n",
              "      <td>-0.719566</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <td>-0.269347</td>\n",
              "      <td>0.923296</td>\n",
              "      <td>0.244382</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>petal length (cm)</th>\n",
              "      <td>0.580413</td>\n",
              "      <td>0.024492</td>\n",
              "      <td>0.142126</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>petal width (cm)</th>\n",
              "      <td>0.564857</td>\n",
              "      <td>0.066942</td>\n",
              "      <td>0.634273</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                        PC1       PC2       PC3\n",
              "sepal length (cm)  0.521066  0.377418 -0.719566\n",
              "sepal width (cm)  -0.269347  0.923296  0.244382\n",
              "petal length (cm)  0.580413  0.024492  0.142126\n",
              "petal width (cm)   0.564857  0.066942  0.634273"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ltOVa090b7EN",
        "colab_type": "text"
      },
      "source": [
        "#### 2.6. **Explained variance** for each PC"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tWpnfz3qY6Ip",
        "colab_type": "code",
        "outputId": "467d31e2-60b3-47cc-a04d-a4ae97d0bfb1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "explained_variance = pca.explained_variance_ratio_\n",
        "explained_variance"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.72962445, 0.22850762, 0.03668922])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "epeccObO2_mi",
        "colab_type": "text"
      },
      "source": [
        "## **3. Scree Plot**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b2MBGLQW79MO",
        "colab_type": "text"
      },
      "source": [
        "### 3.1. Import library"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6437d-bE75HO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import plotly.express as px"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AnjyJVWQ8GOd",
        "colab_type": "text"
      },
      "source": [
        "### 3.2. Preparing explained variance and cumulative variance"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v-D9U-xmoA1D",
        "colab_type": "text"
      },
      "source": [
        "#### 3.2.1. Preparing the explained variance data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JX9Pw88l336w",
        "colab_type": "code",
        "outputId": "4d239ce6-5eb8-434b-8b44-6e0228c8bed0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "explained_variance"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.72962445, 0.22850762, 0.03668922])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uBDTjyQad7Qv",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "explained_variance = np.insert(explained_variance, 0, 0)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DArGTefqoGJb",
        "colab_type": "text"
      },
      "source": [
        "#### 3.2.2. Preparing the cumulative variance data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0XRQQBxD71aS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "cumulative_variance = np.cumsum(np.round(explained_variance, decimals=3))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RJeJEaVxoI-F",
        "colab_type": "text"
      },
      "source": [
        "#### 3.2.3. Combining the dataframe"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9jiI53l44kd2",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pc_df = pd.DataFrame(['','PC1', 'PC2', 'PC3'], columns=['PC'])\n",
        "explained_variance_df = pd.DataFrame(explained_variance, columns=['Explained Variance'])\n",
        "cumulative_variance_df = pd.DataFrame(cumulative_variance, columns=['Cumulative Variance'])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L6LUZkeo6S5C",
        "colab_type": "code",
        "outputId": "3abacee2-a2d3-4c27-d37a-3be2b200eca9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        }
      },
      "source": [
        "df_explained_variance = pd.concat([pc_df, explained_variance_df, cumulative_variance_df], axis=1)\n",
        "df_explained_variance"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>PC</th>\n",
              "      <th>Explained Variance</th>\n",
              "      <th>Cumulative Variance</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td></td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>PC1</td>\n",
              "      <td>0.729624</td>\n",
              "      <td>0.730</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>PC2</td>\n",
              "      <td>0.228508</td>\n",
              "      <td>0.959</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>PC3</td>\n",
              "      <td>0.036689</td>\n",
              "      <td>0.996</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    PC  Explained Variance  Cumulative Variance\n",
              "0                 0.000000                0.000\n",
              "1  PC1            0.729624                0.730\n",
              "2  PC2            0.228508                0.959\n",
              "3  PC3            0.036689                0.996"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zH-g7oLwoayT",
        "colab_type": "text"
      },
      "source": [
        "#### 3.2.4. Making the scree plot"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ZLF0ShyojlD",
        "colab_type": "text"
      },
      "source": [
        "##### 3.2.4.1. Explained Variance"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "07omP_Un3Qjk",
        "colab_type": "code",
        "outputId": "c54722d5-d931-4f6d-db36-286c7563a20a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "# https://plotly.com/python/bar-charts/\n",
        "\n",
        "fig = px.bar(df_explained_variance, \n",
        "             x='PC', y='Explained Variance',\n",
        "             text='Explained Variance',\n",
        "             width=800)\n",
        "\n",
        "fig.update_traces(texttemplate='%{text:.3f}', textposition='outside')\n",
        "fig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
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              "        <script src=\"https://cdn.plot.ly/plotly-latest.min.js\"></script>    \n",
              "            <div id=\"81afa9e5-d939-402c-a72e-72e3c3cffb78\" class=\"plotly-graph-div\" style=\"height:525px; width:800px;\"></div>\n",
              "            <script type=\"text/javascript\">\n",
