PCA_Abdi_in_python.ipynb

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      "source": [
        "## Principal Component Analysis - Part III\n",
        "\n",
        "Author: [Biswajit Sahoo](https://biswajitsahoo1111.github.io/)\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"center\">\n",
        "  <td>\n",
        "    <a href=\"https://colab.research.google.com/github/biswajitsahoo1111/cbm_codes_open/blob/master/notebooks/PCA_Abdi_in_python.ipynb\">\n",
        "    <img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />\n",
        "    Run Python code in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://www.dropbox.com/s/gn415uh3quou3a8/PCA_Abdi_in_python.ipynb?dl=1\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download Python code</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://www.dropbox.com/s/tp56l6v7upa1apf/PCA_blog_Biswajit_Sahoo_part_3.Rmd?dl=1\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download R code (R Markdown)</a>\n",
        "  </td>\n",
        "</table>\n",
        "\n",
        "In this post, we will reproduce the results of a popular paper on PCA. The paper is titled '[Principal component analysis](https://personal.utdallas.edu/~herve/abdi-awPCA2010.pdf)' and is authored by [Herve Abdi](https://personal.utdallas.edu/~herve/) and [Lynne J. Williams](https://ljwilliams.github.io/). It got published in 2010 and since then its popularity has only grown. Its number of citations are more than 4800 as per Google Scholar data (This was the number when this post was last revised).\n",
        "\n",
        "This post is Part-III of a three part series on PCA. Other parts of the series can be found at the links below. \n",
        "\n",
        "* [Part-I: Basic Theory of PCA](https://biswajitsahoo1111.github.io/post/principal-component-analysis-part-i/)\n",
        "* [Part-II: PCA Implementation with and without using built-in functions](https://biswajitsahoo1111.github.io/post/principal-component-analysis-part-ii/)\n",
        "\n",
        "This post contains code snippets in `Python`. To produce `ggplot` like plots, we have used `plotnine` package of `Python`. If that package is not availabe, it can be installed by using the command `pip install plotnine`.\n",
        "\n",
        "### Structure of the paper\n",
        "Along with basic theory, the paper contains three examples on PCA, one example on correspondence analysis, and one example on multiple factor analysis. We will only focus on PCA examples in this post."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-3a9R8DjmBQG"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "from plotnine import ggplot, aes, geom_point, geom_text, geom_hline, geom_vline, labs, xlim, ylim, geom_abline, annotate, geom_path"
      ],
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fj6WW23NmBQb"
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      "source": [
        "### How to get data\n",
        "Data for the following examples have been taken from the paper. These datasets are pretty small. So one way to read it is to create a dataframe itself in `Pandas` using the values given in paper. Otherwise, the values can first be saved in a csv file and then read from it. To make this post self-sufficient, we will adopt the former approach."
      ]
    },
    {
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          "height": 639
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        "id": "lD04ezf3mBQf",
        "outputId": "2e6db366-59af-44cb-915c-ecd1820e36a1"
      },
      "source": [
        "words = pd.DataFrame(data = {\"Words\": [\"Bag\", \"Across\", \"On\", \"Insane\", \"By\", \"Monastery\", \"Relief\", \"Slope\", \"Scoundrel\", \n",
        "                                       \"With\", \"Neither\", \"Pretentious\", \"Solid\", \"This\", \"For\", \"Therefore\", \"Generality\", \n",
        "                                       \"Arise\", \"Blot\", \"Infectious\"],\n",
        "                             \"Word_length\": [3, 6, 2, 6, 2, 9, 6, 5, 9, 4, 7, 11, 5, 4, 3, 9, 10, 5, 4, 10],\n",
        "                             \"Lines_in_dict\": [14, 7, 11, 9, 9, 4, 8, 11, 5, 8, 2, 4, 12, 9, 8, 1, 4, 13, 15, 6]})\n",
        "words"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Words</th>\n",
              "      <th>Word_length</th>\n",
              "      <th>Lines_in_dict</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Bag</td>\n",
              "      <td>3</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Across</td>\n",
              "      <td>6</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>On</td>\n",
              "      <td>2</td>\n",
              "      <td>11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Insane</td>\n",
              "      <td>6</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>By</td>\n",
              "      <td>2</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Monastery</td>\n",
              "      <td>9</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Relief</td>\n",
              "      <td>6</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Slope</td>\n",
              "      <td>5</td>\n",
              "      <td>11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Scoundrel</td>\n",
              "      <td>9</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>With</td>\n",
              "      <td>4</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Neither</td>\n",
              "      <td>7</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Pretentious</td>\n",
              "      <td>11</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Solid</td>\n",
              "      <td>5</td>\n",
              "      <td>12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>This</td>\n",
              "      <td>4</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>For</td>\n",
              "      <td>3</td>\n",
              "      <td>8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Therefore</td>\n",
              "      <td>9</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Generality</td>\n",
              "      <td>10</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Arise</td>\n",
              "      <td>5</td>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Blot</td>\n",
              "      <td>4</td>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Infectious</td>\n",
              "      <td>10</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "          Words  Word_length  Lines_in_dict\n",
              "0           Bag            3             14\n",
              "1        Across            6              7\n",
              "2            On            2             11\n",
              "3        Insane            6              9\n",
              "4            By            2              9\n",
              "5     Monastery            9              4\n",
              "6        Relief            6              8\n",
              "7         Slope            5             11\n",
              "8     Scoundrel            9              5\n",
              "9          With            4              8\n",
              "10      Neither            7              2\n",
              "11  Pretentious           11              4\n",
              "12        Solid            5             12\n",
              "13         This            4              9\n",
              "14          For            3              8\n",
              "15    Therefore            9              1\n",
              "16   Generality           10              4\n",
              "17        Arise            5             13\n",
              "18         Blot            4             15\n",
              "19   Infectious           10              6"
            ]
          },
          "metadata": {
            "tags": []
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          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9IyN7RGdmBQ1"
      },
      "source": [
        "Change data types from int to float. This will facilitate our analysis later. Otherwise some warnings will be generated."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "15OD5m9omBQ4",
        "outputId": "3d27c7b7-3892-4ddd-c0a4-0bbbc89bb37f"
      },
      "source": [
        "words.iloc[:,1:3] = words.iloc[:,1:3].astype(np.float64)\n",
        "words.dtypes"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Words             object\n",
              "Word_length      float64\n",
              "Lines_in_dict    float64\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
