LogisticRegression.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "LogisticRegression.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyP7xj2CYpcVXr3Mo0SrJE7J",
      "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/JohnEaganFS/CSCI191T/blob/main/LogisticRegression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1rsy9XGLcWb1"
      },
      "source": [
        "## CSCI 191T - Machine Learning\n",
        "##Name: John Eagan \n",
        "##Assignment: Logistic Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WCCovhUOfVOI"
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "import random"
      ],
      "execution_count": 692,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dLjVNQ5Kh8qf"
      },
      "source": [
        "## Sigmoid, F(w, x), and Classify Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y5HE0OZ1hWno"
      },
      "source": [
        "def sigmoid(x):\n",
        "  return 1.0/(1+math.exp(-x))"
      ],
      "execution_count": 693,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J5h1clQmiAf7"
      },
      "source": [
        "def F(W,X):\n",
        "  return sum([w*x for w,x in zip(W,X)])"
      ],
      "execution_count": 694,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7yJE2H8FkbTI"
      },
      "source": [
        "def classify(model, X): # Uses model to classify list of x values [(x0, x1, x2),...] into either 1 (positive) or 0 (negative).\n",
        "  return [1 if sigmoid(F(model, x)) > 0.5 else 0 for x in X]"
      ],
      "execution_count": 695,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F2a-5mIHdBPc"
      },
      "source": [
        "## Training Data 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "C_fI2aeNdQc2"
      },
      "source": [
        "data = [((1, 0, 0), 1), ((1, 1, 7), 0), ((1, -3, -2), 0), ((1, 8, 9), 1), ((1, 4, 3), 1), ((1, 5, -2), 1), ((1, 0, 0), 1), ((1, 6, 9), 1), ((1, 4, 2), 1), ((1, 1, -9), 1), ((1, -7, 7), 0), ((1, 0, -1), 1), ((1, 9, -4), 1), ((1, 1, 0), 1), ((1, -2, -5), 1), ((1, 2, 3), 1), ((1, -7, 2), 0), ((1, -3, 0), 0), ((1, 5, 0), 1), ((1, 0, -3), 1), ((1, -2, 3), 0), ((1, 9, 6), 1), ((1, 0, -8), 1), ((1, 0, 2), 0), ((1, -8, 6), 0), ((1, 1, 9), 0), ((1, 0, 5), 0), ((1, -4, 9), 0), ((1, 8, 2), 1), ((1, 2, 6), 0)]"
      ],
      "execution_count": 696,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vKf7PnzCdj5f"
      },
      "source": [
        "### Visualizing the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AudcIhE7dnZL"
      },
      "source": [
        "def plotClasses(data): # Plots the data points according to if they are a positive or negative example (the class they belong to)\n",
        "  X = [x for (x,r) in data]\n",
        "  R = [r for (x,r) in data]\n",
        "\n",
        "  xNeg = [x for (x,r) in data if r == 0] # Negative examples\n",
        "  xPos = [x for (x,r) in data if r != 0] # Positive examples\n",
        "\n",
        "  x1Pos = [x[1] for x in xPos]\n",
        "  x2Pos = [x[2] for x in xPos]\n",
        "  x1Neg = [x[1] for x in xNeg]\n",
        "  x2Neg = [x[2] for x in xNeg]\n",
        "\n",
        "  plt.xlabel(\"x1\")\n",
        "  plt.ylabel(\"x2\")\n",
        "  plt.plot(x1Pos, x2Pos, \"g+\") # Positive examples shown as green plus symbols\n",
        "  plt.plot(x1Neg, x2Neg, \"ro\") # Negative examples shown as red dots\n",
        "  plt.show()"
      ],
      "execution_count": 697,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "COJR5TomfxIR",
        "outputId": "e9a4fae5-00ae-44b2-cd44-3ff00e5db9c6"
      },
      "source": [
        "plotClasses(data)"
      ],
      "execution_count": 698,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0I4HHXSlgoWc"
      },
      "source": [
        "### Building Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fTEzrKpngwyY"
      },
