PCA_Project.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyPuiHJUCn5l3vxChfT/ivag",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/frm1789/100DaysOfPython/blob/main/PCA_Project.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# PCA Application"
      ],
      "metadata": {
        "id": "ibApCPN8XXEr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "* Grasp the fundamental linear algebra techniques which are used to compute PCA.\n",
        "* Utilize NumPy to transition your newly gained mathematical knowledge into code.\n",
        "* Apply scikit-learn’s PCA and learn about its nuances while using it.\n",
        "* Understand the benefits of dimensionality reduction and the trade-off between speed and accuracy.\n"
      ],
      "metadata": {
        "id": "1Rb0nuDIXaEB"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Project outline"
      ],
      "metadata": {
        "id": "qj2tpJreXuhN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This project is divided into 3 milestones.\n",
        "\n",
        "1. Computing eigenvalues and eigenvectors\n",
        "Estimated duration: 1-2 hours\n",
        "\n",
        "2. Implementation of PCA and Logistic Regression\n",
        "Estimated duration: 1.5 -2 hours\n",
        "\n",
        "3. Plot, analyze, and compare results\n",
        "Estimated duration: 3.5-4 hours"
      ],
      "metadata": {
        "id": "BLCx_oIlXwhN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Part I: Milestone"
      ],
      "metadata": {
        "id": "iXXq7Kz2WWGe"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "This `Jupyter Notebook` is the starter notebook for the second milestone of the project <b>Principal Component Analysis</b>. It consists of the following tasks:\n",
        "\n",
        "- Implementation of the covariance matrix and eigendecomposition in the custom PCA class.\n",
        "- Prepare data for training: train/test-split and normalization of the dataset.\n",
        "- Implement logistic regression with [sklearn](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LogisticRegression.html?highlight=logistic%20regression#sklearn.linear_model.LogisticRegression) and validate its accuracy."
      ],
      "metadata": {
        "id": "0E32JgLtWXbM"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "ktqYDr4WTjhm"
      },
      "outputs": [],
      "source": [
        "# standard imports\n",
        "import numpy as np\n",
        "\n",
        "\n",
        "# sklearn\n",
        "import sklearn\n",
        "from sklearn.decomposition import PCA\n",
        "from sklearn.datasets import fetch_openml\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "\n",
        "# other useful imports\n",
        "from importlib import reload\n",
        "from time import time\n",
        "\n",
        "\n",
        "# imports for plotting\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "#ignore warnings\n",
        "import warnings\n",
        "warnings.filterwarnings(action='ignore')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# change data_home path where you wnat to store the data\n",
        "# important: as_frame needs to be set as False otherwise we would get a data frame\n",
        "# and would have to convert the dataset to numpy arrays later on\n",
        "mnist = fetch_openml('mnist_784', data_home='data/', as_frame=False)"
      ],
      "metadata": {
        "id": "u_8TdHh9azzn"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# the dataset is split into the images and the labels\n",
        "# we expect values between 0 and 255 for images\n",
        "print('Images shape: ', mnist.data.shape)\n",
        "print('Images range: ', mnist.data.min(), ' - ', mnist.data.max(), 'pixel')\n",
        "print('Labels shape: ', mnist.target.shape)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NY_JyunZbQCj",
        "outputId": "0b3ccde7-8412-4eb6-a858-de55caf4188e"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Images shape:  (70000, 784)\n",
            "Images range:  0.0  -  255.0 pixel\n",
            "Labels shape:  (70000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_train, x_test, y_train, y_test = train_test_split(\n",
        "    mnist.data, mnist.target, test_size=1/7.0, random_state=0)"
      ],
      "metadata": {
        "id": "lY1b0KRabYGF"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "# check the split\n",
        "print('x_train: ' + str(x_train.shape))\n",
        "print('y_train: ' + str(y_train.shape))\n",
        "print('x_test:  '  + str(x_test.shape))\n",
        "print('y_test:  '  + str(y_test.shape))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q8VEvT6mbdnC",
        "outputId": "07b82692-6948-4bd0-f6c1-35c9f7f6e0e7"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "x_train: (60000, 784)\n",
            "y_train: (60000,)\n",
            "x_test:  (10000, 784)\n",
            "y_test:  (10000,)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        " from\n",
        " https://stackoverflow.com/questions/42353676/display-mnist-image-using-matplotlib"
      ],
      "metadata": {
        "id": "zWqHLJDlcpcG"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def gen_image(arr):\n",
        "    two_d = (np.reshape(arr, (28, 28)) * 255).astype(np.uint8)\n",
        "    plt.imshow(two_d, interpolation='nearest')\n",
        "    return plt\n",
        "\n",
        "# Get a batch of two random images and show in a pop-up window.\n",
        "gen_image(x_train[0]).show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "Oji0b6MiboBh",
        "outputId": "3330da39-c532-49e0-d5b2-0e350103e487"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_train[0])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qyGMmHhNc-DA",
        "outputId": "d8cf4233-60cc-420c-b08f-f53c78a32be3"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[  0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.  40. 195. 126.   6.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.  52. 222. 254. 254. 203.  77.   5.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0. 111. 254. 254. 254. 254. 254. 205.  65.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0. 111. 254. 247.  86. 127. 222. 254. 242. 201.\n",
            "  79.  21.  66. 159.  62.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.  39. 228. 254. 254.  94.  58. 186. 254. 254.\n",
            " 254. 254. 254. 254. 129.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.  16. 104.  94.  22.   0.   4.  25. 142.\n",
            " 224. 231. 254. 254. 129.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  17. 226. 254. 129.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  48. 246. 254. 129.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  47. 245. 254. 129.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0. 116.  92.\n",
            "  90.  99. 254. 254. 154.  15.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.  16. 215. 254.\n",
            " 254. 254. 254. 254. 254. 220. 205. 166.   4.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0. 113.\n",
            " 195. 254. 254. 254. 254. 254. 209.  24.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   1. 175. 254. 254. 104.  40.  19.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0. 132. 254. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0. 100. 254. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  61. 254. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  61. 254. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  61. 254. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.  26. 232. 254.  30.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0. 176. 160.   7.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.\n",
            "   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.   0.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Normalize the data \n",
        "By dividing by 255"
      ],
      "metadata": {
        "id": "0YDTVrANdHnS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### How to NOT normalize a dataset?"
      ],
      "metadata": {
        "id": "-gl8YEuCjabg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x_train  = np.array(x_train)/255\n",
        "x_test = np.array(x_test)/255"
      ],
      "metadata": {
        "id": "6qR_DoMMdLSn"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_train[:,10])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G5X8DMvwjhE5",
        "outputId": "61e2d31a-7f49-4217-840a-b98c1c5a6f7b"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0. 0. 0. ... 0. 0. 0.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = (x_train - x_train.min())/(x_train.max() - x_train.min()) \n",
        "x_test = (x_test - x_train.min())/(x_train.max() - x_train.min())  "
      ],
      "metadata": {
        "id": "t5JS_A1zjeBE"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_train[:,10])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "gvASYBzTjkIp",
        "outputId": "0e279c96-1631-43ac-fbbc-ed5c54f1f81a"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0. 0. 0. ... 0. 0. 0.]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Implement LG \n",
        "\n",
        "From scikit learn to classify images without any modification via PCA and evaluation accuracy."