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      "cell_type": "markdown",
      "metadata": {
        "id": "JZaXVbVHmBRH"
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      "source": [
        "`sklearn`'s PCA centers data by default before applying SVD. In this example, we will explicitly center the data before giving it as an argument to PCA's `fit` method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KbjSZoQcmBRJ",
        "outputId": "c016195a-250a-46a5-ec70-5cc2923e0d49"
      },
      "source": [
        "cent_data = StandardScaler(with_mean= True, with_std = False)\n",
        "centered_words = cent_data.fit_transform(words.iloc[:,1:3])\n",
        "centered_words"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-3.,  6.],\n",
              "       [ 0., -1.],\n",
              "       [-4.,  3.],\n",
              "       [ 0.,  1.],\n",
              "       [-4.,  1.],\n",
              "       [ 3., -4.],\n",
              "       [ 0.,  0.],\n",
              "       [-1.,  3.],\n",
              "       [ 3., -3.],\n",
              "       [-2.,  0.],\n",
              "       [ 1., -6.],\n",
              "       [ 5., -4.],\n",
              "       [-1.,  4.],\n",
              "       [-2.,  1.],\n",
              "       [-3.,  0.],\n",
              "       [ 3., -7.],\n",
              "       [ 4., -4.],\n",
              "       [-1.,  5.],\n",
              "       [-2.,  7.],\n",
              "       [ 4., -2.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y3dCl4-emBRY"
      },
      "source": [
        "### Covariance PCA\n",
        "Covariance PCA uses centered data matrix. But data matrix is not scaled. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CaeUE5LymBRb"
      },
      "source": [
        "pca_words_cov = PCA().fit(centered_words)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jsFoX5DEmBRp",
        "outputId": "75502d23-34ea-47c0-db73-bf7787074312"
      },
      "source": [
        "factor_scores_words = pca_words_cov.transform(centered_words)\n",
        "print(np.round(factor_scores_words,2))"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-6.67 -0.69]\n",
            " [ 0.84  0.54]\n",
            " [-4.68  1.76]\n",
            " [-0.84 -0.54]\n",
            " [-2.99  2.84]\n",
            " [ 4.99 -0.38]\n",
            " [ 0.    0.  ]\n",
            " [-3.07 -0.77]\n",
            " [ 4.14 -0.92]\n",
            " [-1.07  1.69]\n",
            " [ 5.6   2.38]\n",
            " [ 6.06 -2.07]\n",
            " [-3.91 -1.3 ]\n",
            " [-1.92  1.15]\n",
            " [-1.61  2.53]\n",
            " [ 7.52  1.23]\n",
            " [ 5.52 -1.23]\n",
            " [-4.76 -1.84]\n",
            " [-6.98 -2.07]\n",
            " [ 3.83 -2.3 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HOk1mBarmBR6"
      },
      "source": [
        "Note that both of our factor scores are negative of that given in paper. It doesn't matter as principal directions are orthogonal. But to match the results of this notebook with that of the paper, we will multiply `factor scores` with -1 so that it matches with the values given in the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "UxseLR_DmBR9",
        "outputId": "cdc1cf2a-2e03-471f-bedf-430eaa2dacac"
      },
      "source": [
        "factor_scores_words = -factor_scores_words\n",
        "np.round(factor_scores_words,2)"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 6.67,  0.69],\n",
              "       [-0.84, -0.54],\n",
              "       [ 4.68, -1.76],\n",
              "       [ 0.84,  0.54],\n",
              "       [ 2.99, -2.84],\n",
              "       [-4.99,  0.38],\n",
              "       [-0.  , -0.  ],\n",
              "       [ 3.07,  0.77],\n",
              "       [-4.14,  0.92],\n",
              "       [ 1.07, -1.69],\n",
              "       [-5.6 , -2.38],\n",
              "       [-6.06,  2.07],\n",
              "       [ 3.91,  1.3 ],\n",
              "       [ 1.92, -1.15],\n",
              "       [ 1.61, -2.53],\n",
              "       [-7.52, -1.23],\n",
              "       [-5.52,  1.23],\n",
              "       [ 4.76,  1.84],\n",
              "       [ 6.98,  2.07],\n",
              "       [-3.83,  2.3 ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Du2IiaJTmBSK"
      },
      "source": [
        "### Principal directions are orthogonal"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PnlZA6VbmBSN",
        "outputId": "82f666d1-b5fd-4b91-e704-a2748e9ce4da"
      },
      "source": [
        "np.sum(factor_scores_words[:,0] * factor_scores_words[:,1])"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3.552713678800501e-15"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y4hv6yghmBSa"
      },
      "source": [
        "### Contribution of each factor"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "diakdaaEmBSd",
        "outputId": "e338e741-cae4-46b6-ec11-da2c1ddd2a35"
      },
      "source": [
        "np.round(factor_scores_words[:,0]**2/sum(factor_scores_words[:,0]**2)*100,2)"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([11.36,  0.18,  5.58,  0.18,  2.28,  6.34,  0.  ,  2.4 ,  4.38,\n",
              "        0.29,  8.  ,  9.37,  3.9 ,  0.94,  0.66, 14.41,  7.78,  5.77,\n",
              "       12.43,  3.75])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
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        },
        "id": "XPsINXKPmBSq",
        "outputId": "fed0b9d0-1313-4c3e-e8d7-093dc98b1c1d"
      },
      "source": [
        "np.round(factor_scores_words[:,1]**2/sum(factor_scores_words[:,1]**2)*100,2)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 0.92,  0.55,  5.98,  0.55, 15.49,  0.28,  0.  ,  1.13,  1.63,\n",
              "        5.48, 10.87,  8.25,  3.27,  2.55, 12.32,  2.9 ,  2.9 ,  6.52,\n",
              "        8.25, 10.18])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jz2gewKqmBS6"
      },
      "source": [
        "### Squared distance to center of gravity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "l5EGhDwOmBS9",
        "outputId": "751adb05-ff07-4b4d-856a-c6bce2fc64f4"
      },
      "source": [
        "np.sum(factor_scores_words**2,axis = 1)"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([45.,  1., 25.,  1., 17., 25.,  0., 10., 18.,  4., 37., 41., 17.,\n",
              "        5.,  9., 58., 32., 26., 53., 20.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TjaYpjCMmBTK"
      },
      "source": [
        "### Squared cosine of observations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lVq9xJ82mBTN",
        "outputId": "4346678d-ae69-4b46-e680-167ae67093c6"
      },
      "source": [
        "sq_cos = factor_scores_words**2/np.sum(factor_scores_words**2, axis = 1).reshape((20,1))*100\n",
        "print(np.round(sq_cos))"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[99.  1.]\n",
            " [71. 29.]\n",
            " [88. 12.]\n",
            " [71. 29.]\n",
            " [53. 47.]\n",
            " [99.  1.]\n",
            " [nan nan]\n",
            " [94.  6.]\n",
            " [95.  5.]\n",
            " [29. 71.]\n",
            " [85. 15.]\n",
            " [90. 10.]\n",
            " [90. 10.]\n",
            " [74. 26.]\n",
            " [29. 71.]\n",
            " [97.  3.]\n",
            " [95.  5.]\n",
            " [87. 13.]\n",
            " [92.  8.]\n",
            " [74. 26.]]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in true_divide\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ST4tmAfCmBTZ"
      },
      "source": [
        "`nan`s are produced because of division by zero."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "id": "Q8-xpvfSmBTo",
        "outputId": "ce9e3370-4326-4675-fb9c-14c50eeaeb45"
      },
      "source": [
        "# Figure 1\n",
        "p = (ggplot(words,aes(x = \"Lines_in_dict\", y = \"Word_length\", label = \"Words\"))\n",
        " + geom_point()+ geom_text(size = 7, ha = \"left\", va = \"bottom\", angle = 20)\n",
        " + geom_hline(yintercept = 6)+geom_vline(xintercept = 8)\n",
        " + labs(x = \"Lines in dictionary\",y = \"Word length\")\n",
        " + ylim([0,12]))\n",
        "print(p)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/plotnine/utils.py:1246: FutureWarning: is_categorical is deprecated and will be removed in a future version.  Use is_categorical_dtype instead\n",
            "  if pdtypes.is_categorical(arr):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "<ggplot: (8775119316077)>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9laI4cW7mBT4",
        "outputId": "8280c0ba-63f7-4886-f4dd-7a9625dc1bae"