      "source": [
        "alpha = 0.01\n",
        "model = [0.01, 0.01, 0.01] # Initial model\n",
        "X = [x for (x,r) in data]\n",
        "R = [r for (x,r) in data]"
      ],
      "execution_count": 699,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LmSOB4kLioZD"
      },
      "source": [
        "def LogisticRegression(alpha, model, X, R, iterations): # Performs iterations of the Logistic Regression with Gradient Descent algorithm\n",
        "  dimensions = len(X[0]) # number of dimensions\n",
        "  N = len(X) # number of data points\n",
        "  for i in range(iterations):\n",
        "    deltaW = [0]*dimensions # initially, changes to each weight is 0\n",
        "    for t in range(N): # for each data point\n",
        "      yPredicted = sigmoid(F(model, X[t])) # calculate the predicted value using sigmoid(F(W,X)) with current model\n",
        "      for j in range(dimensions): # for each weight\n",
        "        deltaW[j] += -2 * (R[t] - yPredicted)*(yPredicted)*(1 - yPredicted)*X[t][j] # calculate the derivative (gradient) and increment change in weight by this amount\n",
        "    for j in range(dimensions): # for each weight\n",
        "      model[j] = model[j] - (1/N)*alpha*deltaW[j] # update current model by going in opposite direction of gradient\n",
        "  return model"
      ],
      "execution_count": 700,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2BHEKeK1mweE"
      },
      "source": [
        "model = LogisticRegression(alpha, model, X, R, 100)"
      ],
      "execution_count": 701,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HePLSCkZtnsv"
      },
      "source": [
        "#### <font color=\"green\">Final Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w4BRhLZ7nPn4",
        "outputId": "c945278c-8716-4c4d-9dfb-efc7ef564421"
      },
      "source": [
        "print(\"Model Learned:\", model) # Model after 100 iterations"
      ],
      "execution_count": 702,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model Learned: [0.05161759068489734, 0.3099093240157539, -0.16724731105964472]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HjYiV45PncNO"
      },
      "source": [
        "def plotModel(data, model): # Plots the original dataset with the line defined by the model included\n",
        "  X = [x for (x,r) in data]\n",
        "  R = [r for (x,r) in data]\n",
        "\n",
        "  xNeg = [x for (x,r) in data if r == 0]\n",
        "  xPos = [x for (x,r) in data if r != 0]\n",
        "\n",
        "  x1Pos = [x[1] for x in xPos]\n",
        "  x2Pos = [x[2] for x in xPos]\n",
        "  x1Neg = [x[1] for x in xNeg]\n",
        "  x2Neg = [x[2] for x in xNeg]\n",
        "\n",
        "  M = lambda W, X1: [(-W[0]/W[2]) - (W[1]/W[2]) * x1 for x1 in X1] # calculates the X2 values for a set of X1 values according to a model\n",
        "  modelX1 = [x[1] for x in X]\n",
        "  modelX2 = M(model, modelX1)\n",
        "\n",
        "  plt.xlabel(\"x1\")\n",
        "  plt.ylabel(\"x2\")\n",
        "  plt.plot(x1Pos, x2Pos, \"g+\")\n",
        "  plt.plot(x1Neg, x2Neg, \"ro\")\n",
        "  plt.plot(modelX1, modelX2, \"b\", linewidth=0.5) # Plot the model line in blue\n",
        "  plt.show()"
      ],
      "execution_count": 703,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "SoBE4vzwpirS",
        "outputId": "5d24dc09-e649-4e12-94d9-a5d6a0ee15b5"
      },
      "source": [
        "plotModel(data, model)"
      ],
      "execution_count": 704,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xaa27mAGuHVZ"
      },
      "source": [
        "The model creates a clear distinction between the two classes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_ald5Q5-jozE"
      },
      "source": [
        "#### Model Results on Original Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D4sX3mZBjr2U"
