Linear_Discriminant_Analysis.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Linear Discriminant Analysis.ipynb",
      "version": "0.3.2",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "wdGV_hFKEnpC",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "# A Geometric Intuition for Linear Discrminant Analysis\n",
        "\n",
        "This notebook supplements the article at https://omarshehata.github.io/lda-explorable/. \n",
        "\n",
        "It's provided as a reference for performing LDA in Python."
      ]
    },
    {
      "metadata": {
        "id": "YE231r3rn6na",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "# Import the libraries we need\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from numpy.linalg import matrix_rank\n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.preprocessing import scale\n",
        "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "DSnJLl4OFIxY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Peform LDA on the 2D case. First we load the same data used in the article from the GitHub repository."
      ]
    },
    {
      "metadata": {
        "id": "XorPB9QnFIRf",
        "colab_type": "code",
        "outputId": "aa01bba8-7a79-4480-919f-ab194f8156ce",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        }
      },
      "cell_type": "code",
      "source": [
        "data_url = 'https://omarshehata.github.io/lda-explorable/data/sample-2d.csv'\n",
        "data = pd.read_csv(data_url)\n",
        "\n",
        "# Flip the Y to match the JavaScript graph \n",
        "data['Distance'] = -data['Distance']\n",
        "\n",
        "ax = data[data['class'] == 0].plot.scatter(x='Price', y='Distance', c='red', s=40);\n",
        "ax = data[data['class'] == 1].plot.scatter(x='Price', y='Distance', c='blue', s=40,ax=ax);"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KPiTn7MUp+5Ccsxf20fdEay/dfSPQbbT/8pe/RHSQ1NRU1dTUdLxfXV0tj8cT0TUAAHCq\nbqOdkZER0cXuvPNOFRYWyu/36+DBg0pNTe321jgAAPhKWL/GNFJGjx6tm2++WX6/XzExMVqwYIGV\nywMAYDRLoy1d+D3mAACg58J6lS8AAGA/og0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDa\nAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGI\nNgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAI\ny6NdVlamcePGadeuXVYvDQCA0VxWLnb8+HG99tprGj16tJXLoo9ylX+oxOAKqapSg7zpagrkqMWX\nafdYANCt8vJYBYMJqqqSvN5EBQLN8vnaLFnb0mh7PB4tXrxY+fn5Vi6LPshV/qGSAj+Tq7JCkuSW\nFL/3XdUF1xBuAH1WeXmsAgG3Kisv3qiO1969cQoGGy0Jt6W3x91ut+Li4qxcEn1UYnBFR7AvclVW\nXLjyBoA+KhhM6BTsCyorL1x5WyFqV9olJSUqKSnpciw3N1fjx4/v0XlSUgbK5Yps6D2epIiez07G\n7qWq8oqH3dWn5DZ1T/9j7OfkEk7Zh+ScvbAP+1VVXfl4dXW8PJ74qK8ftWhnZ2crOzv7ms9TW9sQ\ngWm+4vEkKRSqi+g57WLyXgZ50+W+wvHG1DTVG7onyezPSWdO2YfknL2wj77B602UdHmcU1PPKxRq\nisga3X1Tw498wRZNgRy1pGd0OdaSnqGmQI5NEwHA1wsEmpWe3vWx6/T0NgUCzZasb+kT0UpLSxUM\nBvXxxx/r4MGDWrt2rYqKiqwcAX1Eiy9TdcE1SgyukLv6lBpT03j2OIA+z+drUzDYqGAwQdXV8UpN\nPe/cZ49PnDhREydOtHJJ9GEtvkzV+zLl9iQZfUscQP/i87XJ52uSxxMfsVvi4eL2OAAAhiDaAAAY\ngmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAA\nhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0A\ngCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhiDaAAAYwmXlYi0tLcrPz9fx48fV2tqqOXPmaMyY\nMVaOAKCfcJV/qMTgCqmqUoO86WoK5KjFl2n3WMA1sTTab731ltxutzZs2KAjR45o3rx52rRpk5Uj\nAOgHXOUfKinwM7kqKyRJbknxe99VXXAN4YbRLI325MmTNWnSJEnS0KFDdfbsWSuXB9BPJAZXdAT7\nIldlhRKDK1RPtGEwS6MdHx/f8fbq1as7At6dlJSBcrniIjqHx5MU0fPZySl7cco+JOfsxeh9VFVe\n8bC7+pTcBu/L6M9JJ07Zh2T9XqIW7ZKSEpWUlHQ5lpubq/Hjx2v9+vU6ePCgli1b9rXnqa1tiOhc\nHk+SQqG6iJ7TLk7Zi1P2ITlnL6bvY5A3Xe4rHG9MTVO9ofsy/XNykVP2IUVvL919IxC1aGdnZys7\nO/uy4yUlJdq5c6eWLFnS5cobACKlKZCj+L3vdrlF3pKeoaZAjo1TAdfO0tvjJ06cUHFxsdatW6cB\nAwZYuTSAfqTFl6m64BolBlfIXX1KjalpPHscjmBptEtKSnT27Fnl5Hz13W4wGFRCQoKVYwDoB1p8\nmar3ZcrtSTL2ljhwKUujPWvWLM2aNcvKJQEAcAx+IxoAAIYg2gAAGIJoAwBgCKINAIAhiDYAAIYg\n2gAAGIJoAwBgCKINAIAhiDYAAIYg2gAAGIJoAwBgCKINAIAhiDYAAIYg2gAAGIJoAwBgCKINAIAh\niDYAAIYg2gAAGIJoAwBgCKINAIAhiDYAAIYg2gAAGIJoAwBgCKINAIAhiDYAAIYg2gAAGIJoAwBg\nCKINAIAhiDYAAIZwWbnY6dOnNXfuXH355Zc6f/685s2bp1tvvdXKEQAAMJalV9qbN2/W/fffr7Vr\n12rWrFlatGiRlcsD+Bqu8g81aOZj0oQJGjTzMbnKP7R7JACdWHql/cgjj3S8ferUKXm9XiuXB9AN\nV/mHSgr8TK7KCkmSW1L83ndVF1yjFl+mvcMBkGRxtCUpFArp8ccf1xdffKHVq1dbvTyAq0gMrugI\n9kWuygolBleonmgDfUJMe3t7ezROXFJSopKSki7HcnNzNX78eEnS7t27tXr1ahUVFXV7npaWVrlc\ncdEYEUBnEyZIe/Zc+fju3dbPA+AyUYv2lZSVlel73/ueBg8eLEm6/fbb9cEHH3T7MaFQXURn8HiS\nIn5OuzhlL07Zh2T2XgbNfEzuTRsvO974f1NVv2SlDRNFhsmfk87YR98Trb14PElX/TNLn4i2bds2\n/fnPf5YkffTRR0pLS7NyeQDdaArkqCU9o8uxlvQMNQVybJoIwKUsfUx75syZysvL0/bt29Xc3Kzn\nnnvOyuUBdKPFl6m64BolBlfIXX1KjalpF0LO49lAn2FptIcOHaoVK1ZYuSSAHmjxZarelym3J0n1\nDrmFCTgJvxENAABDEG0AAAxBtAEAMATRBgDAEEQbAABDEG0AAAxBtAEAMATRBgDAEEQbAABDWPqC\nIQAAoPe40gYAwBBEGwAAQxBtAAAMQbQBADAE0QYAwBBEGwAAQ/TbaNfU1CgzM1MffPCB3aP02unT\np/WLX/xCDz30kPx+v/71r3/ZPVKvtLS0aO7cuXrwwQf1k5/8RPv27bN7pF4rKyvTuHHjtGvXLrtH\n6bUXX3xRU6dOld/v1/79++0ep9cOHz6srKwsrVu3zu5RrtnChQs1depUPfDAA9q2bZvd4/RKY2Oj\nnnrqKU2fPl3Z2dlG/z8iSU1NTcrKytIbb7xh6