      },
      "source": [
        "# Show directions of PCs\n",
        "# Note that intercept argument in geom_abline considers the line to be at the origin. In our case the data are mean shifted.\n",
        "# So we have to adjust the intercept taking new origin into consideration. These adjustments have been made below.\n",
        "slope1 = pca_words_cov.components_.T[0,0]/pca_words_cov.components_.T[1,0] # Slope of first PC\n",
        "slope2 = pca_words_cov.components_.T[0,1]/pca_words_cov.components_.T[1,1] # Slope of second PC\n",
        "new_origin = [np.mean(words[\"Lines_in_dict\"]), np.mean(words[\"Word_length\"])]\n",
        "print(\"New Origin: \" ,new_origin)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "New Origin:  [8.0, 6.0]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 502
        },
        "id": "8xSXC80ZmBUF",
        "outputId": "7d3d4e0e-d2d4-45f0-9534-0bc48534f853"
      },
      "source": [
        "intercept1 = 6 - slope1*8\n",
        "intercept2 = 6 - slope2*8\n",
        "(p + geom_abline(slope = slope1,intercept = intercept1,linetype = \"dashed\",size = 1.2,color = \"red\")\n",
        "   + geom_abline(slope = slope2,intercept = intercept2,linetype = \"dashed\",size = 1.2,color = \"blue\"))"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/plotnine/utils.py:1246: FutureWarning: is_categorical is deprecated and will be removed in a future version.  Use is_categorical_dtype instead\n",
            "  if pdtypes.is_categorical(arr):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108817261)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2TD5FrMAmBUl"
      },
      "source": [
        "In the above figure red dashed line is the 1st principal component (PC) and blue dashed line is the 2nd PC.\n",
        "\n",
        "### Rotated PCs\n",
        "This figure is obtained by plotting factor scores. Note that we will plot negative of the factor scores of 1st PC to make the figure consistent with the paper."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "Csqfuk6PmBUn",
        "outputId": "9b93f5aa-91c4-4764-9e5f-96b8e799193e"
      },
      "source": [
        "(ggplot(pd.DataFrame(data = {\"factor_scores_1\": -factor_scores_words[:,0], \"factor_scores_2\": -factor_scores_words[:,1]}),\n",
        "       aes(x = \"factor_scores_1\", y = \"factor_scores_2\", label = words[\"Words\"]))\n",
        " + geom_point()+geom_text(size = 7, ha = \"left\", va = \"bottom\")+geom_hline(yintercept = 0)+geom_vline(xintercept = 0)\n",
        " + labs(x = \"Factor score along PC1\", y = \"Factor score along PC2\") + xlim([-8,9]))"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/plotnine/utils.py:1246: FutureWarning: is_categorical is deprecated and will be removed in a future version.  Use is_categorical_dtype instead\n",
            "  if pdtypes.is_categorical(arr):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108768277)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "acm5A0uUmBUy"
      },
      "source": [
        "### With supplementray data\n",
        "Given a supplementary point (a point previously not used in finding principal components),we have to first center the data point. Its factor scores can then be obtained by multiplying it with the loading matrix."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "D1I_WIf7mBU0",
        "outputId": "df24711e-d102-42af-d123-f4e6453f275b"
      },
      "source": [
        "sur = np.array([3,12])\n",
        "sur_centered = sur - np.mean(words.iloc[:,1:3], axis = 0)\n",
        "sur_centered"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Word_length     -3.0\n",
              "Lines_in_dict    4.0\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b1tiz8xkmBU_"
      },
      "source": [
        "### Factor score of the new word 'sur'."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JgPCXC0AmBVB",
        "outputId": "a822444a-2826-4ef1-9fe4-d187053d0b14"
      },
      "source": [
        "np.round(pca_words_cov.transform(sur_centered.values.reshape(-1,2)),2)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-4.99,  0.38]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F5n4eZDmmBVL"
      },
      "source": [
        "### Total variance before"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "apdeA8vpmBVN",
        "outputId": "15de2b3d-6325-431c-aff3-960197a2af36"
      },
      "source": [
        "np.round(np.sum(np.var(words.values[:,1:3], axis = 0, ddof = 1)),3)"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "23.368"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jpVqlasDmBVZ"
      },
      "source": [
        "### Total variance after transformation."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CH1_W0kemBVb",
        "outputId": "aa867bd6-6d50-42a3-f35d-0b28341ce414"
      },
      "source": [
        "np.round(np.sum(pca_words_cov.explained_variance_),3)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "23.368"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sm4eoVvgmBVm"
      },
      "source": [
        "### Correlation matrix\n",
        "We have taken a convoluted path to find correlation matrix. But there might exist simpler ways."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "lpAGXOyemBVo",
        "outputId": "11b11d92-9c5c-48b4-ce09-a9242ccf225f"
      },
      "source": [
        "cor_matrix = np.repeat(np.nan, 4).reshape(2,2)\n",
        "for i in range(2):\n",
        "    for j in range(2):\n",
        "        cor_matrix[i,j] = np.corrcoef(factor_scores_words[:,i], centered_words[:,j])[0,1]\n",
        "cor_matrix"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.86790259,  0.97417637],\n",
              "       [ 0.49673443,  0.22578838]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ULKLvvWumBV2"
      },
      "source": [
        "Note that the answers for correlation coefficients don’t match with that of the paper. Readers who get actual answers as given in paper are encouraged to send me an email using my contact details. However our procedure is correct and it does indeed give the correct answer for supplementary data as described below."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z3ApxCU7mBV6"
      },
      "source": [
        "### Squared correlation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rb6VyI34mBV8",
        "outputId": "11fb18e0-a515-47d1-88b5-a1e1630e79e6"
      },
      "source": [
        "np.square(cor_matrix)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.7532549 , 0.94901961],\n",
              "       [0.2467451 , 0.05098039]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z8zqeCbEmBWI"
      },
      "source": [
        "Sum of correlation coefficients between variables and principal components is 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XEyngsJ_mBWK",
        "outputId": "bc41e2b2-165d-47f6-f44e-b811d1060a36"
      },
      "source": [
        "np.sum(np.square(cor_matrix),axis = 0)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1., 1.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LDK5W27XmBWV"
      },
      "source": [
        "### Loading matrix matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "V0JaQanJmBWX",
        "outputId": "c1bdc549-e864-4016-d99b-115443551b8a"
      },
      "source": [
        "pca_words_cov.components_.T            # This is the loading matrix"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.53687549, -0.84366149],\n",
              "       [-0.84366149, -0.53687549]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-F1GDjmnmBWh"
      },
      "source": [
        "### Correlation score for supplemenatry variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "1mUkK1RDmBWj",
        "outputId": "35a3d802-935b-4b19-815c-2be5e363044d"
      },
      "source": [
        "# Supplementary variable (Table 4)\n",
        "Frequency = np.array([8,230,700,1,500,1,9,2,1,700,7,1,4,500,900,3,1,10,1,1])\n",
        "Num_entries = np.array([6,3,12,2,7,1,1,6,1,5,2,1,5,9,7,1,1,4,4,2])\n",
        "supp_data = pd.DataFrame({\"Frequency\" : Frequency, \"Num_entries\" : Num_entries})\n",
        "supp_data"
      ],
      "execution_count": 25,
      "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>Frequency</th>\n",
              "      <th>Num_entries</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>8</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>230</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>700</td>\n",