      },
      "source": [
        "def testModel(data, model): # Tests the model on the original data and prints out some statistics about its performance\n",
        "  X = [x for (x,r) in data]\n",
        "  R = [r for (x,r) in data]\n",
        "  R = [r if r == 0 else 1 for r in R] # Had to change R values !=0 to 1's to make things easier for iris dataset\n",
        "  N = len(X)\n",
        "  predictions = classify(model, X) # Classify according to the final model learned\n",
        "  truePos = sum([1 for (r,y) in zip(R, predictions) if r == y and r == 1])\n",
        "  trueNeg = sum([1 for (r,y) in zip(R, predictions) if r == y and r == 0])\n",
        "  falsePos = sum([1 for (r,y) in zip(R, predictions) if r != y and r == 0])\n",
        "  falseNeg = sum([1 for (r,y) in zip(R, predictions) if r != y and r == 1])\n",
        "  \n",
        "  accuracy = (truePos + trueNeg) / N # How often we got the correct result\n",
        "  precision = truePos / (truePos + falsePos) # How often we predicted positive and it actually was\n",
        "  recall = truePos / (truePos + falseNeg) # How many of the actual positive examples were classified positive\n",
        "  f1 = 2*recall*precision / (recall + precision) # Combination of recall and precision for overall performance\n",
        "\n",
        "  print(\"True Pos:\", truePos)\n",
        "  print(\"True Neg:\", trueNeg)\n",
        "  print(\"False Pos:\", falsePos)\n",
        "  print(\"False Neg:\", falseNeg)\n",
        "  print(\"Accuracy:\", accuracy)\n",
        "  print(\"Precision:\", precision)\n",
        "  print(\"Recall:\", recall)\n",
        "  print(\"F1:\", f1)"
      ],
      "execution_count": 705,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Wbmm1q-Cndls",
        "outputId": "9e6e4007-2a06-4db6-ed04-f5a5cd87aa01"
      },
      "source": [
        "testModel(data, model)"
      ],
      "execution_count": 706,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True Pos: 18\n",
            "True Neg: 12\n",
            "False Pos: 0\n",
            "False Neg: 0\n",
            "Accuracy: 1.0\n",
            "Precision: 1.0\n",
            "Recall: 1.0\n",
            "F1: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WyuvMBgauOM7"
      },
      "source": [
        "As expected, the model can classify the two classes perfectly on the original dataset."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mvcgJiKpdNmq"
      },
      "source": [
        "## Training Data 2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hkrXTvKudZqH"
      },
      "source": [
        "data = [((1, 0, 0), 0), ((1, 1, 7), 0), ((1, -3, -2), 0), ((1, 8, 9), 1), ((1, 4, 3), 1), ((1, 5, -2), 1), ((1, 0, 0), 0), ((1, 6, 9), 1), ((1, 4, 2), 1), ((1, 1, -9), 1), ((1, -7, 7), 0), ((1, 0, -1), 1), ((1, 9, -4), 1), ((1, 1, 0), 1), ((1, -2, -5), 1), ((1, 2, 3), 1), ((1, -7, 2), 0), ((1, -3, 0), 0), ((1, 5, 0), 1), ((1, 0, -3), 1), ((1, -2, 3), 0), ((1, 9, 6), 1), ((1, 0, -8), 1), ((1, 0, 2), 1), ((1, -8, 6), 0), ((1, 1, 9), 0), ((1, 0, 5), 0), ((1, -4, 9), 0), ((1, 8, 2), 1), ((1, 2, 6), 0)]"
      ],
      "execution_count": 707,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_esfDhJCgOdu"
      },
      "source": [
        "### Visualizing the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "nS3tc-a1gOd1",
        "outputId": "940e0906-03ac-4c2d-9a64-0978647c6e90"
      },
      "source": [
        "plotClasses(data)"
      ],
      "execution_count": 708,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cw65HsvYqa0r"
      },
      "source": [
        "### Building Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KBsfuYMLqa0x"
      },
      "source": [
        "alpha = 0.01\n",
        "model = [0.01, 0.01, 0.01] # Initial model\n",
        "X = [x for (x,r) in data]\n",
