pca_scree/PCA_+_Scree_Chart_Function_Notebook.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "PCA + Scree Chart Function Notebook.ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "lEsil8VidxE3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-RB2w2a4d0j2",
        "colab_type": "code",
        "outputId": "c2215433-e70f-48e5-e8e5-8f4cccebd68f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 254
        }
      },
      "source": [
        "url = \"https://raw.githubusercontent.com/ryanleeallred/datasets/master/Cancer_Cells.csv\"\n",
        "df = pd.read_csv(url).drop(columns=['Unnamed: 32'])\n",
        "print(df.shape)\n",
        "df.head()"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(569, 32)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
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              "    .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>id</th>\n",
              "      <th>diagnosis</th>\n",
              "      <th>radius_mean</th>\n",
              "      <th>texture_mean</th>\n",
              "      <th>perimeter_mean</th>\n",
              "      <th>area_mean</th>\n",
              "      <th>smoothness_mean</th>\n",
              "      <th>compactness_mean</th>\n",
              "      <th>concavity_mean</th>\n",
              "      <th>concave points_mean</th>\n",
              "      <th>symmetry_mean</th>\n",
              "      <th>fractal_dimension_mean</th>\n",
              "      <th>radius_se</th>\n",
              "      <th>texture_se</th>\n",
              "      <th>perimeter_se</th>\n",
              "      <th>area_se</th>\n",
              "      <th>smoothness_se</th>\n",
              "      <th>compactness_se</th>\n",
              "      <th>concavity_se</th>\n",
              "      <th>concave points_se</th>\n",
              "      <th>symmetry_se</th>\n",
              "      <th>fractal_dimension_se</th>\n",
              "      <th>radius_worst</th>\n",
              "      <th>texture_worst</th>\n",
              "      <th>perimeter_worst</th>\n",
              "      <th>area_worst</th>\n",
              "      <th>smoothness_worst</th>\n",
              "      <th>compactness_worst</th>\n",
              "      <th>concavity_worst</th>\n",
              "      <th>concave points_worst</th>\n",
              "      <th>symmetry_worst</th>\n",
              "      <th>fractal_dimension_worst</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>842302</td>\n",
              "      <td>M</td>\n",
              "      <td>17.99</td>\n",
              "      <td>10.38</td>\n",
              "      <td>122.80</td>\n",
              "      <td>1001.0</td>\n",
              "      <td>0.11840</td>\n",
              "      <td>0.27760</td>\n",
              "      <td>0.3001</td>\n",
              "      <td>0.14710</td>\n",
              "      <td>0.2419</td>\n",
              "      <td>0.07871</td>\n",
              "      <td>1.0950</td>\n",
              "      <td>0.9053</td>\n",
              "      <td>8.589</td>\n",
              "      <td>153.40</td>\n",
              "      <td>0.006399</td>\n",
              "      <td>0.04904</td>\n",
              "      <td>0.05373</td>\n",
              "      <td>0.01587</td>\n",
              "      <td>0.03003</td>\n",
              "      <td>0.006193</td>\n",
              "      <td>25.38</td>\n",
              "      <td>17.33</td>\n",
              "      <td>184.60</td>\n",
              "      <td>2019.0</td>\n",
              "      <td>0.1622</td>\n",
              "      <td>0.6656</td>\n",
              "      <td>0.7119</td>\n",
              "      <td>0.2654</td>\n",
              "      <td>0.4601</td>\n",
              "      <td>0.11890</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>842517</td>\n",
              "      <td>M</td>\n",
              "      <td>20.57</td>\n",
              "      <td>17.77</td>\n",
              "      <td>132.90</td>\n",
              "      <td>1326.0</td>\n",
              "      <td>0.08474</td>\n",
              "      <td>0.07864</td>\n",
              "      <td>0.0869</td>\n",
              "      <td>0.07017</td>\n",
              "      <td>0.1812</td>\n",
              "      <td>0.05667</td>\n",
              "      <td>0.5435</td>\n",