              "      <td>12</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>500</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>9</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>2</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>700</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>7</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>500</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>900</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>10</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    Frequency  Num_entries\n",
              "0           8            6\n",
              "1         230            3\n",
              "2         700           12\n",
              "3           1            2\n",
              "4         500            7\n",
              "5           1            1\n",
              "6           9            1\n",
              "7           2            6\n",
              "8           1            1\n",
              "9         700            5\n",
              "10          7            2\n",
              "11          1            1\n",
              "12          4            5\n",
              "13        500            9\n",
              "14        900            7\n",
              "15          3            1\n",
              "16          1            1\n",
              "17         10            4\n",
              "18          1            4\n",
              "19          1            2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZpFh1kzpmBWv"
      },
      "source": [
        "### Centered suplementary data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "S2GyshCFmBW1",
        "outputId": "f32894f4-9890-433c-cb07-814d42ad1aa2"
      },
      "source": [
        "supp_data_cent = cent_data.fit_transform(supp_data.astype(np.float64))\n",
        "supp_data_cent"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-171.,    2.],\n",
              "       [  51.,   -1.],\n",
              "       [ 521.,    8.],\n",
              "       [-178.,   -2.],\n",
              "       [ 321.,    3.],\n",
              "       [-178.,   -3.],\n",
              "       [-170.,   -3.],\n",
              "       [-177.,    2.],\n",
              "       [-178.,   -3.],\n",
              "       [ 521.,    1.],\n",
              "       [-172.,   -2.],\n",
              "       [-178.,   -3.],\n",
              "       [-175.,    1.],\n",
              "       [ 321.,    5.],\n",
              "       [ 721.,    3.],\n",
              "       [-176.,   -3.],\n",
              "       [-178.,   -3.],\n",
              "       [-169.,    0.],\n",
              "       [-178.,    0.],\n",
              "       [-178.,   -2.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ekGRJtqmBXA"
      },
      "source": [
        "### Corrlation score for supplementary data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PlKCgVJomBXC",
        "outputId": "9c3685fa-6e67-4d67-d0db-85dd27210f70"
      },
      "source": [
        "cor_score_supp = np.repeat(np.nan,4).reshape(2,2)\n",
        "for i in range(2):\n",
        "    for j in range(2):\n",
        "        cor_score_supp[i,j] = np.corrcoef(factor_scores_words[:,i], supp_data_cent[:,j])[0,1]\n",
        "cor_score_supp"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.30118937,  0.69994982],\n",
              "       [-0.72183055, -0.44928258]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VDP62ZA_mBXN"
      },
      "source": [
        "Note that signs of entries of this correlation matrix are different than that of the paper. This is because our factor scores are negative of the factor scores given in paper. As correlation depends on sign of input data, we get different signs for some entries."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b6dGkUGZmBXP"
      },
      "source": [
        "### Squared correlation for support data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Osg9zEc9mBXS",
        "outputId": "062cbaa1-bb19-4bae-d3f5-66854b397b95"
      },
      "source": [
        "np.square(cor_score_supp)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.09071503, 0.48992975],\n",
              "       [0.52103934, 0.20185483]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-5nrYyr0mBXc"
      },
      "source": [
        "### Column sums of squared correlation for support data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uWkdjZbrmBXe",
        "outputId": "09b29277-4a39-43c8-a2f7-806ebe24c50d"
      },
      "source": [
        "np.sum(np.square(cor_score_supp), axis = 0)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.61175437, 0.69178458])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z2h-RsFOmBXp"
      },
      "source": [
        "### Corrlation circle plot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "GGB2LrqcmBXq",
        "outputId": "0c37d691-7197-4ae3-a4f0-eef89f30d5ab"
      },
      "source": [
        "x = np.linspace(0, 2*np.pi, num = 300)\n",
        "circle = (ggplot() + geom_path(pd.DataFrame(data = {\"a\": np.cos(x), \"b\": np.sin(x)}),\n",
        "                     aes(np.cos(x),np.sin(x)),alpha = 0.3, size = 1.5)+\n",
        "            geom_hline(yintercept = 0)+geom_vline(xintercept = 0)\n",
        "    + annotate(\"text\",x = [1.08,0.05],y = [0.05,1.15],label = [\"PC1\",\"PC2\"],angle = [0,90])+\n",
        "            labs(x = None, y = None))\n",
        "\n",
        "cor_score = np.repeat(np.nan,4).reshape(2,2)\n",
        "for i in range(2):\n",
        "    for j in range(2):\n",
        "        cor_score[i,j] = np.corrcoef(centered_words[:,i], factor_scores_words[:,j])[0,1]\n",
        "        \n",
        "cor_score = pd.DataFrame(data = cor_score, index = [\"Length of words\",\"Number of lines in Dict.\"], columns = [\"PC1\",\"PC2\"])\n",
        "variable_original_plot = (circle + geom_point(cor_score , aes(cor_score[\"PC1\"],cor_score[\"PC2\"]), inherit_aes = False)\n",
        "                         + annotate(\"text\",x = [cor_score.iloc[0,0],cor_score.iloc[1,0]],\n",
        "                                    y = [cor_score.iloc[0,1],cor_score.iloc[1,1]],\n",
        "                                    label = [\"Length of words\",\"Number of lines in Dict.\"], size = 9, ha = \"center\",\n",
        "                                    va = \"baseline\")+xlim([-1.5, 1.5]))\n",
        "print(variable_original_plot)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "<ggplot: (8775108715957)>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p45jMjtSmBX2"
      },
      "source": [
        "### Plotting supplementary variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "91liAK-nmBX5",
        "outputId": "7befc51c-ccc5-4562-8ebb-116c6532bbda"
      },
      "source": [
        "pd.DataFrame(cor_score_supp)"
      ],
      "execution_count": 31,
      "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>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.301189</td>\n",
              "      <td>0.699950</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.721831</td>\n",
              "      <td>-0.449283</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          0         1\n",
              "0  0.301189  0.699950\n",
              "1 -0.721831 -0.449283"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "DKB6Je9VmBYH",
        "outputId": "47db59b6-f02c-4611-c6cb-ed4e491abb17"
      },
      "source": [
        "(variable_original_plot+ geom_point(pd.DataFrame(cor_score_supp), aes(cor_score_supp[0], cor_score_supp[1])) +\n",
        "  annotate(\"text\",x = [cor_score_supp[0,0],cor_score_supp[0,1]],\n",
        "                                    y = [cor_score_supp[1,0],cor_score_supp[1,1]],\n",
        "                                    label = [\"Frequency\",\"Number of entries\"], size = 9, ha = \"left\",\n",
        "                                    va = \"baseline\")+xlim([-1.25, 1.5]))"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/plotnine/scales/scales.py:29: PlotnineWarning: Scale for 'x' is already present.\n",
            "Adding another scale for 'x',\n",
            "which will replace the existing scale.\n",
            "\n",
            "  warn(_TPL_DUPLICATE_SCALE.format(ae), PlotnineWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108670245)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ftuvdsgQmBYU"
      },
      "source": [
        "## Example 2\n",
        "### Wine example"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "euI7p_-smBYX"
      },
      "source": [
        "### Correlation PCA with wine data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "iNS45fNgmBYZ",
        "outputId": "7175f28c-edde-4cc0-e658-811459679a9a"
      },
      "source": [