        "R = [r for (x,r) in data]"
      ],
      "execution_count": 709,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZBqAfRwdqa0x"
      },
      "source": [
        "model = LogisticRegression(alpha, model, X, R, 100)"
      ],
      "execution_count": 710,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IZQCqnqrty-b"
      },
      "source": [
        "#### <font color=\"green\">Final Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dv3JIfmcqa0x",
        "outputId": "1a7d1950-02a4-476b-8283-0e7b19b57bd5"
      },
      "source": [
        "print(\"Model Learned:\", model)  # Model after 100 iterations"
      ],
      "execution_count": 711,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model Learned: [0.03431692304020504, 0.3063478176860939, -0.15441062746292988]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "aUF3Ehszqa0x",
        "outputId": "c8b77139-359d-4a66-abc9-28322ef2eda7"
      },
      "source": [
        "plotModel(data, model)"
      ],
      "execution_count": 712,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VT_F3qHHuYKT"
      },
      "source": [
        "This time, there are a couple data points that make it impossible to draw a perfect separating line between the two classes."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2hI3hX6cnqrz"
      },
      "source": [
        "#### Model Results on Original Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Nqrruslmnqr4",
        "outputId": "7252b239-6f25-4602-bd94-f6ea61289683"
      },
      "source": [
        "testModel(data, model)"
      ],
      "execution_count": 713,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True Pos: 16\n",
            "True Neg: 11\n",
            "False Pos: 2\n",
            "False Neg: 1\n",
            "Accuracy: 0.9\n",
            "Precision: 0.8888888888888888\n",
            "Recall: 0.9411764705882353\n",
            "F1: 0.9142857142857143\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gOE7uP6xufWY"
      },
      "source": [
        "Predictably, the model misclassifies a few data points."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V2usa2rHdNs5"
      },
      "source": [
        "## Training Data 3"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HRAQWV33daQR"
      },
      "source": [
        "data = [((1, 2, 7), 0), ((1, 19, 72), 0), ((1, -39, -20), 0), ((1, 86, 95), 1), ((1, 45, 37), 1), ((1, 52, -23), 1), ((1, -8, -8), 0), ((1, 67, 93), 1), ((1, 46, 21), 1), ((1, 18, -97), 1), ((1, -78, 70), 0), ((1, -9, -17), 1), ((1, 94, -40), 1), ((1, 11, -3), 1), ((1, -24, -59), 1), ((1, 25, 33), 1), ((1, -71, 23), 0), ((1, -34, -7), 0), ((1, 55, -3), 1), ((1, -5, -33), 1), ((1, -22, 38), 0), ((1, 94, 66), 1), ((1, 4, -89), 1), ((1, -9, 26), 0), ((1, -83, 61), 0), ((1, 19, 98), 0), ((1, -1, 55), 0), ((1, -43, 90), 0), ((1, 86, 27), 1), ((1, 24, 69), 0)]"
      ],
      "execution_count": 714,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1CbrcuUigPrr"
      },
      "source": [
        "### Visualizing the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "q5Jjk3hVgPrr",
        "outputId": "13cb51cb-c220-40d6-e1d7-4146fda660de"
      },
      "source": [
        "plotClasses(data)"
      ],
      "execution_count": 715,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEGCAYAAACkQqisAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAXv0lEQVR4nO3df5DkdX3n8ecLjCaoKfDYQ6LsLhr0Dq3cqiOxyiCoGNFKSUjlPKgtRePdhovUxdxdJSh37ox1WxU1aFUuVyZrhYq5W39gEQLFGRWsLPkjhzKrBEEwLMgieytMtKJW4RFx3/dHf2fpHWZme3qn+/vtnuejqmu+/enu6TdfeufV38/38/18UlVIkjSME9ouQJI0uQwRSdLQDBFJ0tAMEUnS0AwRSdLQntZ2AaN06qmn1tatW9suQ5Imyr59+/6hqjYN8typDpGtW7cyPz/fdhmSNFGSHBj0uXZnSZKGZohIkoZmiEiShtZqiCS5JsmjSe7qa3tOkpuT3Nf8PKVpT5I/TLI/yZ1JXt5e5ZIkaP9I5M+AC5e0XQl8qarOAr7U3Ad4E3BWc9sBfGxMNUqSVtBqiFTV3wDfW9J8EfCJZvsTwK/2tf959dwGnJzk9PFUKk