              "      <td>0.7339</td>\n",
              "      <td>3.398</td>\n",
              "      <td>74.08</td>\n",
              "      <td>0.005225</td>\n",
              "      <td>0.01308</td>\n",
              "      <td>0.01860</td>\n",
              "      <td>0.01340</td>\n",
              "      <td>0.01389</td>\n",
              "      <td>0.003532</td>\n",
              "      <td>24.99</td>\n",
              "      <td>23.41</td>\n",
              "      <td>158.80</td>\n",
              "      <td>1956.0</td>\n",
              "      <td>0.1238</td>\n",
              "      <td>0.1866</td>\n",
              "      <td>0.2416</td>\n",
              "      <td>0.1860</td>\n",
              "      <td>0.2750</td>\n",
              "      <td>0.08902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>84300903</td>\n",
              "      <td>M</td>\n",
              "      <td>19.69</td>\n",
              "      <td>21.25</td>\n",
              "      <td>130.00</td>\n",
              "      <td>1203.0</td>\n",
              "      <td>0.10960</td>\n",
              "      <td>0.15990</td>\n",
              "      <td>0.1974</td>\n",
              "      <td>0.12790</td>\n",
              "      <td>0.2069</td>\n",
              "      <td>0.05999</td>\n",
              "      <td>0.7456</td>\n",
              "      <td>0.7869</td>\n",
              "      <td>4.585</td>\n",
              "      <td>94.03</td>\n",
              "      <td>0.006150</td>\n",
              "      <td>0.04006</td>\n",
              "      <td>0.03832</td>\n",
              "      <td>0.02058</td>\n",
              "      <td>0.02250</td>\n",
              "      <td>0.004571</td>\n",
              "      <td>23.57</td>\n",
              "      <td>25.53</td>\n",
              "      <td>152.50</td>\n",
              "      <td>1709.0</td>\n",
              "      <td>0.1444</td>\n",
              "      <td>0.4245</td>\n",
              "      <td>0.4504</td>\n",
              "      <td>0.2430</td>\n",
              "      <td>0.3613</td>\n",
              "      <td>0.08758</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>84348301</td>\n",
              "      <td>M</td>\n",
              "      <td>11.42</td>\n",
              "      <td>20.38</td>\n",
              "      <td>77.58</td>\n",
              "      <td>386.1</td>\n",
              "      <td>0.14250</td>\n",
              "      <td>0.28390</td>\n",
              "      <td>0.2414</td>\n",
              "      <td>0.10520</td>\n",
              "      <td>0.2597</td>\n",
              "      <td>0.09744</td>\n",
              "      <td>0.4956</td>\n",
              "      <td>1.1560</td>\n",
              "      <td>3.445</td>\n",
              "      <td>27.23</td>\n",
              "      <td>0.009110</td>\n",
              "      <td>0.07458</td>\n",
              "      <td>0.05661</td>\n",
              "      <td>0.01867</td>\n",
              "      <td>0.05963</td>\n",
              "      <td>0.009208</td>\n",
              "      <td>14.91</td>\n",
              "      <td>26.50</td>\n",
              "      <td>98.87</td>\n",
              "      <td>567.7</td>\n",
              "      <td>0.2098</td>\n",
              "      <td>0.8663</td>\n",
              "      <td>0.6869</td>\n",
              "      <td>0.2575</td>\n",
              "      <td>0.6638</td>\n",
              "      <td>0.17300</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84358402</td>\n",
              "      <td>M</td>\n",
              "      <td>20.29</td>\n",
              "      <td>14.34</td>\n",
              "      <td>135.10</td>\n",
              "      <td>1297.0</td>\n",
              "      <td>0.10030</td>\n",
              "      <td>0.13280</td>\n",
              "      <td>0.1980</td>\n",
              "      <td>0.10430</td>\n",
              "      <td>0.1809</td>\n",
              "      <td>0.05883</td>\n",
              "      <td>0.7572</td>\n",
              "      <td>0.7813</td>\n",
              "      <td>5.438</td>\n",
              "      <td>94.44</td>\n",
              "      <td>0.011490</td>\n",
              "      <td>0.02461</td>\n",
              "      <td>0.05688</td>\n",
              "      <td>0.01885</td>\n",
              "      <td>0.01756</td>\n",
              "      <td>0.005115</td>\n",