      ],
      "metadata": {
        "id": "ppBLsB1_dh35"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "start = time()\n",
        "\n",
        "lreg = LogisticRegression(solver='lbfgs')\n",
        "lreg.fit(x_train, y_train)\n",
        "pred_train = lreg.predict(x_train)\n",
        "pred_test = lreg.predict(x_test)\n"
      ],
      "metadata": {
        "id": "-d_776_cdhdF"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy = accuracy_score(y_train, pred_train)\n",
        "print(\"Accuracy on test set: \", accuracy)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QhoNrJUWkeuh",
        "outputId": "d52656f8-fa25-4138-cf71-c2b040f6e698"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set:  0.9363166666666667\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "accuracy = accuracy_score(y_test, pred_test)\n",
        "print(\"Accuracy on test set: \", accuracy)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QoBJGgHUkMX4",
        "outputId": "84237a81-d8d3-4f24-ca41-ae7b0eb4ca25"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy on test set:  0.9196\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "end = time()\n",
        "\n",
        "running_time = end-start\n",
        "print('Time to fit: {}s'.format(running_time))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Q9mgPrzfh1DZ",
        "outputId": "5409f9f3-8526-4ccf-ed18-f24e8cc7da17"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time to fit: 45.71583271026611s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Part II: Milestone"
      ],
      "metadata": {
        "id": "EpcxXk8WlDUA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "It consists of the following tasks:\n",
        "\n",
        "- Use sklearn's `explained_variance_ratio_`to determine the number of components needed for a given threshold.\n",
        "- Use the `explained_variance_ratio_` function to plot the cumulative explained variance ratio.\n",
        "\n",
        "- Use the `variance_explained` function to plot the first digit of the dataset with different thresholds.\n",
        "- Compare the running time of the logistic regression with and without PCA.\n",
        "- Compare the accuracy between the prediction with and without PCA. "
      ],
      "metadata": {
        "id": "NOVFiAJMldQE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mnist = fetch_openml('mnist_784', data_home='data/', as_frame=False)"
      ],
      "metadata": {
        "id": "EWX1NAgBoxi_"
      },
      "execution_count": 16,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_train, x_test, y_train, y_test = train_test_split(\n",
        "    mnist.data, mnist.target, train_size= 0.8, test_size=0.2, random_state=0)"
      ],
      "metadata": {
        "id": "X99NRoaNqCg1"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_train = (x_train - x_train.min())/(x_train.max() - x_train.min()) \n",
        "x_test = (x_test - x_train.min())/(x_train.max() - x_train.min()) "
      ],
      "metadata": {
        "id": "fyUDWoCTqI9o"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(mnist.data.max()) \n",
        "print(mnist.data.min())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2wKxyDuIqLpU",
        "outputId": "c53b9104-4b2f-494f-bfd2-e3936660b3e7"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "255.0\n",
            "0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_train.max()) \n",
        "print(x_train.min())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "x9lkD_oaqaJx",
        "outputId": "30dc1b8a-196e-442c-8615-25524fb79765"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n",
            "0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(x_test.max()) \n",
        "print(x_test.min())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fuDyhTAYqirE",
        "outputId": "883f0216-0cd2-408b-ba5e-c58615ee16b0"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "255.0\n",
            "0.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "start = time()\n",
        "#‘lbfgs’ solver handles multinomial loss in multiclass problems \n",
        "log_normal = LogisticRegression(solver='lbfgs').fit(x_train, y_train)\n",
        "end = time()\n",
        "\n",
        "time_log_normal = end-start\n",
        "print('Time to fit: {}s'.format(time_log_normal))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GyISpw54q-Zt",
        "outputId": "899d22f7-9b5f-4215-b556-1e23f5167278"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time to fit: 40.95360732078552s\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_pred_train = log_normal.predict(x_train)\n",
        "y_pred_test = log_normal.predict(x_test)\n"
      ],
      "metadata": {
        "id": "e1BOItKrryXW"
      },
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "log_normal_score_train = accuracy_score(y_train, y_pred_train)\n",
        "log_normal_score_test = accuracy_score(y_test, y_pred_test)"
      ],
      "metadata": {
        "id": "0SE3pgFBsDvU"
      },
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Evaluation\n",
        "print('Training Set Score: {}'.format(log_normal_score_train.round(4)))\n",
        "print('Test Set Score: {}'.format(log_normal_score_test.round(4)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JAZ1jex2r_VV",
        "outputId": "c11be4c8-8907-4cad-f638-ae3a954f209b"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training Set Score: 0.9369\n",
            "Test Set Score: 0.8604\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pca = PCA(n_components=100) \n",
        "pca.fit(x_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 75
        },
        "id": "XbtkmHb6sOGx",
        "outputId": "cf6469e4-6d5d-47fe-f48a-2db83d80251b"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(n_components=100)"
            ],
            "text/html": [
              "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PCA(n_components=100)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">PCA</label><div class=\"sk-toggleable__content\"><pre>PCA(n_components=100)</pre></div></div></div></div></div>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#### Determining the number of Principal Components"
      ],
      "metadata": {
        "id": "PWQN2kzqsVEc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Sklearn provides a function where we can access the [percentage of variance explained](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html) by each of the selected components. We can use this to calculate the number of components we will have for instanace for having an explained variance of 90%. "
      ],
      "metadata": {
        "id": "Ekj2xrTbtAcu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "-  **np.cumsum en NumPy** se utiliza para calcular la suma acumulativa de los elementos de un array. \n",
        "- **pca.explained_variance_ratio_**, que es un array que contiene las proporciones de varianza explicada por cada componente principal en PCA\n"
      ],
      "metadata": {
        "id": "ChNlw76CtmV-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "cum_sum = np.cumsum(pca.explained_variance_ratio_)"
      ],
      "metadata": {
        "id": "kAo-t4DCtGvs"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Create a bar plot\n",
        "n_components = len(pca.explained_variance_ratio_)\n",
        "components = np.arange(1, n_components + 1)\n",
        "plt.bar(components, pca.explained_variance_ratio_)\n",
        "plt.xlabel('Component')\n",
        "plt.ylabel('Explained Variance Ratio')\n",
        "plt.title('Explained Variance Ratio by Component')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "iS7oSE_luxSF",
        "outputId": "612aada8-2200-4e73-a1d1-02400bbd6e68"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "threshold=0.90 # set the threshold to desired amount\n",
        "r = [np.argmax(cum_sum > threshold) + 1][0] # get the number of ideal r\n",
        "PC = (cum_sum[r-1]) # get the value of the optimal PC\n",
        "print('The smallest number of PCs retaining {}% of variance is reached with {} components'.format(threshold,r))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bE1-i6J_uF6L",
        "outputId": "28b2d7f2-3849-4d65-d12a-2f2c7b1a0e32"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The smallest number of PCs retaining 0.9% of variance is reached with 87 components\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def variance_explained_plot(ratio):\n",
        "    fig, ax = plt.subplots(figsize=(10, 7))\n",
        "    ax.plot(range(1, len(ratio) + 1), np.cumsum(ratio), color='r', label='Cumulative Explained Variance Ratio')\n",
        "    ax.axhline(y=0.95, color='k', linestyle='--', label='95% Explained Variance')\n",
        "    ax.axhline(y=0.90, color='c', linestyle='--', label='90% Explained Variance')\n",
        "    ax.axhline(y=0.85, color='grey', linestyle='--', label='85% Explained Variance')\n",
        "    ax.set_title('Cumulative Sum of Explained Variance Ratio PCA', fontsize=20)\n",
        "    ax.set_ylabel('Cumulative Sum of Explained Variance Ratio', fontsize=14)\n",
        "    ax.set_xlabel('Number of Components', fontsize=14)\n",
        "    plt.legend(loc=0);"
      ],
      "metadata": {
        "id": "TFwommJWR8Xu"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ratio = pca.explained_variance_ratio_\n",
        "variance_explained_plot(ratio)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 654
        },
        "id": "oKbcag0pSBjH",
        "outputId": "108a5ee8-c8c4-4c47-b4d3-041b99e2e8f2"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "HdwscRWZ9wvv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def variance_explained(percent, images): \n",
        "    # percent of variance | float from 0 to 1 \n",
        "    pca = PCA(percent) # Instance of PCA object\n",
        "    pca.fit(images)    # Adjust the PCA model to the images.\n",
        "    components = pca.transform(images)              # Transform original images to PCA \n",
        "    approx = pca.inverse_transform(components)      \n",
        "    return approx"
      ],
      "metadata": {
        "id": "l2hI-AI8UQZJ"
      },
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Use the `variance_explained` function, which is provided for you above to plot the first digit of the MNIST training dataset and the different thresholds:\n",
        "- Orignal image (784 components)\n",
        "- 95% of explained variance\n",
        "- 90% of explained variance\n",
        "- 85% of explained variance\n",
        "\n",
        "You can use the `show_images` function from milestone 2, which can be found here: `customlib/plotting.py` as an example how to plot images."