2IPXtg61Y44YTezz172q5IU67tI5HlnFZVh5rt7wCnNdvPA77d97yHm7ajJNmRZD7J/MLCwmgrlbpkzx7YsQMOHICq3s8dOwwSjVQXQ+SI6s1Tv6a56qtqd1XNVNXMpk0DXSsjTYerroLHHju67bHHeu3SiHQxRB5Z7KZqfj7atB8Ezuh73vObNkkADz20tnZNhNm9s22XsKouhsiNwGXN9mXADX3tb29Gab0K+H5ft5ekzZvX1q6JMHfrXNslrKrtIb6fAv4P8OIkDyd5F/D7wBuS3Adc0NwH+BzwALAf+DjwWy2ULHXXrl1w0klHt510Uq9dQ+v6kUDbMs3L487MzJRzZ2lD2bOndw7koYd6RyC7dsH27W1XNdEyF2rneP9Ozu6dXfYIZOd5O5k9f3bk759kX1XNDPRcQ0SSVtZGiLT9/msJkS6eE1HXeO2BNpjZvbNkLmQuAEe27dp6qqmeCl7rYPHag8Who4vXHoDdJJpas+fPHuk2avtIZOd5O1t770F4JKLVee2B1KpxnAM5HoaIVue1B9rgun4k0DZDRKvz2gNtcF0/EmibIaLVee2BpFUYIlrd9u2wezds2QJJ7+fu3Z5UlwQ4OkuD2L7d0JC0LI9EJElDM0QkSUMzRCRJQzNEJElDM0QkSUMzRCRJQzNEJElD6+R1IkleDHymr+kFwPuBk4F/Byw07e+rqs+NuTxJUqOTIVJV3wS2ASQ5ETgIXA+8E/hoVf1Bi+VJkhqT0J31euD+qjrQdiGSpKNNQohcAnyq7/4VSe5Mck2SU9oqSpLU8RBJ8nTgLcBnm6aPAS+k19V1CLh6mdfsSDKfZH5hYWHpw9J0cyljjVmnQwR4E/DVqnoEoKoeqaqfVNVh4OPAOUtfUFW7q2qmqmY2bdo05nKlFi0uZXzgAFQ9uZSxQaIR6nqIXEpfV1aS0/seuxi4a+wVgd/21E0uZawWdDZEkjwTeAPwF33NH0ry9SR3Aq8FfmfshfltT1016FLGfgnSOkpVtV3DyMzMzNT8/Pz6/tKtW3vBsdSWLfDgg+v7XtJaDPLZXPwS1H/EctJJLjSmoyTZV1Uzgzy3s0cinTXotz1p3AZZytguL60zQ2StNm9eW7s0LoMsZeyXoA1jdu/sWN7HEFmrQb7tSW3Zvr3XdXX4cO/n0i4qvwRtGHO3zo3lfQyRtRrk257UVX4J0jozRIZxrG97Ulf5JWiqze6dJXMhcwE4sj3Kri1HZ0nSFMpcqJ3D/X13dNbxchy9JA2kk1PBt2rpOPrFiwnBQ35JE2PneTvH8j52Zy3lxYSSNji7s46H4+glaWCGyFKOo5ekgRkiSzmOXpIGZogs5Th6DcMRfdqgHJ21nO3bDQ0NzhF92sA8EpGOlzPjagMzRKTj5Yg+bWCGiHS8HNGnDayzIZLkwWYp3DuSzDdtz0lyc5L7mp+ntF2n5Ig+bWSdDZHGa6tqW9+Vk1cCX6qqs4AvNfeldjmiTxvYpI3Ougg4v9n+BLAX+L22ipGOcESfNqguH4kU8MUk+5I04yU5raoONdvfAU5b+qIkO5LMJ5lfWFgYV62StCF1+Ujkl6rqYJJ/Dtyc5N7+B6uqkjxl9siq2g3sht4EjOMpVZI2ps4eiVTVwebno8D1wDnAI0lOB2h+PtpehZKkToZIkmcmefbiNvDLwF3AjcBlzdMuA25op0JJEnS3O+s04Pok0Kvxk1X1+SS3A9cmeRdwAHhrizVK0obXyRCpqgeAf7VM+3eB14+/IknScjrZnSVJmgyGiCRpaIaIJGlohogmk4tASZ1giGjyLC4CdeAAVD25CJRBMtFm9862XYKGYIho8rgI1FSau3Wu7RI0BENEk8dFoKTOMEQ0eVwEamrM7p0lcyFzATiybdfW5DBENHlcBGrdtP3Hevb8WWpnUTt7c6Uubs+e325dGpwhosnjIlDrxvMQOl6dnPZEOiYXgZo6O8/b2XYJGoJHItIG09XzEHZhTaZUTe+6TTMzMzU/P992GVJnZS5HzkdIi5Lsq6qZQZ7rkYgkaWiGiLSBeR6i+9ruZjwWQ0Tqt8Hm5PI8RPd1fQRd50IkyRlJ/jrJN5LcneS3m/bZJAeT3NHc3tx2rZoyzsklrVnnQgR4AvhPVXU28Crg3UnObh77aFVta26fa69ETSXn5FJHdHUE3XI6FyJVdaiqvtps/xC4B3heu1Udpw3WRTKxnJNLHTFJV/J3LkT6JdkKvAz4ctN0RZI7k1yT5JQVXrMjyXyS+YWFhTFVugq7SCaHc3JJa9bZEEnyLOA64D1V9QPgY8ALgW3AIeDq5V5XVburaqaqZjZt2jS2eldkF8nkcE6u1nWxu6ZtXR9B18mLDZP8FHAT8IWq+sgyj28Fbqqql672ezpxseEJJ/SOQJZK4PDh8dej1e3Z0wv4hx7qHYHs2uX0KmPkxY/dsJaLDTs3d1aSAH8K3NMfIElOr6pDzd2LgbvaqG/NNm/udWEt167ucU4uaU262J31auBtwOuWDOf9UJKvJ7kTeC3wO61WOSi7SKRVTdJIJD1VJ7uz1ksnurPALhJpQHZndcNEd2dNJbtIJE2pLnZnSdqguj4SSU9liEjqjC5eTKfVGSKSpKEZIpKkoRkikqShGSKSpKEZIpKkoRkikqShGSLSqLiOjDYAr1iXRmFxHZnFZQAW15EBZy/QVPFIRBoF15HRBmGISKPgUrvaIAwRaRRcalcbhCEijYLryGiDMESkUdi+HXbvhi1bekshb9nSu+9JdU2ZVUMkyc8meeEy7b8wupJWl+TCJN9Msj/JlW3VIR3T9u3w4INw+HDvpwGiKbRiiCR5K3AvcF2Su5O8su/hPxt1YSvUdCLwP4A3AWcDlyY5u41aJEmrH4m8D3hFVW0D3gn8zyQXN49l5JUt7xxgf1U9UFX/BHwauKilWiRpw1vtYsMTq+oQQFV9JclrgZuSnAG0tQjy84Bv991/GPjFlmqRpA1vtSORH/afD2kC5Xx63/xfMuK6hpZkR5L5JPMLCwttlyMdl9m9s22XMFHcX+O3Woj8e+CE/nMOVfVD4ELg3466sBUcBM7ou//8pu2IqtpdVTNVNbNp06axFiett7lb59ouYaK4v8ZvxRCpqr+rqvuAa5P8Xnp+BvgI8Ftjq/BotwNnJTkzydOBS4AbW6pFkja8Qa4T+UV63/7/lt4f8f8LvHqURa2kqp4ArgC+ANwDXFtVd7dRizQqs3tnyVzIXG/8yuK2XTXLc3+1K1WrnyNvvvHvAt4APAv4L1X16THUdtxmZmZqfn6+7TK0Z09v4sGHHupN+7Frl9dMDChzoXa2NY5l8ri/1keSfVU1M8hzBzkSuR34EfBK4Fx612Z89jjq00ayOCX6gQNQ9eSU6F1fW8O1QKSBDBIi76qq91fVj6vqUFVdhOchNKhJnBK9Q8G387ydY3/PSeb+Gr9jdmdNMruzOuCEE3p/iJdKetOBdNHWrb3gWGrLlt70JdKUW+/uLGl4kzglumuBSAMzRDRakzgl+iQGn9QSQ0SjNYlTok9i8EktWW3uLGl9bN/e7dBYarFWhyVLx2SISMuZtOCTWmJ3liRpaIaItAynzJAGY4hIy3A2WGkwhogkaWiGiI7PFM0x5Wyw0to57YmGtzjHVP/cWCed1P3rQAbgbLDayJz2ROMxiZMrSlpXhoiGN8VzTDkbbPfZzdgNhoiGN8VzTM2eP9t2CToGR9B1Q6dCJMmHk9yb5M4k1yc5uWnfmuRHSe5obn/cdq3COaYkdStEgJuBl1bVLwB/D7y377H7q2pbc7u8nfJ0lEmcXFETzRF03dPZ0VlJLgZ+vaq2J9kK3FRVL13L73B0ljS9