        "wine = pd.DataFrame(data = {\"wine_type\": [\"wine_1\", \"wine_2\", \"wine_3\", \"wine_4\", \"wine_5\"],\n",
        "                            \"hedonic\": [14, 10, 8, 2, 6],\n",
        "                            \"for_meat\": [7, 7, 5, 4, 2],\n",
        "                            \"for_dessert\": [8, 6, 5, 7, 4],\n",
        "                            \"price\": [7, 4, 10, 16, 13],\n",
        "                            \"sugar\": [7, 3, 5, 7, 3],\n",
        "                            \"alcohol\": [13, 14, 12, 11, 10],\n",
        "                            \"acidity\": [7, 7, 5, 3, 3]})\n",
        "wine"
      ],
      "execution_count": 33,
      "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>wine_type</th>\n",
              "      <th>hedonic</th>\n",
              "      <th>for_meat</th>\n",
              "      <th>for_dessert</th>\n",
              "      <th>price</th>\n",
              "      <th>sugar</th>\n",
              "      <th>alcohol</th>\n",
              "      <th>acidity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>wine_1</td>\n",
              "      <td>14</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>7</td>\n",
              "      <td>7</td>\n",
              "      <td>13</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>wine_2</td>\n",
              "      <td>10</td>\n",
              "      <td>7</td>\n",
              "      <td>6</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>14</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>wine_3</td>\n",
              "      <td>8</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>10</td>\n",
              "      <td>5</td>\n",
              "      <td>12</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>wine_4</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>7</td>\n",
              "      <td>16</td>\n",
              "      <td>7</td>\n",
              "      <td>11</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>wine_5</td>\n",
              "      <td>6</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>13</td>\n",
              "      <td>3</td>\n",
              "      <td>10</td>\n",
              "      <td>3</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "  wine_type  hedonic  for_meat  for_dessert  price  sugar  alcohol  acidity\n",
              "0    wine_1       14         7            8      7      7       13        7\n",
              "1    wine_2       10         7            6      4      3       14        7\n",
              "2    wine_3        8         5            5     10      5       12        5\n",
              "3    wine_4        2         4            7     16      7       11        3\n",
              "4    wine_5        6         2            4     13      3       10        3"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t5a7-oJvmBYk"
      },
      "source": [
        "### Centered and scaled wine data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jC4IQiX7mBYp"
      },
      "source": [
        "scale_data = StandardScaler()\n",
        "scaled_wine_data = scale_data.fit_transform(wine.iloc[:,1:8].astype(np.float64))"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ehkUxP2nmBZF"
      },
      "source": [
        "**Note**: Standard scaler centers each colulmn and divides each coulmn by its standard deviation to produce scaled data for each column. But standard deviation for each column is computed using numpy's `np.std()` command. By default `np.std()` is biased. In contrast, in **R** standard deviation is unbiased by default. So we will use unbiased standard deviation values to make scaled data in python. In this way we get same results as in `R`. This conversion is obtained by a scalar multiplication.\n",
        "\n",
        "The factor is $$\\frac{1}{\\sqrt{\\frac{N}{N-1}}}$$ Where $N$ is number of data points. In our case $N=5$ as there are five wine types in this example."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pj1NRjMHmBZH"
      },
      "source": [
        "scaled_wine_data = scaled_wine_data* (1/np.sqrt(5/4))   "
      ],
      "execution_count": 35,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zPZbkNRrmBZQ"
      },
      "source": [
        "### PCA on scaled wine data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dGfzUD3YmBZS"
      },
      "source": [
        "pca_wine_cor = PCA().fit(scaled_wine_data)"
      ],
      "execution_count": 36,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jr5Qhmo6mBZi"
      },
      "source": [
        "transformed_data_wine = pca_wine_cor.transform(scaled_wine_data)"
      ],
      "execution_count": 37,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A4K0Pn-dmBZs"
      },
      "source": [
        "### First two principal components"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2w5M1WWRmBZy",
        "outputId": "dfa6a4ed-dcb8-43cf-a363-c0b7ca5de1cb"
      },
      "source": [
        "np.round(transformed_data_wine[:,0:2],4)"
      ],
      "execution_count": 38,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-2.3302,  1.0953],\n",
              "       [-2.0842, -1.2232],\n",
              "       [ 0.1673, -0.3703],\n",
              "       [ 1.7842,  1.7126],\n",
              "       [ 2.4628, -1.2144]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "cWwV9x9hmBaH",
        "outputId": "bfc8c9f7-4e58-4f65-a61d-62d2e1aa3c5b"
      },
      "source": [
        "transformed_data_wine_2PCs = pd.DataFrame(data = transformed_data_wine[:,:2], columns = [\"PC1\", \"PC2\"])\n",
        "(ggplot(transformed_data_wine_2PCs, aes(x = \"PC1\", y = \"PC2\", label = [\"wine 1\", \"wine 2\", \"wine 3\", \"wine 4\", \"wine 5\"]))\n",
        "       + geom_point() + geom_text(va = \"bottom\") + geom_vline(xintercept = 0)+ geom_hline(yintercept = 0)\n",
        "       + labs(x = \"Factor score along PC1\", y = \"Factor score along PC2\") + xlim([-3,3]))"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/plotnine/utils.py:1246: FutureWarning: is_categorical is deprecated and will be removed in a future version.  Use is_categorical_dtype instead\n",
            "  if pdtypes.is_categorical(arr):\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775109120153)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9uWZCl3HmBaR"
      },
      "source": [
        "Our figure seems upside down than that of the paper. This is a minor discrepancy. Our 2nd eigenvector is negative of the one considered in paper. We can match the plot with that of the paper by just flipping the second principal component but we will not do that here."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jW-tPCMomBaS"
      },
      "source": [
        "### Contribution of each observation to principal component"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "423pGOnmmBaX",
        "outputId": "aa1cf399-2b7a-450d-9b74-bce9367f9325"
      },
      "source": [
        "np.round(transformed_data_wine[:,0:2]**2/np.sum(transformed_data_wine[:,0:2]**2, axis = 0 )*100,2)"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[28.5 , 16.57],\n",
              "       [22.8 , 20.66],\n",
              "       [ 0.15,  1.89],\n",
              "       [16.71, 40.51],\n",
              "       [31.84, 20.37]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Yn5fC8EZmBah"
      },
      "source": [
        "### Squared cosine of observations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G2xmXcGSmBai",
        "outputId": "7b7678d1-c0e5-4e9c-c0b0-e7c2050c942a"
      },
      "source": [
        "np.round(transformed_data_wine[:,0:2]**2/np.sum(transformed_data_wine**2, axis = 1).reshape(5,1)*100)"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[77., 17.],\n",
              "       [69., 24.],\n",
              "       [ 7., 34.],\n",
              "       [50., 46.],\n",
              "       [78., 19.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jg38WyfHmBat"
      },
      "source": [
        "### Loading scores corresponding to first two principal components"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vRyFqo4zmBav",
        "outputId": "ce8063e5-b330-4c85-8343-e617b0798d80"
      },
      "source": [
        "np.round(pca_wine_cor.components_[0:2,:].T,2)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.4 , -0.11],\n",
              "       [-0.45,  0.11],\n",
              "       [-0.26,  0.59],\n",
              "       [ 0.42,  0.31],\n",
              "       [-0.05,  0.72],\n",
              "       [-0.44, -0.06],\n",
              "       [-0.45, -0.09]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vChXJrMimBa5"
      },
      "source": [