              "      <td>22.54</td>\n",
              "      <td>16.67</td>\n",
              "      <td>152.20</td>\n",
              "      <td>1575.0</td>\n",
              "      <td>0.1374</td>\n",
              "      <td>0.2050</td>\n",
              "      <td>0.4000</td>\n",
              "      <td>0.1625</td>\n",
              "      <td>0.2364</td>\n",
              "      <td>0.07678</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         id diagnosis  ...  symmetry_worst  fractal_dimension_worst\n",
              "0    842302         M  ...          0.4601                  0.11890\n",
              "1    842517         M  ...          0.2750                  0.08902\n",
              "2  84300903         M  ...          0.3613                  0.08758\n",
              "3  84348301         M  ...          0.6638                  0.17300\n",
              "4  84358402         M  ...          0.2364                  0.07678\n",
              "\n",
              "[5 rows x 32 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "acZKwwDo5qyC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 617
        },
        "outputId": "5190a3b9-46f8-48db-b84a-6e5bce5b601a"
      },
      "source": [
        "df.dtypes"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "id                           int64\n",
              "diagnosis                   object\n",
              "radius_mean                float64\n",
              "texture_mean               float64\n",
              "perimeter_mean             float64\n",
              "area_mean                  float64\n",
              "smoothness_mean            float64\n",
              "compactness_mean           float64\n",
              "concavity_mean             float64\n",
              "concave points_mean        float64\n",
              "symmetry_mean              float64\n",
              "fractal_dimension_mean     float64\n",
              "radius_se                  float64\n",
              "texture_se                 float64\n",
              "perimeter_se               float64\n",
              "area_se                    float64\n",
              "smoothness_se              float64\n",
              "compactness_se             float64\n",
              "concavity_se               float64\n",
              "concave points_se          float64\n",
              "symmetry_se                float64\n",
              "fractal_dimension_se       float64\n",
              "radius_worst               float64\n",
              "texture_worst              float64\n",
              "perimeter_worst            float64\n",
              "area_worst                 float64\n",
              "smoothness_worst           float64\n",
              "compactness_worst          float64\n",
              "concavity_worst            float64\n",
              "concave points_worst       float64\n",
              "symmetry_worst             float64\n",
              "fractal_dimension_worst    float64\n",
              "dtype: object"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q2DMiXegeCli",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def pca_function(df, threshold, show_scree_plot=True, \n",
        "                 scaled=False, excluded_cols=None):\n",
        "  '''\n",
        "  Takes a pandas dataframe and a desired threshold, scales the numeric features \n",
        "  and performs principal component analysis dimension reduction, and returns\n",
        "  a pandas dataframe of lower dimensionality and variance explained to the given\n",
        "  threshold\n",
        "    \n",
        "  Parameters\n",
        "  ----------\n",
        "  df : pandas dataframe\n",
        "      The dataframe containing data to perform PCA on\n",
        "      \n",
        "  threshold : The desired % of variance explained to be included in the return;\n",
        "              must be an number between 0 and 100\n",
        "  \n",
        "  show_scree_plot : Bool indicating whether or not to display scree plot showing \n",
        "                    the % variance explained by each principal component; \n",
        "                    default set to True\n",
        "  \n",
        "  scaled : Bool indicating whether the numeric data has been scaled; default set \n",