HEE3OtMyOus3gL/qu39mkq8luTXJuSu9KMmOJPNJ5hcWFkZfpSRtYGOfxTfJLcBzl3noqqq6oXnOVcATwOKVa4eAzVX13SSvAP4yyUuq6gdLf0lV7QZ2Q+9IZBT/DZLa5wi6bhh7iFTVBas9nuQdwK8Ar6+mr62qHgceb7b3JbkfeBFgX5W0QTmCrhs61Z2V5ELgd4G3VNVjfe2bkpzYbL8AOAt4oJ0qJUmLurYo1R8BzwBuTgJwWzMS6zXAB5L8GDgMXF5V32uvTEkSdCxEqurnV2i/DrhuzOVIy5rdO2tXitToVHeWNAm8Ulp6kiEiSRqaISINwCulpeV19or19eAV6xoFr5TWtJuWK9YlSR1niEhr5JXS0pMMEWmNHN6rSTCu83WGiCRNoXENRTdEJElDM0QkaUq0MRTdIb6SNIWOZyi6Q3wlSWNhiEjSFBrXUHRDRJKm0LiGohsikqShGSKSpKF1LkSSzCY5mOSO5vbmvsfem2R/km8meWObdUqSOrayYZ+PVtUf9DckORu4BHgJ8HPALUleVFU/aaNASVIHj0RWcRHw6ap6vKq+BewHzmm5Jkna0LoaIlckuTPJNUlOadqeB3y77zkPN21HSbIjyXyS+YWFhXHUKkkbVishkuSWJHctc7sI+BjwQmAbcAi4ei2/u6p2V9VMVc1s2rRpBNVLkha1ck6kqi4Y5HlJPg7c1Nw9CJzR9/DzmzZJUks6152V5PS+uxcDdzXbNwKXJHlGkjOBs4CvjLs+SdKTujg660NJtgEFPAj8JkBV3Z3kWuAbwBPAux2ZJUnt6lyIVNXbVnlsF7BrjOVIklbRue4saTXjWvJT0mAMEU2UcS35KWkwhogkaWiGiDqvjSU/JQ3G5XE1UY5nyU9Jg3F5XEnSWBgimijjWvJT0mAMEU2UcS35KWkwhogkaWiGiCRpaIaIJGlohogkaWiGiCRpaIaIJGlohogkaWiGiCRpaJ1alCrJZ4AXN3dPBv6xqrYl2QrcA3yzeey2qrp8/BVKkvp1KkSq6t8sbie5Gvh+38P3V9W28VclSVpJp0JkUZIAbwVe13YtkqSVdfWcyLnAI1V1X1/bmUm+luTWJOe2VZgk6UljPxJJcgvw3GUeuqqqbmi2LwU+1ffYIWBzVX03ySuAv0zykqr6wTK/fwewA2Dz5s3rW7wk6ShjD5GqumC1x5M8Dfg14BV9r3kceLzZ3pfkfuBFwFNWnKqq3cBu6C1KtX6VS5KW6mJ31gXAvVX18GJDkk1JTmy2XwCcBTzQUn2SpEYXT6xfwtFdWQCvAT6Q5MfAYeDyqvre2CuTJB2lcyFSVe9Ypu064LrxVyNJWk0Xu7MkSRPCEJEkDc0QkSQNzRCRJA3NEJEkDc0QkSQNzRCRxmh272zbJUjryhCRxmju1rm2S5DWlSEiSRqaISKN2OzeWTIXMheAI9t2bWkapGp6J7qdmZmp+fmnTPQrtSZzoXZO7785TYck+6pqZpDneiQiSRqaISKN0c7zdrZdgrSuDBFpjGbPn227BGldGSLSFPFkvcbNEJGmiNehaNwMEUnS0FoJkST/OsndSQ4nmVny2HuT7E/yzSRv7Gu/sGnbn+TK8VctdZPXoahNrVwnkuRf0lsr/U+A/1xV80372fTWVz8H+DngFuBFzcv+HngD8DBwO3BpVX1jtffxOhFtNF6HovWwlutEWlljvaruAUiy9KGLgE9X1ePAt5LspxcoAPur6oHmdZ9unrtqiEiSRqtr50SeB3y77/7DTdtK7U+RZEeS+STzCwsLIytU6iKvQ9G4jexIJMktwHOXeeiqqrphVO9bVbuB3dDrzhrV+0hd5HUoGreRhUhVXTDEyw4CZ/Tdf37TxirtkqSWdK0760bgkiTPSHImcBbwFXon0s9KcmaSpwOXNM+VJLWolRPrSS4G/juwCfjfSe6oqjdW1d1JrqV3wvwJ4N1V9ZPmNVcAXwBOBK6pqrvbqF2S9CSngpckHcWp4CVJYzHVRyJJFoADY37bU4F/GPN7DstaR8NaR8NaR2O5WrdU1aZBXjzVIdKGJPODHga2zVpHw1pHw1pH43hrtTtLkjQ0Q0SSNDRDZP3tbruANbDW0bDW0bDW0TiuWj0nIkkamkcikqShGSKSpKEZIuskyWeS3NHcHkxyR9O+NcmP+h774w7UOpvkYF9Nb+57bNmVJduS5MNJ7k1yZ5Lrk5zctHduv0K3V+BMckaSv07yjWZl0d9u2lf8PLSp+Xf09aamxYXrnpPk5iT3NT9P6UCdL+7bd3ck+UGS93Rlvya5JsmjSe7qa1t2P6bnD5vP751JXn7MN6gqb+t8A64G3t9sbwXuarumJfXN0ltRcmn72cDfAc8AzgTuB05sudZfBp7WbH8Q+GCH9+uJzT57AfD0Zl+e3XZdffWdDry82X42vdVCz17p89D2DXgQOHVJ24eAK5vtKxc/D125NZ+B7wBburJfgdcAL+//97LSfgTeDPwVEOBVwJeP9fs9Elln6S3X+FZ6y/xOmiMrS1bVt4D+lSVbUVVfrKonmru30VsGoKvOoVmBs6r+CVhcgbMTqupQVX212f4hcA8rLO7WYRcBn2i2PwH8aou1LOf1wP1VNe6ZMlZUVX8DfG9J80r78SLgz6vnNuDkJKev9vsNkfV3LvBIVd3X13Zmkq8luTXJuW0VtsQVzeHqNX1dAgOvINmS36D3LWlR1/Zr1/ffEUm2Ai8Dvtw0Lfd5aFsBX0yyL8mOpu20qjrUbH8HOK2d0lZ0CUd/gezifoWV9+OaP8OGyBokuSXJXcvc+r9tXsrRH6JDwOaqehnwH4FPJvnZlmv9GPBCYFtT39Wjruc4al18zlX0lgfY0zS1sl+nQZJnAdcB76mqH9Cxz0OfX6qqlwNvAt6d5DX9D1av/6Uz1yikt9bRW4DPNk1d3a9HOd792Mp6IpOqjrFaY5KnAb8GvKLvNY8Djzfb+5LcD7wIGOkc9ceqdVGSjwM3NXdXW1lyZAbYr+8AfgV4ffOBb22/HkMr+28tkvwUvQDZU1V/AVBVj/Q93v95aFVVHWx+PprkenrdhY8kOb2qDjXdLI+2WuTR3gR8dXF/dnW/Nlbaj2v+DHsksr4uAO6tqocXG5JsSnJis/0Ceqs1PtBSfYs19fdxXgwsjtpYaWXJ1iS5EPhd4C1V9Vhfe+f2Kx1fgbM5X/enwD1V9ZG+9pU+D61J8swkz17cpjfA4i56+/Oy5mmXATe0U+GyjuqF6OJ+7bPSfrwReHszSutVwPf7ur2W5ZHI+lraHwq9kREfSPJj4DBweVUtPck1bh9Kso3eIeyDwG8C1CorS7boj+iNFru59zeQ26rqcjq4X6vqiXR7Bc5XA28Dvp5mCDrwPuDS5T4PLTsNuL75f/404JNV9fkktwPXJnkXvWUe3tpijUc0QfcGjt53y/47G7cknwLOB05N8jCwE/h9lt+Pn6M3Qms/8BjwzmP+/qZ3QJKkNbM7S5I0NENEkjQ0Q0SSNDRDRJI0NENEkjQ0Q0RqSZLPJ/nHJF26CE1aE0NEas+H6V23IU0sQ0QasSSvbCbh++nmSuy7k7y0qr4E/LDt+qTj4RXr0ohV1e1JbgT+G/AzwP+qqi5NgSENzRCRxuMD9ObW+n/Af2i5Fmnd2J0ljcc/A55Fb0XBn265FmndGCLSePwJ8F/prYfywZZrkdaN3VnSiCV5O/DjqvpkM3393yZ5HTAH/AvgWc3squ+qqi+0Wau0Vs7iK0kamt1ZkqShGSKSpKEZIpKkoRkikqShGSKSpKEZIpKkoRkikqSh/X9Tm7ixPcqjhQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3HWcOZWWqhE7"