        "### Correlation score of variables with first two principal components\n",
        "Rows correspond to PC1 and PC2 respectively and columns correspond to featuers in wine data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9M2-B_1WmBa-",
        "outputId": "91571ef3-c73d-45a5-e00e-5f53cb237ea1"
      },
      "source": [
        "cor_score_wine = np.repeat(np.nan,14).reshape(2,7)\n",
        "for i in range(2):\n",
        "    for j in range(7):\n",
        "        cor_score_wine[i,j] = np.corrcoef(transformed_data_wine[:,i], wine.values[:,j+1].astype(np.float64))[0,1]\n",
        "np.round(cor_score_wine,2)"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.87, -0.97, -0.58,  0.91, -0.11, -0.96, -0.99],\n",
              "       [-0.15,  0.15,  0.79,  0.42,  0.97, -0.07, -0.12]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FlL9Y_l5mBbI"
      },
      "source": [
        "### Correlation circle for wine data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 443
        },
        "id": "eIG4e4zzmBbK",
        "outputId": "160c28eb-0050-4835-ca49-10fbf55280bf"
      },
      "source": [
        "# Figure 6\n",
        "cor_score_wine = cor_score_wine.T\n",
        "(circle +geom_point( aes(\"PC1\",\"PC2\"), data = pd.DataFrame(cor_score_wine,columns = [\"PC1\", \"PC2\"]))\n",
        "+ annotate(\"text\", x = cor_score_wine[:,0], y = cor_score_wine[:,1], \n",
        "           label = [\"Hedonic\",\"For Meat\",\"For dessert\",\"Price\",\"Sugar\",\"Alcohol\",\"Acidity\"],\n",
        "           va = \"top\", ha = \"left\", size = 7, nudge_x = 0.01))"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108660581)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MRcvMLcXmBbZ"
      },
      "source": [
        "## Varimax roation\n",
        "\n",
        "There is no function in python that performs varimax rotation. However, there are public codes to perform it in python. We use the code from this [Wikipedia page](https://en.wikipedia.org/wiki/Talk:Varimax_rotation). The function below is exact copy of the funciton in that page with minor changes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CBfxgz6kmBba"
      },
      "source": [
        "def varimax(Phi, gamma = 1.0, q = 20, tol = 1e-6):\n",
        "    import numpy as np\n",
        "    from numpy import eye, dot, asarray, sum\n",
        "    from scipy.linalg import svd\n",
        "    p,k = Phi.shape\n",
        "    R = eye(k)\n",
        "    d=0\n",
        "    for i in np.arange(q):\n",
        "        d_old = d\n",
        "        Lambda = dot(Phi, R)\n",
        "        u,s,vh = svd(dot(Phi.T,asarray(Lambda)**3 - (gamma/p) * dot(Lambda, np.diag(np.diag(dot(Lambda.T,Lambda))))))\n",
        "        R = dot(u,vh)\n",
        "        d = sum(s)\n",
        "        if d_old!=0 and d/d_old < 1 + tol: break\n",
        "    return dot(Phi, R)"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hiDOfIxBmBbj"
      },
      "source": [
        "We will compute rotated scores for first two columns of loading matrix that correspond to first two principal components."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dtx4nkN7mBbl",
        "outputId": "7b88d447-fadf-4e2d-e02a-3ca9ad440ab8"
      },
      "source": [
        "np.round(varimax(pca_wine_cor.components_.T[:,0:2]),2)"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-0.41, -0.03],\n",
              "       [-0.41,  0.2 ],\n",
              "       [-0.14,  0.63],\n",
              "       [ 0.47,  0.22],\n",
              "       [ 0.1 ,  0.72],\n",
              "       [-0.44,  0.04],\n",
              "       [-0.46,  0.01]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZMVb-cpSmBb2"
      },
      "source": [
        "In the above result, rows correspond to features in wine data. First column is the modified loading scores corresponding to first principal component and similarly for second column. Note that this result doesn't match with the paper. Neither does it match with `R` results. But it is close to the results given in paper."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zHiCVsAnmBb4"
      },
      "source": [
        "### Plot of loading scores before rotation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uvV-Cgs2mBcC",
        "outputId": "c2269542-e5bc-4526-bfda-1f5fa43dfa37"
      },
      "source": [
        "pca_wine_cor.components_.shape"
      ],
      "execution_count": 47,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(5, 7)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "UEurr8hvmBcL",
        "outputId": "b120dd3b-c5bc-4f71-b1b3-28c5c89c36ee"
      },
      "source": [
        "#Figure 7\n",
        "(ggplot(pd.DataFrame(pca_wine_cor.components_.T[:,:2], columns = [\"loadings_1\", \"loadings_2\"]),\n",
        "       aes(x = \"loadings_1\", y = \"loadings_2\"))\n",
        "+ geom_point() + geom_hline(yintercept = 0)+geom_vline(xintercept = 0)\n",
        "+ annotate(\"text\", x = pca_wine_cor.components_.T[:,0], y = pca_wine_cor.components_.T[:,1],\n",
        "           label = [\"Hedonic\",\"For Meat\",\"For dessert\",\"Price\",\"Sugar\",\"Alcohol\",\"Acidity\"],\n",
        "           va = \"top\", ha = \"left\", size = 8)+ xlim([-0.5, 0.5])\n",
        "+ labs(x = \"Loading score along PC1\", y = \"Loading score along PC2\"))"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108637577)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-Z_R71DkmBcU"
      },
      "source": [
        "### Plot of loading scores after rotation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 0
        },
        "id": "t4hUeg3emBcW",
        "outputId": "44ae8d83-26c3-4bd8-d2de-167dab1cce8d"
      },
      "source": [
        "rotated_loading_scores = varimax(pca_wine_cor.components_.T[:,0:2])\n",
        "(ggplot(pd.DataFrame(rotated_loading_scores, columns = [\"rotated_loadings_1\", \"rotated_loadings_2\"]),\n",
        "        aes(x = \"rotated_loadings_1\", y = \"rotated_loadings_2\"))\n",
        "+ geom_point() + geom_hline(yintercept = 0)+geom_vline(xintercept = 0)\n",
        "+ annotate(\"text\", x = rotated_loading_scores[:,0], y = rotated_loading_scores[:,1],\n",
        "           label = [\"Hedonic\",\"For Meat\",\"For dessert\",\"Price\",\"Sugar\",\"Alcohol\",\"Acidity\"],\n",
        "           va = \"top\", ha = \"left\", size = 8) + xlim([-0.5, 0.5])\n",
        "+ labs(x = \"Loading score along PC1 after rotation\", y = \"Loading score along PC2 after rotation\"))                                 "
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108766077)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RAjwExkmmBce"
      },
      "source": [
        "## Example 3\n",
        "### French food example (Covariance PCA)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 402
        },
        "id": "hId387ZVmBcg",
        "outputId": "e0eb9fb0-d3fc-42c3-f2a3-e37f15e133a8"
      },
      "source": [
        "food = pd.DataFrame(data = {\"class\": [\"Blue_collar\", \"White_collar\", \"Upper_class\", \"Blue_collar\", \"White_collar\", \"Upper_class\",\n",
        "                                      \"Blue_collar\", \"White_collar\", \"Upper_class\", \"Blue_collar\", \"White_collar\", \"Upper_class\"],\n",
        "                            \"children\": np.repeat([2,3,4,5], 3),\n",
        "                            \"bread\": [332, 293, 372, 406, 386, 438, 534, 460, 385, 655, 584, 515],\n",
        "                            \"vegetables\": [428, 559, 767, 563, 608, 843, 660, 699, 789, 776, 995, 1097],\n",
        "                            \"fruit\": [354, 388, 562, 341, 396, 689, 367, 484, 621, 423, 548, 887],\n",
        "                            \"meat\": [1437, 1527, 1948, 1507, 1501, 2345, 1620, 1856, 2366, 1848, 2056, 2630],\n",
        "                            \"poultry\": [526, 567, 927, 544, 558, 1148, 638, 762, 1149, 759, 893, 1167],\n",
        "                            \"milk\": [247, 239, 235, 324, 319, 243, 414, 400, 304, 495, 518, 561],\n",
        "                            \"wine\": [427, 258, 433, 407, 363, 341, 407, 416, 282, 486, 319, 284]})\n",
        "food"
      ],
      "execution_count": 50,
      "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>class</th>\n",
              "      <th>children</th>\n",
              "      <th>bread</th>\n",
              "      <th>vegetables</th>\n",
              "      <th>fruit</th>\n",
              "      <th>meat</th>\n",
              "      <th>poultry</th>\n",
              "      <th>milk</th>\n",
              "      <th>wine</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Blue_collar</td>\n",