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              "                        {\"responsive\": true}\n",
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              "            Plotly.purge(gd);\n",
              "            observer.disconnect();\n",
              "        }}\n",
              "}});\n",
              "\n",
              "// Listen for the removal of the full notebook cells\n",
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              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ur58j9ZosQy",
        "colab_type": "text"
      },
      "source": [
        "##### 3.2.4.2. Explained Variance + Cumulative Variance"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9zzGeB2J-NJk",
        "colab_type": "code",
        "outputId": "98656f05-c601-40f3-c2dd-ebcf5b480242",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "# https://plotly.com/python/creating-and-updating-figures/\n",
        "\n",
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = go.Figure()\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Scatter(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Cumulative Variance'],\n",
        "        marker=dict(size=15, color=\"LightSeaGreen\")\n",
        "    ))\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Bar(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Explained Variance'],\n",
        "        marker=dict(color=\"RoyalBlue\")\n",
        "    ))\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IPPD1wHIo4MG",
        "colab_type": "text"
      },
      "source": [
        "##### 3.2.4.3. Explained Variance + Cumulative Variance (Separate Plot)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cL4QwGhTgFhV",
        "colab_type": "code",
        "outputId": "e5b5d2f3-5644-4a20-9f98-1ee9a3daa4a6",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "from plotly.subplots import make_subplots\n",
        "import plotly.graph_objects as go\n",
        "\n",
        "fig = make_subplots(rows=1, cols=2)\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Scatter(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Cumulative Variance'],\n",
        "        marker=dict(size=15, color=\"LightSeaGreen\")\n",
        "    ), row=1, col=1\n",
        "    )\n",
        "\n",
        "fig.add_trace(\n",
        "    go.Bar(\n",
        "        x=df_explained_variance['PC'],\n",
        "        y=df_explained_variance['Explained Variance'],\n",
        "        marker=dict(color=\"RoyalBlue\"),\n",
        "    ), row=1, col=2\n",
        "    )\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "                        {\"responsive\": true}\n",
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              "            Plotly.purge(gd);\n",
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              "}});\n",
              "\n",
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              "var notebookContainer = gd.closest('#notebook-container');\n",
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              "    x.observe(notebookContainer, {childList: true});\n",
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              "var outputEl = gd.closest('.output');\n",
              "if (outputEl) {{\n",
              "    x.observe(outputEl, {childList: true});\n",
              "}}\n",
              "\n",
              "                        })\n",
              "                };\n",
              "                \n",
              "            </script>\n",
              "        </div>\n",
              "</body>\n",
              "</html>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OB_LvOxNW5Wx",
        "colab_type": "text"
      },
      "source": [
        "## **4. Scores Plot**\n",
        "\n",
        "Source: https://plotly.com/python/3d-scatter-plots/"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1RSpqvmUXhoT",
        "colab_type": "text"
      },
      "source": [
        "### 4.1. Load library\n",
        "[API Documentation](https://plotly.com/python-api-reference/plotly.express.html) for *plotly.express* package"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SnyRnEjYXkQN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import plotly.express as px"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZtXU3cBsYJH9",
        "colab_type": "text"
      },
      "source": [
        "### 4.2. Basic 3D Scatter Plot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IPdv7qpmUcLS",
        "colab_type": "code",
        "outputId": "25d242ef-5223-4018-dc70-7df02a611ece",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "fig = px.scatter_3d(df_scores, x='PC1', y='PC2', z='PC3',\n",
        "              color='Species')\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3U22Q0PYXKp3",
        "colab_type": "text"
      },
      "source": [
        "### 4.3. Customized 3D Scatter Plot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LL_cAqrIUcOv",
        "colab_type": "code",
        "outputId": "66fe6f44-81e6-4444-d75f-651c61bc214f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "fig = px.scatter_3d(df_scores, x='PC1', y='PC2', z='PC3',\n",
        "              color='Species',\n",
        "              symbol='Species',\n",
        "              opacity=0.5)\n",
        "\n",
        "# tight layout\n",
        "fig.update_layout(margin=dict(l=0, r=0, b=0, t=0))\n",
        "\n",
        "# https://plotly.com/python/templates/\n",
        "#fig.update_layout(template='plotly_white') # \"plotly\", \"plotly_white\", \"plotly_dark\", \"ggplot2\", \"seaborn\", \"simple_white\", \"none\""
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZtIDXw_AfOwW",
        "colab_type": "text"
      },
      "source": [
        "## **5. Loadings Plot**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zLT3HjU0fRj3",
        "colab_type": "code",
        "outputId": "bd99a07c-8fb8-43d4-b185-93b9a8f8c3a4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 542
        }
      },
      "source": [
        "loadings_label = df_loadings.index\n",
        "# loadings_label = df_loadings.index.str.strip(' (cm)')\n",
        "\n",
        "fig = px.scatter_3d(df_loadings, x='PC1', y='PC2', z='PC3',\n",
        "                    text = loadings_label)\n",
        "\n",
        "fig.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
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