      },
      "source": [
        "### Building Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bmnPu4jbqhE7"
      },
      "source": [
        "alpha = 0.01\n",
        "model = [0.01, 0.01, 0.01] # Initial model\n",
        "X = [x for (x,r) in data]\n",
        "R = [r for (x,r) in data]"
      ],
      "execution_count": 716,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W6ylrvXaqhE7"
      },
      "source": [
        "model = LogisticRegression(alpha, model, X, R, 100)"
      ],
      "execution_count": 717,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YWBxMplztzzK"
      },
      "source": [
        "#### <font color=\"green\">Final Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7luU4yE7qhE7",
        "outputId": "a753f6be-d3d0-411f-b7a9-838b2fb7ef7d"
      },
      "source": [
        "print(\"Model Learned:\", model)  # Model after 100 iterations"
      ],
      "execution_count": 718,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model Learned: [0.013023555787017707, 0.18933092869711407, -0.11157264987117092]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "qOc2i1K1qhE8",
        "outputId": "00581917-a5f1-4fb8-a201-b4620ed837a5"
      },
      "source": [
        "plotModel(data, model)"
      ],
      "execution_count": 719,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hmDnpzDUupcA"
      },
      "source": [
        "The model is very close to not being able to classify a few of the data points, but it seems to have learned just enough."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "78VEgav2nr3W"
      },
      "source": [
        "#### Model Results on Original Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HRJt3KXDnr3W",
        "outputId": "f8f7d51c-166b-40fe-8e01-467a71e249ef"
      },
      "source": [
        "testModel(data, model)"
      ],
      "execution_count": 720,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True Pos: 16\n",
            "True Neg: 14\n",
            "False Pos: 0\n",
            "False Neg: 0\n",
            "Accuracy: 1.0\n",
            "Precision: 1.0\n",
            "Recall: 1.0\n",
            "F1: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XT3aCpoiuzHS"
      },
      "source": [
        "The model ended up being able to classify all of the points perfectly."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q6JcE_fEdNxc"
      },
      "source": [
        "## Training Data 4"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "t_jWEKQQcY7E"
      },
      "source": [
        "data = [((1, 5.1, 3.5), 0), ((1, 4.9, 3.0), 0), ((1, 4.7, 3.2), 0), ((1, 4.6, 3.1), 0), ((1, 5.0, 3.6), 0), ((1, 5.4, 3.9), 0), ((1, 4.6, 3.4), 0), ((1, 5.0, 3.4), 0), ((1, 4.4, 2.9), 0), ((1, 4.9, 3.1), 0), ((1, 5.4, 3.7), 0), ((1, 4.8, 3.4), 0), ((1, 4.8, 3.0), 0), ((1, 4.3, 3.0), 0), ((1, 5.8, 4.0), 0), ((1, 5.7, 4.4), 0), ((1, 5.4, 3.9), 0), ((1, 5.1, 3.5), 0), ((1, 5.7, 3.8), 0), ((1, 5.1, 3.8), 0), ((1, 5.4, 3.4), 0), ((1, 5.1, 3.7), 0), ((1, 4.6, 3.6), 0), ((1, 5.1, 3.3), 0), ((1, 4.8, 3.4), 0), ((1, 5.0, 3.0), 0), ((1, 5.0, 3.4), 0), ((1, 5.2, 3.5), 0), ((1, 5.2, 3.4), 0), ((1, 4.7, 3.2), 0), ((1, 4.8, 3.1), 0), ((1, 5.4, 3.4), 0), ((1, 5.2, 4.1), 0), ((1, 5.5, 4.2), 0), ((1, 4.9, 3.1), 0), ((1, 5.0, 3.2), 0), ((1, 5.5, 3.5), 0), ((1, 4.9, 3.6), 0), ((1, 4.4, 3.0), 0), ((1, 5.1, 3.4), 0), ((1, 5.0, 3.5), 0), ((1, 4.5, 2.3), 0), ((1, 4.4, 3.2), 0), ((1, 5.0, 3.5), 0), ((1, 5.1, 3.8), 0), ((1, 4.8, 3.0), 0), ((1, 5.1, 3.8), 0), ((1, 4.6, 3.2), 0), ((1, 5.3, 3.7), 0), ((1, 5.0, 3.3), 0), ((1, 7.0, 3.2), 1), ((1, 6.4, 3.2), 1), ((1, 6.9, 3.1), 1), ((1, 5.5, 2.3), 1), ((1, 6.5, 2.8), 1), ((1, 5.7, 2.8), 1), ((1, 6.3, 3.3), 1), ((1, 4.9, 2.4), 1), ((1, 6.6, 2.9), 1), ((1, 5.2, 2.7), 1), ((1, 5.0, 2.0), 1), ((1, 5.9, 3.0), 1), ((1, 6.0, 2.2), 1), ((1, 