              "      <td>2</td>\n",
              "      <td>332</td>\n",
              "      <td>428</td>\n",
              "      <td>354</td>\n",
              "      <td>1437</td>\n",
              "      <td>526</td>\n",
              "      <td>247</td>\n",
              "      <td>427</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>White_collar</td>\n",
              "      <td>2</td>\n",
              "      <td>293</td>\n",
              "      <td>559</td>\n",
              "      <td>388</td>\n",
              "      <td>1527</td>\n",
              "      <td>567</td>\n",
              "      <td>239</td>\n",
              "      <td>258</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Upper_class</td>\n",
              "      <td>2</td>\n",
              "      <td>372</td>\n",
              "      <td>767</td>\n",
              "      <td>562</td>\n",
              "      <td>1948</td>\n",
              "      <td>927</td>\n",
              "      <td>235</td>\n",
              "      <td>433</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Blue_collar</td>\n",
              "      <td>3</td>\n",
              "      <td>406</td>\n",
              "      <td>563</td>\n",
              "      <td>341</td>\n",
              "      <td>1507</td>\n",
              "      <td>544</td>\n",
              "      <td>324</td>\n",
              "      <td>407</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>White_collar</td>\n",
              "      <td>3</td>\n",
              "      <td>386</td>\n",
              "      <td>608</td>\n",
              "      <td>396</td>\n",
              "      <td>1501</td>\n",
              "      <td>558</td>\n",
              "      <td>319</td>\n",
              "      <td>363</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Upper_class</td>\n",
              "      <td>3</td>\n",
              "      <td>438</td>\n",
              "      <td>843</td>\n",
              "      <td>689</td>\n",
              "      <td>2345</td>\n",
              "      <td>1148</td>\n",
              "      <td>243</td>\n",
              "      <td>341</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Blue_collar</td>\n",
              "      <td>4</td>\n",
              "      <td>534</td>\n",
              "      <td>660</td>\n",
              "      <td>367</td>\n",
              "      <td>1620</td>\n",
              "      <td>638</td>\n",
              "      <td>414</td>\n",
              "      <td>407</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>White_collar</td>\n",
              "      <td>4</td>\n",
              "      <td>460</td>\n",
              "      <td>699</td>\n",
              "      <td>484</td>\n",
              "      <td>1856</td>\n",
              "      <td>762</td>\n",
              "      <td>400</td>\n",
              "      <td>416</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Upper_class</td>\n",
              "      <td>4</td>\n",
              "      <td>385</td>\n",
              "      <td>789</td>\n",
              "      <td>621</td>\n",
              "      <td>2366</td>\n",
              "      <td>1149</td>\n",
              "      <td>304</td>\n",
              "      <td>282</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Blue_collar</td>\n",
              "      <td>5</td>\n",
              "      <td>655</td>\n",
              "      <td>776</td>\n",
              "      <td>423</td>\n",
              "      <td>1848</td>\n",
              "      <td>759</td>\n",
              "      <td>495</td>\n",
              "      <td>486</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>White_collar</td>\n",
              "      <td>5</td>\n",
              "      <td>584</td>\n",
              "      <td>995</td>\n",
              "      <td>548</td>\n",
              "      <td>2056</td>\n",
              "      <td>893</td>\n",
              "      <td>518</td>\n",
              "      <td>319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Upper_class</td>\n",
              "      <td>5</td>\n",
              "      <td>515</td>\n",
              "      <td>1097</td>\n",
              "      <td>887</td>\n",
              "      <td>2630</td>\n",
              "      <td>1167</td>\n",
              "      <td>561</td>\n",
              "      <td>284</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           class  children  bread  vegetables  fruit  meat  poultry  milk  wine\n",
              "0    Blue_collar         2    332         428    354  1437      526   247   427\n",
              "1   White_collar         2    293         559    388  1527      567   239   258\n",
              "2    Upper_class         2    372         767    562  1948      927   235   433\n",
              "3    Blue_collar         3    406         563    341  1507      544   324   407\n",
              "4   White_collar         3    386         608    396  1501      558   319   363\n",
              "5    Upper_class         3    438         843    689  2345     1148   243   341\n",
              "6    Blue_collar         4    534         660    367  1620      638   414   407\n",
              "7   White_collar         4    460         699    484  1856      762   400   416\n",
              "8    Upper_class         4    385         789    621  2366     1149   304   282\n",
              "9    Blue_collar         5    655         776    423  1848      759   495   486\n",
              "10  White_collar         5    584         995    548  2056      893   518   319\n",
              "11   Upper_class         5    515        1097    887  2630     1167   561   284"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SHXp0kB2mBcp"
      },
      "source": [
        "food_cov = PCA().fit(food.iloc[:,2:9])"
      ],
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Al9hJcR9mBc1"
      },
      "source": [
        "### Factor scores\n",
        "`sklearn`'s PCA centers data by default before applying the algorithm. We can also center data manually before giving it as an argument to fit method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AgTnWTZnmBc2",
        "outputId": "55e6dcea-fd6d-43d8-cae7-b39a34034815"
      },
      "source": [
        "factor_scores_food = food_cov.transform(food.iloc[:,2:9])\n",
        "np.round(factor_scores_food[:,0:2],2)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-635.05, -120.89],\n",
              "       [-488.56, -142.33],\n",
              "       [ 112.03, -139.75],\n",
              "       [-520.01,   12.05],\n",
              "       [-485.94,    1.17],\n",
              "       [ 588.17, -188.44],\n",
              "       [-333.95,  144.54],\n",
              "       [ -57.51,   42.86],\n",
              "       [ 571.32, -206.76],\n",
              "       [ -39.38,  264.47],\n",
              "       [ 296.04,  235.92],\n",
              "       [ 992.83,   97.15]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 52
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mXvdSJEDmBdA"
      },
      "source": [
        "### Contribution of each observation to principal component"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-FNbBLCQmBdC",
        "outputId": "ed9f5d45-d42c-4156-9d22-08dc389b3841"
      },
      "source": [
        "np.round(factor_scores_food[:,0:2]**2/np.sum(factor_scores_food[:,0:2]**2, axis = 0)*100,2)"
      ],
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[13.34,  5.03],\n",
              "       [ 7.9 ,  6.97],\n",
              "       [ 0.42,  6.72],\n",
              "       [ 8.94,  0.05],\n",
              "       [ 7.81,  0.  ],\n",
              "       [11.44, 12.22],\n",
              "       [ 3.69,  7.19],\n",
              "       [ 0.11,  0.63],\n",
              "       [10.8 , 14.71],\n",
              "       [ 0.05, 24.07],\n",
              "       [ 2.9 , 19.15],\n",
              "       [32.61,  3.25]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "erIu0z8WmBdd"
      },
      "source": [
        "### Squared cosine of observations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dLwfRA-KmBdf",
        "outputId": "0b39b8fb-c375-44e6-815b-6c0b38402758"
      },
      "source": [
        "np.round(factor_scores_food[:,0:2]**2/np.sum(factor_scores_food**2, axis = 1).reshape(12,1)*100)"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 95.,   3.],\n",
              "       [ 86.,   7.],\n",
              "       [ 26.,  40.],\n",
              "       [100.,   0.],\n",
              "       [ 98.,   0.],\n",
              "       [ 89.,   9.],\n",
              "       [ 83.,  15.],\n",