      ],
      "metadata": {
        "id": "v-3U6L6YUoqM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.rcParams['axes.grid'] = False # don't use grid for image plots"
      ],
      "metadata": {
        "id": "_LFhLr_bU7MI"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def explained_variance_plot(x_train):\n",
        "    \n",
        "    ranges = [2, 3, 4] # ranges for subplots\n",
        "    percentages = [0.95, 0.90, 0.85] # diffrent percentages\n",
        "    components_ = [154, 87, 59] # number of different components\n",
        "    \n",
        "    \n",
        "    # plot first original image, with no PCA used\n",
        "    plt.subplot(1, 4, 1);\n",
        "    plt.imshow(x_train[0].reshape(28,28),\n",
        "                  cmap = plt.cm.binary_r);\n",
        "    plt.xlabel('784 Components', fontsize = 8)\n",
        "    plt.title('Original Image', fontsize = 8);\n",
        "    \n",
        "    "
      ],
      "metadata": {
        "id": "Z_nOtveuU7wd"
      },
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "explained_variance_plot(x_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "67NzOpg0VCUF",
        "outputId": "ace5b0e6-f290-4c0d-b958-d440f7f54d39"
      },
      "execution_count": 44,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def explained_variance_plot(x_train):\n",
        "    \n",
        "    ranges = [2, 3, 4] # ranges for subplots\n",
        "    percentages = [0.95, 0.90, 0.85] # diffrent percentages\n",
        "    components_ = [154, 87, 59] # number of different components\n",
        "    \n",
        "    \n",
        "    # plot first original image, with no PCA used\n",
        "    plt.subplot(1, 4, 1); #row #columns # position of the plot that I am creating.\n",
        "    plt.imshow(x_train[0].reshape(28,28),\n",
        "                  cmap = plt.cm.viridis); # paleta de colores: cmap = plt.cm.binary_r\n",
        "    plt.xlabel('784 Components', fontsize = 8)\n",
        "    plt.title('Original Image', fontsize = 8);\n",
        "\n",
        "\n",
        "# loop over the subplots\n",
        "    for range_, percent, components in zip(ranges, percentages, components_):\n",
        "        plt.subplot(1, 4, range_);\n",
        "        plt.imshow(variance_explained(percent, x_train)[0].reshape(28, 28),\n",
        "              cmap = plt.cm.viridis);\n",
        "        plt.xlabel('{} Components'.format(components), fontsize = 8)\n",
        "        plt.title('{}% of Explained Variance'.format(percent), fontsize = 8);"
      ],
      "metadata": {
        "id": "FkJEHi6372wL"
      },
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "explained_variance_plot(x_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        },
        "id": "nvcq2Zv79Z0O",
        "outputId": "87aa510e-f8a6-40b5-b825-2a11d51a932e"
      },
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 4 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "89_DoHJFBzRg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Compare the running time of the logistic regression with and without PCA."
      ],
      "metadata": {
        "id": "xqx_yEBDB_9t"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "start = time()\n",
        "pca = PCA(0.9).fit(x_train)\n",
        "\n",
        "x_train_pca = pca.transform(x_train)\n",
        "x_test_pca = pca.transform(x_test)\n",
        "\n",
        "end = time()\n",
        "time_pca = end-start\n",
        "\n",
        "#print(x_train_pca.shape, x_test_pca.shape)\n",
        "print(time_pca)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "N7IGfZ1g_ASD",
        "outputId": "8e370827-9a29-45f6-d8c8-2c891371acdb"
      },
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "12.106742858886719\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def time_plot(start, end, x_train_pca):\n",