bouS1frQxYuXKgbbrjB7jGuyebNm3X//ffrxz/+\nscrKyrRo0SIVFRXZPVaPvfXWW3K73dqwYYOOHDmiefPmadOmTXaP1WPHjx/Xa6+9ptGjR9s9Sq+V\nlZXp008/1caNG3Xs2DE9++yz2rhxo91j9VhDQ4Oef/55jRs3zu5Rrtn777+vI0eOaOPGjaqtrdWU\nKVN0zz332D1Wj+3atUsjR47UY489poqKCj366KO6++677R6r15YuXarBgwdbvm6/jPZ7772n6667\nTt/97nftHuWaPPLIIx1vnzp1Sl6v18Zpem/y5MmaNGmSJGno0KE6e/aszRP1jsfj0eLFi5Wfn2/3\nKL323nvvKSsrS5I0YsQInTt3TvX19Ro0aJDNk/VMQkKCVq5cqZUrV9o9yjXLzMzULbfcIklKTk5W\nY2OjWltbFRcXZ/NkPXPfffd1vG3yv1eSdOzYMR09elQTJ060fO1+d3u8ublZf/zjH/XLX/7S7lEi\nIhQK6YEHHtDSpUv19NNP2z1Or8THx2vAgAGSpNWrV3cE3DRut9u4f0gvVVNTo5SUlI73hw4dqlAo\nZONEveNyuZSYmGj3GBERFxengQMHSpI2bdqkCRMmGP115vf79cwzz+jZZ5+1e5ReKygoUF5eni1r\nO/pKu6SkRCUlJV2OTZgwQdnZ2UpOTrZpqt650l5yc3M1fvx4vf7669q9e7fmzZvX52+Pd7eP9evX\n6+DBg1q2bJlN04Wvu304Cb/luO/YsWOHNm3a1Of/H/86xcXFOnTokGbPnq3NmzcrJibG7pF65M03\n39Rtt91m28Orjo52dna2srOzuxzz+/1qa2vT+vXrdfz4ce3fv1+LFi3Sd77zHZumDM+V9lJWVqZz\n585p8ODBuuuuuzRnzhybpgvflfYhXYjgzp07tWTJEsXHx9swWc9cbR+mS01NVU1NTcf71dXV8ng8\nNk4ESdqzZ4+WLVumV199VUlJSXaP0ysHDhzQsGHDlJaWpptuukmtra06c+aMhg0bZvdoPVJaWqoT\nJ06otLRUn332mRISEnT99dfrjjvusGR9R0f7SoqLizvezsvL05QpU/p8sK9m27Zt+s9//qOHH35Y\nH330kdLS0uweqVdOnDih4uJirVu3ruM2Oexx5513qrCwUH6/XwcPHlRqaqpxj2c7TV1dnRYuXKhV\nq1ZpyJAhdo/Ta/v27VNFRYXy8/NVU1OjhoaGLg/FmOLll1/ueLuwsFAZGRmWBVvqh9F2kpkzZyov\nL0/bt29Xc3OznnvuObtH6pWSkhKdPXtWOTk5HceCwaASEhJsnKrnSktLFQwG9fHHH+vgwYNau3at\ncbcyR48erZtvvll+v18xMTFasGCB3SP1yoEDB1RQUKCKigq5XC698847KiwsNDJ6W7duVW1tbZfn\nrBQUFCg9Pd3GqXrO7/crPz9f06ZNU1NTk+bPn6/Y2H73tKprxktzAgBgCL7NAQDAEEQbAABDEG0A\nAAxBtAEAMATRBgDAEPzIF9BPnDx5Uvfee69GjRolSTp//rwyMjK0YMGCLr8hMBQK6fnnn9crr7xi\n16gAroIf+QL6iZMnT2ratGn661//2nGsoKBAkjR37ly7xgLQA9weB/qxzMxMffzxx/rRj36k3//+\n93ryySd18uRJTZgwQdKF12zPycnRgw8+qOnTp+vw4cOSLvzCj2nTpunBBx/UE088odraWju3AfQb\nRBvop1pbW7V9+3b5fD5J0je/+c3Lbom/9NJLuuuuu7RhwwY9+eSTeuutt3Tq1CktW7ZMq1at0oYN\nGzR27FgtX77cji0A/Q6PaQP9yJkzZ/TQQw9Jktra2jRmzBg9/PDDKi4u7nisu7P9+/d3vG772LFj\nNXbsWG3dulWhUEiBQEDShZe7/cY3vmHdJoB+jGgD/cjQoUO1du3aK/7ZlV5dLSYmRm1tbV2OJSQk\n6JZbbuHqGrABt8cBXNWoUaO0Z88eSRdepWnu3Ln64Q9/qP379ysUCkmS3n77be3YscPOMYF+gytt\nAFf11FNPad68edq1a5ck6de//rW8Xq/y8/M1Y8YMud1uJSYmdjwLHUB08SNfAAAYgtvjAAAYgmgD\nAGAIog0AgCGINgAAhiDaAAAYgmgDAGAIog0AgCGINgAAhvh/rDUAQLgsG8MAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f97c5d5acf8>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "zwyRS65UFfjY",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "Now we perform LDA and reduce the data down to 1 dimension."