              "       [ 40.,  22.],\n",
              "       [ 86.,  11.],\n",
              "       [  2.,  79.],\n",
              "       [ 57.,  36.],\n",
              "       [ 97.,   1.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k0uTDdwImBdq"
      },
      "source": [
        "### Squared loading scores"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7AhQX2I1mBds",
        "outputId": "983678d7-63b9-4974-b0aa-2294f06af8d2"
      },
      "source": [
        "np.round(food_cov.components_.T[:,0:2]**2, 2)"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.01, 0.33],\n",
              "       [0.11, 0.17],\n",
              "       [0.09, 0.01],\n",
              "       [0.57, 0.01],\n",
              "       [0.22, 0.06],\n",
              "       [0.01, 0.4 ],\n",
              "       [0.  , 0.02]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DIIfUOPCmBdz"
      },
      "source": [
        "Note that this answer doesn't match with the answers given in paper (Table 13). But we will stick with our result."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aWnXQWg0mBd1"
      },
      "source": [
        "### Correlation score"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oHm0QcUWmBd3",
        "outputId": "6db493b8-6fba-449a-a492-e0955ead06e6"
      },
      "source": [
        "corr_score_food = np.repeat(np.nan,14).reshape(2,7)\n",
        "for i in range(2):\n",
        "    for j in range(7):\n",
        "        corr_score_food[i,j] = np.corrcoef(factor_scores_food[:,i], food.values[:,j+2].astype(np.float64))[0,1]\n",
        "np.round(corr_score_food,2)"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.36,  0.91,  0.96,  1.  ,  0.98,  0.41, -0.43],\n",
              "       [ 0.87,  0.35, -0.1 , -0.04, -0.16,  0.88,  0.33]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DkhGxuG0mBd-"
      },
      "source": [
        "In the above answer, each column corresponds to a feature in food data excluding class and children. The two rows correspond to first two principal components. Second row of above answer also differs in sign from the results of `R`. This is due to the fact that second principal component factor scores of `R` are negative of python's."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gd38ZBOfmBeA"
      },
      "source": [
        "### Squared correlation score"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OqNdkprjmBeB",
        "outputId": "a2928350-ae7d-4385-f2d5-c825e03a0934"
      },
      "source": [
        "np.round(corr_score_food**2,2)"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.13, 0.83, 0.92, 1.  , 0.96, 0.17, 0.18],\n",
              "       [0.76, 0.12, 0.01, 0.  , 0.03, 0.77, 0.11]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ORf1DcCGmBeK"
      },
      "source": [
        "### Correlation circle for food data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 443
        },
        "id": "zymPgn0kmBeM",
        "outputId": "5a058cad-eb6f-4cb8-eba8-13c03a83800b"
      },
      "source": [
        "# Figure 9\n",
        "(circle + geom_point(aes(x = \"PC1\", y = \"PC2\"), data = pd.DataFrame(corr_score_food.T, columns = [\"PC1\", \"PC2\"]))\n",
        "+ annotate(\"text\", x = corr_score_food[0,:], y = corr_score_food[1,:],\n",
        "           label = [\"Bread\",\"Vegetables\",\"Fruit\",\"Meat\",\"Poultry\",\"Milk\",\"Wine\"],\n",
        "           va = \"top\", ha = \"left\",angle = -20, size = 7))"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<ggplot: (8775108791353)>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QlGttbS1mBeW"
      },
      "source": [
        "Now observe that our correlation circle plot is almost close to that of the papers though in opposite quadrants. This is because our first principal component is negative of the one given in the paper."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tPlI-CX8mBeY"
      },
      "source": [
        "### Eigenvalues"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ite_TcZQmBeZ"
      },
      "source": [
        "Eigen values of data covariance matrix is square of singular values of centered data matrix. Hence eigen values of data covariance matrix can be obtained as below."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4jqoNPMHmBeb",
        "outputId": "0dad78bf-884a-474e-d960-d25efea5052c"
      },
      "source": [
        "# Table 14\n",
        "eigen_values = food_cov.singular_values_.reshape(7,1)**2\n",
        "np.set_printoptions(suppress= True)\n",
        "np.round(eigen_values,2)"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3023141.24],\n",
              "       [ 290575.84],\n",
              "       [  68795.23],\n",
              "       [  25298.95],\n",
              "       [  22992.25],\n",
              "       [   3722.32],\n",
              "       [    723.92]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gjQnaGojmBer"
      },
      "source": [
        "**Important Note**: These eigenvalues are not the same as variance of factor scores in principal components. Variance of principal component factor scores can be obtained by dividing the eigenvalues by $(n-1)$ , where $n$ is number of data points (in this case $n = 12$ ). If this point is still not clear, refer to [Part-II](https://biswajitsahoo1111.github.io/post/principal-component-analysis-part-ii/)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6Z_kW27mBes"
      },
      "source": [
        "### Percentage contribution of each principal component"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8AVbRjFImBeu",
        "outputId": "921fdfaf-5443-444e-b050-d1a78eeb0359"
      },
      "source": [
        "np.round(eigen_values/np.sum(eigen_values),2)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0.88],\n",
              "       [0.08],\n",
              "       [0.02],\n",
              "       [0.01],\n",
              "       [0.01],\n",
              "       [0.  ],\n",
              "       [0.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MeGcrEg8mBe2"
      },
      "source": [
        "### Cumulative sum of eigenvalues"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vmNmDi8ZmBe3",
        "outputId": "6e9b5b04-0f69-4f01-e277-75d1d4b85681"
      },
      "source": [
        "np.round(np.cumsum(eigen_values).reshape(7,1),2)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3023141.24],\n",
              "       [3313717.07],\n",
              "       [3382512.31],\n",
              "       [3407811.26],\n",
              "       [3430803.5 ],\n",
              "       [3434525.83],\n",
              "       [3435249.75]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WV-xKRjemBe-"
      },
      "source": [
        "### Cumulative percentage contribution"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KzIcIhtamBfA",
        "outputId": "9983bfb5-39c8-4379-a312-d4f27b462699"
      },
      "source": [
        "np.round(np.cumsum(eigen_values)/np.sum(eigen_values),2)"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.88, 0.96, 0.98, 0.99, 1.  , 1.  , 1.  ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "voOyp4DmmBfJ"
      },
      "source": [
        "### RESS (Refer to the paper for a description)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jpyTu108mBfK",
        "outputId": "a9153af2-9114-418c-a684-53284b6775c8"
      },
      "source": [
        "RESS = np.repeat(np.nan, 7)\n",
        "for i in range(7):\n",
        "    RESS[i] = np.sum(eigen_values) - np.sum(eigen_values[:i+1])\n",
        "np.round(RESS.reshape(7,1),2)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[412108.51],\n",
              "       [121532.68],\n",
              "       [ 52737.44],\n",
              "       [ 27438.49],\n",
              "       [  4446.25],\n",
              "       [   723.92],\n",
              "       [     0.  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "enWIk1jKmBfR"
      },
      "source": [
        "### Ration of RESS and sum of eigenvalues"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C_aTkelfmBfU",
        "outputId": "adff3951-b2d2-4e3c-bd3f-0f9f97901a81"
      },
      "source": [
        "np.round(RESS/np.sum(eigen_values),2)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.12, 0.04, 0.02, 0.01, 0.  , 0.  , 0.  ])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "38OhZ-FTmBfb"
      },
      "source": [
        "We will not calculate the value of PRESS in this post as it requires us to consider random models. We will not pursue that here. Comments regarding any errors or omissions may be sent to the author's email."
      ]
    }
  ]
}