        "    fig, ax = plt.subplots(figsize=(6, 5))\n",
        "    ax.bar(0, time_log_normal, width=0.5)\n",
        "    ax.bar(1, end-start, width=0.5)\n",
        "    ax.set_xlabel('Model')\n",
        "    ax.set_xticks([0,1])\n",
        "    ax.set_xticklabels(['Full Dataset', '{} PCs'.format(x_train_pca.shape[1])])\n",
        "    ax.set_ylabel('Time in s')\n",
        "    ax.set_title('Time (s) taken to fit the two models');"
      ],
      "metadata": {
        "id": "gsWbvs0qJ3Fv"
      },
      "execution_count": 51,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "time_plot(start, end, x_train_pca)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 487
        },
        "id": "z6vqytVJKEBy",
        "outputId": "f7aab6df-a90c-4ba3-f7fc-8fca8c6a1af2"
      },
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x500 with 1 Axes>"
            ],
            "image/png": 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llkaNGikyMlJz587VtWvX1KhRI/s2wcHBSktL0+HDhx0GniYkJCgxMTHHjnNmgoODdfDgwXTtN/87BwcH66effpIxxuEY3LxtTrx369Wrp3r16umtt95STEyMevbsqS+//NLhUg7uDsZMIF8JDw+Xt7e3xo0bl+G10t9+++2W29epU0dubm7avn27Q3tGt59e/2vp5lvaduzYoWrVqjlcisiIp6enJKV7Aub1vwJv/KsvKSlJ0dHRmfZVunRpfffdd/rjjz/06KOP2sd+1KlTR+XLl9e///3vDB8NfrvjkR2enp4Zjudo3bq1Tp8+rTlz5tjb/vzzT73//vvy8vJS48aNc2z/UvrjmVPr36xEiRJq0qSJPv74Y506dSrd8tsd28KFC99y/w0bNtSaNWv0ww8/2MNErVq1VKRIEU2YMEEeHh6qU6eOff3WrVtLUrqnkE6aNEmS1KZNmyy9rjvVunVr/fDDD9q8ebO9LSUlRdOmTVOZMmVUtWpV+3onT57UvHnz7OtdunRJ06ZNc+jPynv3/Pnz6c6aZPbziruDMxPIV7y9vRUVFaUnn3xStWvX1hNPPKHixYvr+PHjWrZsmerXr68PPvgg0+0LFSqkFi1a6LvvvnN46NSYMWO0fv16tWnTRsHBwTpz5ow+/PBDlS5d2mHA2dWrVxUbG6t//etft631+gfB8OHD9cQTT6hgwYJq166dWrRoITc3N7Vr107PPfecLl68qOnTp6tEiRIZfmhdV6FCBa1atUpNmjRReHi41qxZI29vb33yySdq1aqVqlWrpt69e+v+++/X//3f/2nt2rXy9vbWkiVLsnJos/R65syZo8jISD300EPy8vJSu3bt9Oyzz+rjjz9Wr169tGPHDpUpU0bz5s3T999/rylTpqhIkSI5sv9atWqpQIECevvtt5WUlCR3d3f7szoyq1eSBg0apPDwcBUoUEBPPPFEtvY5depUNWjQQDVq1FDfvn1Vrlw5JSQkaPPmzfr111+1e/fuTLf18PBQ1apVNWfOHD3wwAPy8/NT9erV7QMqGzZsqNmzZ8tms9nfYwUKFNAjjzyilStXqkmTJg4P8qpZs6YiIiI0bdo0JSYmqnHjxvrhhx80c+ZMdejQQU2bNs3Wa8uuoUOH6osvvlCrVq00aNAg+fn5aebMmYqPj9f8+fPtZ6X69u2rDz74QE899ZR27NihUqVKadasWfZwdZ2Li8sdv3dnzpypDz/8UI8//rjKly+vCxcuaPr06fL29raHLtxlzrqNBH8fd3Jr6DvvvOOw3tq1a40kM3fuXIf267eE3XwL2Nq1a014eLjx8fExhQoVMuXLlze9evUy27dvv229CxYsMDabzRw/ftzetnr1atO+fXsTEBBg3NzcTEBAgOnevbs5dOiQw7bLly83kszhw4dvux9jjBk7dqy5//77jYuLi8OtbYsXLzYhISGmUKFCpkyZMubtt982n332WbpbSW+8NfS6rVu3miJFiphGjRrZbzH98ccfTceOHU3RokWNu7u7CQ4ONl27djWrV6+2b3f91tCbb3+9+ba7zFy8eNH06NHD+Pr6GkkO/64JCQmmd+/eplixYsbNzc3UqFHDREdHZ+kYZfXWUGOMmT59uilXrpwpUKDAbW8T/fPPP83AgQNN8eLFjc1ms79HM3sPGmMyvJXzyJEj5qmnnjL+/v6mYMGC5v777zdt27Y18+bNu+1r27Rpk6lTp45xc3NL1/fPP/9sJJkqVao4bPPmm28aSeaNN95I19/Vq1fN6NGjTdmyZU3BggVNYGCgGTZsmMOtq5nJ7Dg3btzYVKtWLV17Ru+9I0eOmM6dOxtfX19TqFAh8/DDD5ulS5em2/bYsWPmscceM4ULFzbFihUzL7zwglmxYkWG/2ZZee/e/B7duXOn6d69uwkKCjLu7u6mRIkSpm3btln6+UfusBlzj426wj3v2rVrqlq1qrp27aqxY8dma9sOHTrIZrNl6QFBAHCvIEzgnjRnzhw9//zzOn78eJZHfu/fv181atTQrl277KeqAQCECQAAYBF3cwAAAEsIEwAAwBLCBAAAsIQwAQAALPnbP7QqLS1NJ0+eVJEiRSw/XhcAgHuJMUYXLlxQQEBAui/zu9HfPkycPHky3TdRAgCArDtx4oTDlyPe7G8fJq4/yvfEiRN39PXKAADcq5KTkxUYGHjbx+L/7cPE9Usb3t7ehAkAAO7A7YYJMAATAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlrs4uIL8qM3SZs0tAPnN0QhtnlwAAuYIzEwAAwBLCBAAAsIQwAQAALCFMAAAAS/JMmJgwYYJsNpsGDx5sb7t8+bL69++vokWLysvLS506dVJCQoLzigQAAOnkiTCxbds2ffzxxwoJCXFoHzJkiJYsWaK5c+cqNjZWJ0+eVMeOHZ1UJQAAyIjTw8TFixfVs2dPTZ8+Xffdd5+9PSkpSZ9++qkmTZqkZs2aqU6dOoqOjtamTZu0ZcsWJ1YMAABu5PQw0b9/f7Vp00bNmzd3aN+xY4euXr3q0F65cmUFBQVp8+bNmfaXmpqq5ORkhwkAAOQepz606ssvv9TOnTu1bdu2dMtOnz4tNzc3+fr6OrSXLFlSp0+fzrTP8ePHa/To0TldKgAAyITTzkycOHFCL7zwgmbPnq1ChQrlWL/Dhg1TUlKSfTpx4kSO9Q0AANJzWpjYsWOHzpw5o9q1a8vV1VWurq6KjY3Ve++9J1dXV5UsWVJXrlxRYmKiw3YJCQny9/fPtF93d3d5e3s7TAAAIPc47TJHWFiY9u7d69DWu3dvVa5cWa+++qoCAwNVsGBBrV69Wp06dZIkHTx4UMePH1doaKgzSgYAABlwWpgoUqSIqlev7tDm6empokWL2tv79OmjyMhI+fn5ydvbWwMHDlRoaKjq1avnjJIBAEAG8vS3hk6ePFkuLi7q1KmTUlNTFR4erg8//NDZZQEAgBvYjDHG2UXkpuTkZPn4+CgpKSlHx0/wFeTILr6CHEB+k9XPUKc/ZwIAAORvhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJU4NE1FRUQoJCZG3t7e8vb0VGhqq5cuX25c3adJENpvNYerXr58TKwYAADdzdebOS5curQkTJqhixYoyxmjmzJlq3769fvzxR1WrVk2S1LdvX40ZM8a+TeHChZ1VLgAAyIBTw0S7du0c5t966y1FRUVpy5Yt9jBRuHBh+fv7O6M8AACQBXlmzMS1a9f05ZdfKiUlRaGhofb22bNnq1ixYqpevbqGDRumS5cu3bKf1NRUJScnO0wAACD3OPXMhCTt3btXoaGhunz5sry8vLRw4UJVrVpVktSjRw8FBwcrICBAe/bs0auvvqqDBw9qwYIFmfY3fvx4jR49+m6VDwDAPc9mjDHOLODKlSs6fvy4kpKSNG/ePH3yySeKjY21B4obrVmzRmFhYYqLi1P58uUz7C81NVWpqan2+eTkZAUGBiopKUne3t45VneZoctyrC/cG45OaOPsEgAgW5KTk+Xj43Pbz1Cnn5lwc3NThQoVJEl16tTRtm3b9O677+rjjz9Ot27dunUl6ZZhwt3dXe7u7rlXMAAAcJBnxkxcl5aW5nBm4Ua7du2SJJUqVeouVgQAAG7FqWcmhg0bplatWikoKEgXLlxQTEyM1q1bp5UrV+rIkSOKiYlR69atVbRoUe3Zs0dDhgxRo0aNFBIS4syyAQDADZwaJs6cOaOnnnpKp06dko+Pj0JCQrRy5Uo9+uijOnHihL777jtNmTJFKSkpCgwMVKdOnfT66687s2QAAHATp4aJTz/9NNNlgYGBio2NvYvVAACAO5HnxkwAAID8hTABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALHFqmIiKilJISIi8vb3l7e2t0NBQLV++3L788uXL6t+/v4oWLSovLy916tRJCQkJTqwYAADczKlhonTp0powYYJ27Nih7du3q1mzZmrfvr1+/vlnSdKQIUO0ZMkSzZ07V7GxsTp58qQ6duzozJIBAMBNbMYY4+wibuTn56d33nlHnTt3VvHixRUTE6POnTtLkg4cOKAqVapo8+bNqlevXpb6S05Olo+Pj5KSkuTt7Z1jdZYZuizH+sK94eiENs4uAQCyJaufoXlmzMS1a9f05ZdfKiUlRaGhodqxY4euXr2q5s2b29epXLmygoKCtHnz5kz7SU1NVXJyssMEAAByj9PDxN69e+Xl5SV3d3f169dPCxcuVNWqVXX69Gm5ubnJ19fXYf2SJUvq9OnTmfY3fvx4+fj42KfAwMBcfgUAANzbnB4mKlWqpF27dmnr1q16/vnnFRERoX379t1xf8OGDVNSUpJ9OnHiRA5WCwAAbubq7ALc3NxUoUIFSVKdOnW0bds2vfvuu+rWrZuuXLmixMREh7MTCQkJ8vf3z7Q/d3d3ubu753bZAADgv5x+ZuJmaWlpSk1NVZ06dVSwYEGtXr3avuzgwYM6fvy4QkNDnVghAAC4kVPPTAwbNkytWrVSUFCQLly4oJiYGK1bt04rV66Uj4+P+vTpo8jISPn5+cnb21sDBw5UaGholu/kAAAAuc+pYeLMmTN66qmndOrUKfn4+CgkJEQrV67Uo48+KkmaPHmyXFxc1KlTJ6Wmpio8PFwffvihM0sGAAA3yXPPmchpPGcCeQXPmQCQ3+S750wAAID8iTABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALHFqmBg/frweeughFSlSRCVKlFCHDh108OBBh3WaNGkim83mMPXr189JFQMAgJs5NUzExsaqf//+2rJli7799ltdvXpVLVq0UEpKisN6ffv21alTp+zTxIkTnVQxAAC4maszd75ixQqH+RkzZqhEiRLasWOHGjVqZG8vXLiw/P3973Z5AAAgC/LUmImkpCRJkp+fn0P77NmzVaxYMVWvXl3Dhg3TpUuXMu0jNTVVycnJDhMAAMg9Tj0zcaO0tDQNHjxY9evXV/Xq1e3tPXr0UHBwsAICArRnzx69+uqrOnjwoBYsWJBhP+PHj9fo0aPvVtkAANzzbMYY4+wiJOn555/X8uXLtXHjRpUuXTrT9dasWaOwsDDFxcWpfPny6ZanpqYqNTXVPp+cnKzAwEAlJSXJ29s7x+otM3RZjvWFe8PRCW2cXQIAZEtycrJ8fHxu+xma7cscK1as0MaNG+3zU6dOVa1atdSjRw+dP3/+joodMGCAli5dqrVr194ySEhS3bp1JUlxcXEZLnd3d5e3t7fDBAAAck+2w8TLL79sH4ewd+9evfjii2rdurXi4+MVGRmZrb6MMRowYIAWLlyoNWvWqGzZsrfdZteuXZKkUqVKZbd0AACQC7I9ZiI+Pl5Vq1aVJM2fP19t27bVuHHjtHPnTrVu3TpbffXv318xMTFatGiRihQpotOnT0uSfHx85OHhoSNHjigmJkatW7dW0aJFtWfPHg0ZMkSNGjVSSEhIdksHAAC5INtnJtzc3Ox3U3z33Xdq0aKFpL/uwMjunRNRUVFKSkpSkyZNVKpUKfs0Z84c+76u76Ny5cp68cUX1alTJy1ZsiS7ZQMAgFyS7TMTDRo0UGRkpOrXr68ffvjB/sF/6NCh2453uNntxn4GBgYqNjY2uyUCAIC7KNtnJj744AO5urpq3rx5ioqK0v333y9JWr58uVq2bJnjBQIAgLwt22cmgoKCtHTp0nTtkydPzpGCAABA/pKnnoAJAADyH8IEAACwhDABAAAsIUwAAABLCBMAAMCSbN/NkZKSogkTJmj16tU6c+aM0tLSHJb/8ssvOVYcAADI+7IdJp555hnFxsbqySefVKlSpWSz2XKjLgAAkE9kO0wsX75cy5YtU/369XOjHgAAkM9ke8zEfffdJz8/v9yoBQAA5EPZDhNjx47ViBEj7F/2BQAA7m3Zvszxn//8R0eOHFHJkiVVpkwZFSxY0GH5zp07c6w4AACQ92U7THTo0CEXygAAAPlVtsPEyJEjc6MOAACQT/HQKgAAYEmWzkz4+fnp0KFDKlasmO67775bPlvi3LlzOVYcAADI+7IUJiZPnqwiRYpIkqZMmZKb9QAAgHwmS2EiIiIiw/8HAABgzAQAALCEMAEAACwhTAAAAEsIEwAAwJI7DhNxcXFauXKl/vjjD0mSMSbHigIAAPlHtsPE2bNn1bx5cz3wwANq3bq1Tp06JUnq06ePXnzxxRwvEAAA5G3ZDhNDhgyRq6urjh8/rsKFC9vbu3XrphUrVuRocQAAIO/L9ndzrFq1SitXrlTp0qUd2itWrKhjx47lWGEAACB/yPaZiZSUFIczEtedO3dO7u7uOVIUAADIP7IdJho2bKjPP//cPm+z2ZSWlqaJEyeqadOmOVocAADI+7J9mWPixIkKCwvT9u3bdeXKFb3yyiv6+eefde7cOX3//fe5USMAAMjDsn1monr16jp06JAaNGig9u3bKyUlRR07dtSPP/6o8uXL50aNAAAgD8v2mQlJ8vHx0fDhw3O6FgAAkA/dUZi4fPmy9uzZozNnzigtLc1h2WOPPZYjhQEAgPwh22FixYoVeuqpp/T777+nW2az2XTt2rUcKQwAAOQP2R4zMXDgQHXp0kWnTp1SWlqaw5TdIDF+/Hg99NBDKlKkiEqUKKEOHTro4MGDDutcvnxZ/fv3V9GiReXl5aVOnTopISEhu2UDAIBcku0wkZCQoMjISJUsWdLyzmNjY9W/f39t2bJF3377ra5evaoWLVooJSXFvs6QIUO0ZMkSzZ07V7GxsTp58qQ6duxoed8AACBnZPsyR+fOnbVu3bocuXPj5sdvz5gxQyVKlNCOHTvUqFEjJSUl6dNPP1VMTIyaNWsmSYqOjlaVKlW0ZcsW1atXz3INAADAmmyHiQ8++EBdunTRhg0bVKNGDRUsWNBh+aBBg+64mKSkJEmSn5+fJGnHjh26evWqmjdvbl+ncuXKCgoK0ubNmzMME6mpqUpNTbXPJycn33E9AADg9rIdJr744gutWrVKhQoV0rp162Sz2ezLbDbbHYeJtLQ0DR48WPXr11f16tUlSadPn5abm5t8fX0d1i1ZsqROnz6dYT/jx4/X6NGj76gGAACQfdkOE8OHD9fo0aM1dOhQubhke8hFpvr376+ffvpJGzdutNTPsGHDFBkZaZ9PTk5WYGCg1fIAAEAmsh0mrly5om7duuVokBgwYICWLl2q9evXO3wbqb+/v65cuaLExESHsxMJCQny9/fPsC93d3e+cAwAgLso24kgIiJCc+bMyZGdG2M0YMAALVy4UGvWrFHZsmUdltepU0cFCxbU6tWr7W0HDx7U8ePHFRoamiM1AAAAa7J9ZuLatWuaOHGiVq5cqZCQkHQDMCdNmpTlvvr376+YmBgtWrRIRYoUsY+D8PHxkYeHh3x8fNSnTx9FRkbKz89P3t7eGjhwoEJDQ7mTAwCAPCLbYWLv3r168MEHJUk//fSTw7IbB2NmRVRUlCSpSZMmDu3R0dHq1auXJGny5MlycXFRp06dlJqaqvDwcH344YfZLRsAAOQSmzHGOLuI3JScnCwfHx8lJSXJ29s7x/otM3RZjvWFe8PRCW2cXQIAZEtWP0NzbhQlAAC4J2XpMkfHjh01Y8YMeXt73/ZR1gsWLMiRwgAAQP6QpTDh4+NjHw/h4+OTqwUBAID8JUthIjo6WmPGjNFLL72k6Ojo3K4JAADkI1keMzF69GhdvHgxN2sBAAD5UJbDxN/8pg8AAHCHsnU3R3afIwEAAP7+svXQqgceeOC2geLcuXOWCgIAAPlLtsLE6NGjuZsDAAA4yFaYeOKJJ1SiRIncqgUAAORDWR4zwXgJAACQEe7mAAAAlmT5MkdaWlpu1gEAAPIpvugLAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWOLUMLF+/Xq1a9dOAQEBstls+vrrrx2W9+rVSzabzWFq2bKlc4oFAAAZcmqYSElJUc2aNTV16tRM12nZsqVOnTpln7744ou7WCEAALgdV2fuvFWrVmrVqtUt13F3d5e/v3+W+0xNTVVqaqp9Pjk5+Y7rAwAAt5fnx0ysW7dOJUqUUKVKlfT888/r7Nmzt1x//Pjx8vHxsU+BgYF3qVIAAO5NeTpMtGzZUp9//rlWr16tt99+W7GxsWrVqpWuXbuW6TbDhg1TUlKSfTpx4sRdrBgAgHuPUy9z3M4TTzxh//8aNWooJCRE5cuX17p16xQWFpbhNu7u7nJ3d79bJQIAcM/L02cmblauXDkVK1ZMcXFxzi4FAAD8V74KE7/++qvOnj2rUqVKObsUAADwX069zHHx4kWHswzx8fHatWuX/Pz85Ofnp9GjR6tTp07y9/fXkSNH9Morr6hChQoKDw93YtUAAOBGTg0T27dvV9OmTe3zkZGRkqSIiAhFRUVpz549mjlzphITExUQEKAWLVpo7NixjIkAACAPcWqYaNKkiYwxmS5fuXLlXawGAADciXw1ZgIAAOQ9hAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYImrswsAAGRilI+zK0B+MyrJKbvlzAQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACxxaphYv3692rVrp4CAANlsNn399dcOy40xGjFihEqVKiUPDw81b95chw8fdk6xAAAgQ04NEykpKapZs6amTp2a4fKJEyfqvffe00cffaStW7fK09NT4eHhunz58l2uFAAAZMbVmTtv1aqVWrVqleEyY4ymTJmi119/Xe3bt5ckff755ypZsqS+/vprPfHEE3ezVAAAkIk8O2YiPj5ep0+fVvPmze1tPj4+qlu3rjZv3pzpdqmpqUpOTnaYAABA7smzYeL06dOSpJIlSzq0lyxZ0r4sI+PHj5ePj499CgwMzNU6AQC41+XZMHGnhg0bpqSkJPt04sQJZ5cEAMDfWp4NE/7+/pKkhIQEh/aEhAT7soy4u7vL29vbYQIAALknz4aJsmXLyt/fX6tXr7a3JScna+vWrQoNDXViZQAA4EZOvZvj4sWLiouLs8/Hx8dr165d8vPzU1BQkAYPHqw333xTFStWVNmyZfXGG28oICBAHTp0cF7RAADAgVPDxPbt29W0aVP7fGRkpCQpIiJCM2bM0CuvvKKUlBQ9++yzSkxMVIMGDbRixQoVKlTIWSUDAICbODVMNGnSRMaYTJfbbDaNGTNGY8aMuYtVAQCA7MizYyYAAED+QJgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAluTpMDFq1CjZbDaHqXLlys4uCwAA3MDV2QXcTrVq1fTdd9/Z511d83zJAADcU/L8J7Orq6v8/f2dXQYAAMhEnr7MIUmHDx9WQECAypUrp549e+r48eO3XD81NVXJyckOEwAAyD15OkzUrVtXM2bM0IoVKxQVFaX4+Hg1bNhQFy5cyHSb8ePHy8fHxz4FBgbexYoBALj35Okw0apVK3Xp0kUhISEKDw/XN998o8TERH311VeZbjNs2DAlJSXZpxMnTtzFigEAuPfk+TETN/L19dUDDzyguLi4TNdxd3eXu7v7XawKAIB7W54+M3Gzixcv6siRIypVqpSzSwEAAP+Vp8PESy+9pNjYWB09elSbNm3S448/rgIFCqh79+7OLg0AAPxXnr7M8euvv6p79+46e/asihcvrgYNGmjLli0qXry4s0sDAAD/lafDxJdffunsEgAAwG3k6cscAAAg7yNMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEsIEwAAwBLCBAAAsIQwAQAALCFMAAAASwgTAADAEsIEAACwhDABAAAsIUwAAABLCBMAAMASwgQAALCEMAEAACwhTAAAAEvyRZiYOnWqypQpo0KFCqlu3br64YcfnF0SAAD4rzwfJubMmaPIyEiNHDlSO3fuVM2aNRUeHq4zZ844uzQAAKB8ECYmTZqkvn37qnfv3qpatao++ugjFS5cWJ999pmzSwMAAJJcnV3ArVy5ckU7duzQsGHD7G0uLi5q3ry5Nm/enOE2qampSk1Ntc8nJSVJkpKTk3O0trTUSznaH/7+cvo9iHtAqnF2Bchvcvj3zPXfW8bc+r2Yp8PE77//rmvXrqlkyZIO7SVLltSBAwcy3Gb8+PEaPXp0uvbAwMBcqRHIKp8pzq4AwN/eBJ9c6fbChQvy8cm87zwdJu7EsGHDFBkZaZ9PS0vTuXPnVLRoUdlsNidW9veXnJyswMBAnThxQt7e3s4uB8DfEL9n7i5jjC5cuKCAgIBbrpenw0SxYsVUoEABJSQkOLQnJCTI398/w23c3d3l7u7u0Obr65tbJSID3t7e/JADyFX8nrl7bnVG4ro8PQDTzc1NderU0erVq+1taWlpWr16tUJDQ51YGQAAuC5Pn5mQpMjISEVEROgf//iHHn74YU2ZMkUpKSnq3bu3s