        "           to False\n",
        "  \n",
        "  exclude_cols : list of numeric columns to exclude from PCA; default set to None\n",
        "\n",
        "  Returns\n",
        "  -------\n",
        "  dataframe:\n",
        "      a pandas dataframe where the numeric columns have been scaled and \n",
        "      dimensions reduced to the number of principal components which explain\n",
        "      the variance at a given threshold\n",
        "  '''\n",
        "  \n",
        "  #confirm proper threshold input:\n",
        "  if threshold < 0 or threshold > 100:\n",
        "    return 'Incorrect threshold input, must be a number between 0 and 100'\n",
        "  \n",
        "  #library imports\n",
        "  from sklearn.decomposition import PCA \n",
        "  from sklearn.preprocessing import StandardScaler \n",
        "  import seaborn as sns\n",
        "  \n",
        "  X = df.copy()\n",
        "  \n",
        "  if excluded_cols != None:\n",
        "    X = X.drop(columns=excluded_cols)\n",
        "    \n",
        "  #use only the numeric columns that have not been excluded\n",
        "  numeric_cols = X.select_dtypes(include='number').columns.tolist()\n",
        "  X = X[numeric_cols].values\n",
        "  \n",
        "  if scaled == False:\n",
        "    #scale the data:\n",
        "    scaler = StandardScaler()\n",
        "    scaled_X = scaler.fit_transform(X)\n",
        "  else:\n",
        "    scaled_X = X\n",
        "    \n",
        "  #calc the principal component variance\n",
        "  n = len(numeric_cols)\n",
        "  covar_matrix = PCA(n_components = n)\n",
        "  covar_matrix.fit(scaled_X)\n",
        "  \n",
        "  ##calculate variance ratios\n",
        "  variance = covar_matrix.explained_variance_ratio_\n",
        "  cumulative_var = np.cumsum(np.round(covar_matrix.explained_variance_ratio_, decimals=3)*100)\n",
        "     \n",
        "  #function for calculating number of principal components to use:\n",
        "  def calc_num_components(cum_var, threshold):\n",
        "    for i in range(n):\n",
        "      if cum_var[i] >= threshold:\n",
        "        return i+1\n",
        "  \n",
        "  #call the function to calulate num_components:\n",
        "  n_components = calc_num_components(cumulative_var, threshold)\n",
        "  \n",
        "  # create the PCA instance\n",
        "  pca = PCA(n_components = n_components)\n",
        "  principal_components = pca.fit_transform(scaled_X)\n",
        "\n",
        "  #scree plot function\n",
        "  '''\n",
        "  colors = ['red' if x == n_components else 'grey' for x in X_vals]\n",
        "  sb.barplot(x=idx, y=values, palette=colors)'''\n",
        "\n",
        "  def make_scree(cumulative_variance, threshold):\n",
        "    import matplotlib.pyplot as plt\n",
        "    import seaborn as sns\n",
        "  \n",
        "    n = len(cumulative_variance)\n",
        "    y_vals = [num for num in cumulative_variance]\n",
        "    x_vals = [num for num in range(1,n+1)]\n",
        "    \n",
        "    colors = ['red' if x == n_components else '#769ddb' for x in x_vals]\n",
        "    width = min(n/3, 20)\n",
        "    height = min(n/4, 16)\n",
        "    fig, ax = plt.subplots(figsize=(width,height))\n",
        "    ax.grid(True)\n",
        "    ax.set_title('Principal Components Cumulative Variance')\n",
        "    ax.set_ylabel('Cumulative Variance % Explained')\n",
        "    ax.set_xlabel('Principal Components')\n",
        "  \n",
        "    # threshold var\n",
        "    ax.axhline(threshold, color='black', linewidth=1);\n",
        "    sns.barplot(x=x_vals, y=y_vals, ax=ax, palette=colors)\n",
        "    plt.show()\n",
        "  \n",
        "  if show_scree_plot:\n",
        "    #plot it:\n",
        "    make_scree(cumulative_var, threshold)\n",
        " \n",
        "  #convert to pandas df:\n",
        "  pc_df = pd.DataFrame(data = principal_components, \n",
        "                       columns = ['component_' + str(i) for i in range(1, n_components+1)])\n",
        "  \n",
        "  #return df which is original df w/ the numeric cols dropped and replaced w/\n",
        "  #principal components df\n",
        "  \n",
        "  df = pd.concat([df, pc_df], axis=1).drop(columns = numeric_cols)\n",