      ]
    },
    {
      "metadata": {
        "id": "kU0QOIoJRutj",
        "colab_type": "code",
        "outputId": "7c2e177c-a5eb-48b4-fe3f-b400e7c8395f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        }
      },
      "cell_type": "code",
      "source": [
        "# Initialize the LDA to reduce to 1 dimension\n",
        "LDA = LinearDiscriminantAnalysis(n_components=1, solver='eigen')\n",
        "# Separate the data and class \n",
        "Features = data.loc[:,'Price':'Distance'].values\n",
        "Classes = data['class']\n",
        "# Find the best projection \n",
        "ProjectedData = LDA.fit_transform(Features, Classes)\n",
        "# Put it in a dataframe and plot it\n",
        "n = ProjectedData.shape[0]\n",
        "newData = pd.DataFrame(data={\n",
        "    'class' : Classes,\n",
        "    'x' : ProjectedData.reshape(n),\n",
        "    'y' : np.zeros(n)\n",
        "})\n",
        "\n",
        "ax = newData[newData['class'] == 0].plot.scatter(x='x', y='y', c='red', s=40);\n",
        "ax = newData[newData['class'] == 1].plot.scatter(x='x', y='y', c='blue', s=40,ax=ax);"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f97996b3908>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "r3a9xx9fIVQS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "LDA for the 3D case."
      ]
    },
    {
      "metadata": {
        "id": "ypPNg_0U5__t",
        "colab_type": "code",
        "outputId": "ac43a4dd-a690-45d5-f9b6-2e7d0d386d8f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361
        }
      },
      "cell_type": "code",
      "source": [
        "# Load the same data in the article\n",
        "data_url = 'https://omarshehata.github.io/lda-explorable/data/sample-3d.csv'\n",
        "data = pd.read_csv(data_url)\n",
        "# Initialize LDA to project to 2 dimensions\n",
        "LDA = LinearDiscriminantAnalysis(n_components=2, solver='eigen')\n",
        "\n",
        "Features = data.loc[:,'X':'Z'].values\n",
        "Classes = data['class']\n",
        "\n",
        "ProjectedData = LDA.fit_transform(Features, Classes)\n",
        "\n",
        "# Put it in a data frame and plot it\n",
        "n = ProjectedData.shape[0]\n",
        "newData = pd.DataFrame(data={\n",
        "    'class' : Classes,\n",
        "    'x' : np.zeros(n),\n",
        "    'y' : np.zeros(n)\n",
        "})\n",
        "newData.loc[:,'x':'y'] = ProjectedData\n",
        "\n",
        "ax = newData[newData['class'] == 0].plot.scatter(x='x', y='y', c='red', s=40);\n",
        "ax = newData[newData['class'] == 1].plot.scatter(x='x', y='y', c='blue', s=40,ax=ax);\n",
        "ax = newData[newData['class'] == 2].plot.scatter(x='x', y='y', c='orange', s=40,ax=ax);"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f9796e33278>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "I_ASdKzeKmAS",
        "colab_type": "text"
      },
      "cell_type": "markdown",
      "source": [
        "LDA in 4D."
      ]
    },
    {
      "metadata": {
        "id": "1RWac-X4Knby",
        "colab_type": "code",
        "colab": {}
      },
      "cell_type": "code",
      "source": [
        "data_url = 'https://omarshehata.github.io/lda-explorable/data/sample-4d.csv'\n",
        "data = pd.read_csv(data_url)\n",
        "\n",
        "LDA = LinearDiscriminantAnalysis(n_components=2, solver='eigen')\n",
        "\n",
        "Features = data.loc[:,'X':'W'].values\n",
        "Classes = data['class']\n",
        "\n",
        "# Try this one yourself. The 3D case is the closest example. \n",
        "# 1 - Run the fit_transform function to get the projected data\n",
        "# 2 - Put it in a data frame \n",
        "# 3 - Plot it in 2D\n",
        "# 4 - Can you find this same projection back in the diagram in the article?"
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}