0sDAADKB2GiW7du+u233zRixAidPn1atWrV0ooVK9INyoTzubu7a+TIkekuMwFATuH3TN5kM7e73wMAAOAW8vSYCQAAkPcRJgAAgCWECQAAYAlh4h7TpEkTDR482D5fpkwZTZkyxWn1AADyP8JEPtOrVy/ZbLZ0U1xcXK7sb9SoUfZ9uLq6qlixYmrUqJGmTJni8B0oWbFu3TrZbDYlJibmSq2ZGTVqlGrVqnVX9wlAunbtmt544w2VLVtWHh4eKl++vMaOHevwPQ8Z/T6z2Wx65513Mu33xt+Dbm5uqlChgsaMGaM///zTvo4xRtOmTVPdunXl5eUlX19f/eMf/9CUKVN06RLfrZTT8vytoUivZcuWio6OdmgrXrx4ru2vWrVq+u6775SWlqazZ89q3bp1evPNNzVr1iytW7dORYoUybV9A8i/3n77bUVFRWnmzJmqVq2atm/frt69e8vHx0eDBg2SJJ06dcphm+XLl6tPnz7q1KnTLfu+/nswNTVV33zzjfr376+CBQvavxjyySef1IIFC/T666/rgw8+UPHixbV7925NmTJFZcqUUYcOHXLlNd+zDPKViIgI0759+ywve+GFF0zjxo3t840bNzYvvPCCfT44ONhMnjw50/2NHDnS1KxZM137/v37jZubmxk+fLi97fPPPzd16tQxXl5epmTJkqZ79+4mISHBGGNMfHy8keQwRUREGGOMWb58ualfv77x8fExfn5+pk2bNiYuLs7eb2pqqunfv7/x9/c37u7uJigoyIwbN86+/Pz586ZPnz6mWLFipkiRIqZp06Zm165dxhhjoqOj0+03Ojo609cLIOe0adPGPP300w5tHTt2ND179sx0m/bt25tmzZrdst+Mftc9+uijpl69esYYY+bMmWMkma+//jrdtmlpaSYxMdEYY8zatWvNQw89ZAoXLmx8fHzMI488Yo4ePZqVl4abcJkDd6Ry5cpq1aqVFixYYG+7evWqxo4dq927d+vrr7/W0aNH1atXL0l/fWvr/PnzJUkHDx7UqVOn9O6770qSUlJSFBkZqe3bt2v16tVycXHR448/rrS0NEnSe++9p8WLF+urr77SwYMHNXv2bJUpU8a+3y5duujMmTNavny5duzYodq1ayssLEznzp1Tt27d9OKLL6patWo6deqUTp06pW7dut2dgwTc4x555BGtXr1ahw4dkiTt3r1bGzduVKtWrTJcPyEhQcuWLVOfPn2yvS8PDw9duXJFkjR79mxVqlRJ7du3T7eezWaTj4+P/vzzT3Xo0EGNGzfWnj17tHnzZj377LN8IeQd4jJHPrR06VJ5eXnZ51u1aqW5c+fe9ToqV66sVatW2eeffvpp+/+XK1dO7733nh566CFdvHhRXl5e8vPzkySVKFHC4cvXbj6d+dlnn6l48eLat2+fqlevruPHj6tixYpq0KCBbDabgoOD7etu3LhRP/zwg86cOWN/It6///1vff3115o3b56effZZeXl5ydXVNdMvhwOQO4YOHark5GRVrlxZBQoU0LVr1/TWW2+pZ8+eGa4/c+ZMFSlSRB07dszyPowxWr16tVauXKmBAwdKkg4fPqxKlSrdcrvk5GQlJSWpbdu2Kl++vCSpSpUqWd4vHBEm8qGmTZsqKirKPu/p6emUOowxDil+x44dGjVqlHbv3q3z58/bzywcP35cVatWzbSfw4cPa8SIEdq6dat+//13h+2qV6+uXr166dFHH1WlSpXUsmVLtW3bVi1atJD01186Fy9eVNGiRR36/OOPP3TkyJGcfskAsuGrr77S7NmzFRMTo2rVqmnXrl0aPHiwAgICFBERkW79zz77TD179lShQoVu2/f1P6quXr2qtLQ09ejRQ6NGjZIkhwGemfHz81OvXr0UHh6uRx99VM2bN1fXrl1VqlSpbL9OECbyJU9PT1WoUCFdu4uLS7ofoqtXr+ZaHfv371fZsmUl/XWpIjw8XOHh4Zo9e7aKFy+u48ePKzw83H7qMTPt2rVTcHCwpk+froCAAKWlpal69er27WrXrq34+HgtX75c3333nbp27armzZtr3rx5unjxokqVKqV169al65evngec6+WXX9bQoUP1xBNPSJJq1KihY8eOafz48enCxIYNG3Tw4EHNmTMnS31f/6PKzc1NAQEBcnX938fZAw88oAMHDty2j+joaA0aNEgrVqzQnDlz9Prrr+vbb79VvXr1svEqIXFr6N9K8eLF042M3rVrV67s68CBA1qxYoX9EsWBAwd09uxZTZgwQQ0bNlTlypV15swZh23c3Nwk/XW72HVnz57VwYMH9frrryssLExVqlTR+fPn0+3P29tb3bp10/Tp0zVnzhzNnz9f586dU+3atXX69Gm5urqqQoUKDlOxYsXs+71xnwDujkuXLsnFxfFjpkCBAvazjzf69NNPVadOHdWsWTNLfV//oyooKMghSEhSjx49dOjQIS1atCjddsYYJSUl2ecffPBBDRs2TJs2bVL16tUVExOTpf3DEWHib6RZs2bavn27Pv/8cx0+fFgjR47UTz/9ZLnfP//8U6dPn9bJkye1d+9evf/++2rcuLFq1aqll19+WZIUFBQkNzc3vf/++/rll1+0ePFijR071qGf4OBg2Ww2LV26VL/99psuXryo++67T0WLFtW0adMUFxenNWvWKDIy0mG7SZMm6YsvvtCBAwd06NAhzZ07V/7+/vL19VXz5s0VGhqqDh06aNWqVTp69Kg2bdqk4cOHa/v27ZL+ejBXfHy8du3apd9//z3bz8cAcGfatWunt956S8uWLdPRo0e1cOFCTZo0SY8//rjDesnJyZo7d66eeeaZHNlv165d1a1bN3Xv3l3jxo3T9u3bdezYMS1dulTNmzfX2rVrFR8fr2HDhmnz5s06duyYVq1apcOHDzNu4k459V4SZNutbg01xpgRI0aYkiVLGh8fHzNkyBAzYMAAy7eG6r+3VBYoUMD4+fmZBg0amMmTJ5vLly87rBsTE2PKlClj3N3dTWhoqFm8eLGRZH788Uf7OmPGjDH+/v7GZrPZbw399ttvTZUqVYy7u7sJCQkx69atM5LMwoULjTHGTJs2zdSqVct4enoab29vExYWZnbu3GnvMzk52QwcONAEBASYggULmsDAQNOzZ09z/PhxY4wxly9fNp06dTK+vr7cGgrcRcnJyeaFF14wQUFBplChQqZcuXJm+PDhJjU11WG9jz/+2Hh4eNhv2byd2/0eNMaYa9eumaioKPutn97e3qZOnTrm3XffNZcuXTKnT582HTp0MKVKlTJubm4mODjYjBgxwly7du1OX+49ja8gBwAAlnCZAwAAWEKYAAAAlhAmAACAJYQJAABgCWECAABYQpgAAACWECYAAIAlhAkAAGAJYQJAnrNu3TrZbDYlJiZmeZsyZcpoypQpuVYTgMwRJgBkW69evWSz2dSvX790y/r37y+bzaZevXrd/cIAOAVhAsAdCQwM1Jdffqk//vjD3nb58mXFxMQoKCjIiZUBuNsIEwDuSO3atRUYGKgFCxbY2xYsWKCgoCA9+OCD9rbU1FQNGjRIJUqUUKFChdSgQQNt27bNoa9vvvlGDzzwgDw8PNS0aVMdPXo03f42btyohg0bysPDQ4GBgRo0aJBSUlJy7fUByDrCBIA79vTTTys6Oto+/9lnn6l3794O67zyyiuaP3++Zs6cqZ07d6pChQoKDw/XuXPnJEknTpxQx44d1a5dO+3atUvPPPOMhg4d6tDHkSNH1LJlS3Xq1El79uzRnDlztHHjRg0YMCD3XySA2yJMALhj//znP7Vx40YdO3ZMx44d0/fff69//vOf9uUpKSmKiorSO++8o1atWqlq1