        "  return df"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7A0yhnOEhoyV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 486
        },
        "outputId": "a3a83455-a5a4-4078-d962-9c41f20f3b23"
      },
      "source": [
        "pca_df = pca_function(df, 90, show_scree_plot=True, excluded_cols=['id'])"
      ],
      "execution_count": 43,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RJ8lQ23taU5IkqUMsziRJkjrE4kySJKlD1ugxZ1o6CzkeQJIk/Yk9Z5IkSR1icSZJktQh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\nR6x5tfW5cppnO58t1rzb+oB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            "text/plain": [
              "<Figure size 720x540 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c8QxK9N9tmvc",
        "colab_type": "code",
        "outputId": "70d0a95d-0585-47cc-f637-00a77086e85d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 216
        }
      },
      "source": [
        "print(pca_df.shape)\n",
        "pca_df.head()"
      ],
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(569, 9)\n"
          ],
          "name": "stdout"
        },
        {
          "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>id</th>\n",
              "      <th>diagnosis</th>\n",
              "      <th>component_1</th>\n",
              "      <th>component_2</th>\n",
              "      <th>component_3</th>\n",
              "      <th>component_4</th>\n",
              "      <th>component_5</th>\n",
              "      <th>component_6</th>\n",
              "      <th>component_7</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>842302</td>\n",
              "      <td>M</td>\n",
              "      <td>9.192837</td>\n",
              "      <td>1.948583</td>\n",
              "      <td>-1.123166</td>\n",
              "      <td>3.633732</td>\n",
              "      <td>-1.195108</td>\n",
              "      <td>1.411435</td>\n",
              "      <td>2.159317</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>842517</td>\n",
              "      <td>M</td>\n",
              "      <td>2.387802</td>\n",
              "      <td>-3.768172</td>\n",
              "      <td>-0.529293</td>\n",
              "      <td>1.118263</td>\n",
              "      <td>0.621774</td>\n",
              "      <td>0.028651</td>\n",
              "      <td>0.013379</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>84300903</td>\n",
              "      <td>M</td>\n",
              "      <td>5.733896</td>\n",
              "      <td>-1.075174</td>\n",
              "      <td>-0.551748</td>\n",
              "      <td>0.912083</td>\n",
              "      <td>-0.177086</td>\n",
              "      <td>0.541454</td>\n",
              "      <td>-0.668177</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>84348301</td>\n",
              "      <td>M</td>\n",
              "      <td>7.122953</td>\n",
              "      <td>10.275589</td>\n",
              "      <td>-3.232790</td>\n",
              "      <td>0.152547</td>\n",
              "      <td>-2.960878</td>\n",
              "      <td>3.053421</td>\n",
              "      <td>1.429915</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84358402</td>\n",
              "      <td>M</td>\n",
              "      <td>3.935302</td>\n",
              "      <td>-1.948072</td>\n",
              "      <td>1.389767</td>\n",
              "      <td>2.940639</td>\n",
              "      <td>0.546747</td>\n",
              "      <td>-1.226500</td>\n",
              "      <td>-0.936181</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         id diagnosis  component_1  ...  component_5  component_6  component_7\n",
              "0    842302         M     9.192837  ...    -1.195108     1.411435     2.159317\n",
              "1    842517         M     2.387802  ...     0.621774     0.028651     0.013379\n",
              "2  84300903         M     5.733896  ...    -0.177086     0.541454    -0.668177\n",
              "3  84348301         M     7.122953  ...    -2.960878     3.053421     1.429915\n",
              "4  84358402         M     3.935302  ...     0.546747    -1.226500    -0.936181\n",
              "\n",
              "[5 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 44
        }
      ]
    }
  ]
}