aqaPn26PDw89Omnn0qSoqKiVL58ef3nP/9RpUqV1LNnz3TjLcaPH6+ePXtq8ODBqlixoh555BG99957+vzzz3X58uW7+ZIBZMDV2QUAyL+KFy+uNm3aaMaMGTLGqE2bNipWrJh9+ZEjR3T16lXVr1/f3lawYEE9/PDD2r9/vyRp//79qlu3rkO/oaGhDvO7d+/Wnj17NHv2bHubMUZpaWmKj49XlSpVcuPlAcgiwgQAS55++mn75YapU6fmyj4uXryo5557ToMGDUq3jMGegPMRJgBY0rJlS125ckU2m03h4eEOy8qXLy83Nzd9//33Cg4OliRdvXpV27Zt0+DBgyVJVapU0eLFix2227Jli8N87dq1tW/fPlWoUCH3XgiAO8aYCQCWFChQQPv379e+fftUoEABh2Wenp56/vnn9fLLL2vFihXat2+f+vbtq0uXLqlPnz6SpH79+unw4cN6+eWXdfDgQcXExGjGjBkO/bz66qvatGmTBgwYoF27dunw4cNatGgRAzCBPIIwAcAyb29veXt7Z7hswoQJ6tSpk5588knVrl1bcXFxWrlype677z5Jf12mmD9/vr7++mvVrFlTH330kcaNG+fQR0hIiGJjY3Xo0CE1bNhQDz74oEaMGKGAgIBcf20Abs9mjDHOLgIAAORfnJkAAACWECYAAIAlhAkAAGAJYQIAAFhCmAAAAJYQJgAAgCWECQAAYAlhAgAAWEKYAAAAlhAmAACAJYQJAABgyf8H4XFsK2v6tDoAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "start = time()\n",
        "log_pca = LogisticRegression(solver='lbfgs').fit(x_train_pca, y_train)\n",
        "end = time()\n",
        "\n",
        "log_pca_time = (end-start) + time_pca\n",
        "\n",
        "print('Time to fit logistic regression with ({} PCs): {}s'.format(x_train_pca.shape[1],end-start))\n",
        "print('Time to fit logistic regression on the full dataset: {}s'.format(time_log_normal))\n",
        "print('Hence, to fit the logistic regression with the reduced dataset is about', np.round(time_log_normal/(end-start),1), 'times faster than without using PCA')\n",
        "print('Time for PCA: ', time_pca)\n",
        "print('Combined time for PCA and logistic regression: {}s'.format(log_pca_time))\n",
        "print('Which results in a total speed-up of {}.'.format(np.round(time_log_normal/(log_pca_time),1)))\n",
        "\n",
        "\n",
        "time_plot(start, end, x_train_pca)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 611
        },
        "id": "PVdzZ0YtK-y2",
        "outputId": "306631bb-1006-45c8-9b5e-ff367d2c9883"
      },
      "execution_count": 53,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Time to fit logistic regression with (87 PCs): 12.987235069274902s\n",
            "Time to fit logistic regression on the full dataset: 40.95360732078552s\n",
            "Hence, to fit the logistic regression with the reduced dataset is about 3.2 times faster than without using PCA\n",
            "Time for PCA:  12.106742858886719\n",
            "Combined time for PCA and logistic regression: 25.09397792816162s\n",
            "Which results in a total speed-up of 1.6.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 600x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Compare the accuracy between prediction with/without PCA "
      ],
      "metadata": {
        "id": "f_IlCX72LbIj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y_preds_train_pca = log_pca.predict(x_train_pca)\n",
        "y_preds_test_pca = log_pca.predict(x_test_pca)\n",
        "\n",
        "model_score_train_pca = accuracy_score(y_train, y_preds_train_pca)\n",
        "model_score_test_pca = accuracy_score(y_test, y_preds_test_pca)\n",
        "\n",
        "# Evaluaiton\n",
        "print('Training Set Score: {}'.format(model_score_train_pca.round(4)))\n",
        "print('Test Set Score: {}'.format(model_score_test_pca.round(4)))\n",
        "\n",
        "print('Training Set Score of the full dataset: {}'.format(log_normal_score_train.round(4)))\n",
        "print('Test Set Score of the full dataset: {}'.format(log_normal_score_test.round(4)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VCfHJ-mULaCq",
        "outputId": "9468f2cd-a2d9-4f2f-de1a-4b1fa454fc22"
      },
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training Set Score: 0.9225\n",
            "Test Set Score: 0.8503\n",
            "Training Set Score of the full dataset: 0.9369\n",
            "Test Set Score of the full dataset: 0.8604\n"
          ]
        }
      ]
    }
  ]
}