6.1, 2.9), 1), ((1, 5.6, 2.9), 1), ((1, 6.7, 3.1), 1), ((1, 5.6, 3.0), 1), ((1, 5.8, 2.7), 1), ((1, 6.2, 2.2), 1), ((1, 5.6, 2.5), 1), ((1, 5.9, 3.2), 1), ((1, 6.1, 2.8), 1), ((1, 6.3, 2.5), 1), ((1, 6.1, 2.8), 1), ((1, 6.4, 2.9), 1), ((1, 6.6, 3.0), 1), ((1, 6.8, 2.8), 1), ((1, 6.7, 3.0), 1), ((1, 6.0, 2.9), 1), ((1, 5.7, 2.6), 1), ((1, 5.5, 2.4), 1), ((1, 5.5, 2.4), 1), ((1, 5.8, 2.7), 1), ((1, 6.0, 2.7), 1), ((1, 5.4, 3.0), 1), ((1, 6.0, 3.4), 1), ((1, 6.7, 3.1), 1), ((1, 6.3, 2.3), 1), ((1, 5.6, 3.0), 1), ((1, 5.5, 2.5), 1), ((1, 5.5, 2.6), 1), ((1, 6.1, 3.0), 1), ((1, 5.8, 2.6), 1), ((1, 5.0, 2.3), 1), ((1, 5.6, 2.7), 1), ((1, 5.7, 3.0), 1), ((1, 5.7, 2.9), 1), ((1, 6.2, 2.9), 1), ((1, 5.1, 2.5), 1), ((1, 5.7, 2.8), 1), ((1, 6.3, 3.3), 2), ((1, 5.8, 2.7), 2), ((1, 7.1, 3.0), 2), ((1, 6.3, 2.9), 2), ((1, 6.5, 3.0), 2), ((1, 7.6, 3.0), 2), ((1, 4.9, 2.5), 2), ((1, 7.3, 2.9), 2), ((1, 6.7, 2.5), 2), ((1, 7.2, 3.6), 2), ((1, 6.5, 3.2), 2), ((1, 6.4, 2.7), 2), ((1, 6.8, 3.0), 2), ((1, 5.7, 2.5), 2), ((1, 5.8, 2.8), 2), ((1, 6.4, 3.2), 2), ((1, 6.5, 3.0), 2), ((1, 7.7, 3.8), 2), ((1, 7.7, 2.6), 2), ((1, 6.0, 2.2), 2), ((1, 6.9, 3.2), 2), ((1, 5.6, 2.8), 2), ((1, 7.7, 2.8), 2), ((1, 6.3, 2.7), 2), ((1, 6.7, 3.3), 2), ((1, 7.2, 3.2), 2), ((1, 6.2, 2.8), 2), ((1, 6.1, 3.0), 2), ((1, 6.4, 2.8), 2), ((1, 7.2, 3.0), 2), ((1, 7.4, 2.8), 2), ((1, 7.9, 3.8), 2), ((1, 6.4, 2.8), 2), ((1, 6.3, 2.8), 2), ((1, 6.1, 2.6), 2), ((1, 7.7, 3.0), 2), ((1, 6.3, 3.4), 2), ((1, 6.4, 3.1), 2), ((1, 6.0, 3.0), 2), ((1, 6.9, 3.1), 2), ((1, 6.7, 3.1), 2), ((1, 6.9, 3.1), 2), ((1, 5.8, 2.7), 2), ((1, 6.8, 3.2), 2), ((1, 6.7, 3.3), 2), ((1, 6.7, 3.0), 2), ((1, 6.3, 2.5), 2), ((1, 6.5, 3.0), 2), ((1, 6.2, 3.4), 2), ((1, 5.9, 3.0), 2)]"
      ],
      "execution_count": 721,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8EHOUwTNgQGi"
      },
      "source": [
        "### Visualizing the Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "YaVmBUVJgQGj",
        "outputId": "51368d70-0897-4dd8-d98a-43a3aad7128c"
      },
      "source": [
        "plotClasses(data)"
      ],
      "execution_count": 722,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iuwML84zwkhR"
      },
      "source": [
        "The negative examples (0) are represented in red as usual. The other examples (1 and 2) are represented together as positive examples in green."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7IC-6dEtw0AR"
      },
      "source": [
        "def plotAllClasses(data):\n",
        "  X = [x for (x,r) in data]\n",
        "  R = [r for (x,r) in data]\n",
        "\n",
        "  random.seed(38)\n",
        "  plt.xlabel(\"x1\")\n",
        "  plt.ylabel(\"x2\")\n",
        "  classes = list(set(R)) # remove duplicates to just get classes\n",
        "  for i in classes:\n",
        "    Xr = [x for (x,r) in data if r == i]\n",
        "    x1r = [x[1] for x in Xr]\n",
        "    x2r = [x[2] for x in Xr]\n",
        "    rgb = [random.random(),random.random(),random.random()]\n",
        "    plt.plot(x1r, x2r, c=rgb, marker=\"o\", linestyle=\"\")\n",
        "  plt.show()"
      ],
      "execution_count": 723,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "EHnZTgzYyeR2",
        "outputId": "46437bbd-df56-4022-b388-c1ba0f6bcae6"
      },
      "source": [
        "plotAllClasses(data)"
      ],
      "execution_count": 724,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jpuS71odz9mF"
      },
      "source": [
        "This is the dataset with all classes as a different color."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B75l24vpqjf5"
      },
      "source": [
        "### Building Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "--6Rdpcau9Eo"
      },
      "source": [
        "It should be noted that I had to increase the learning rate drastically for this dataset. 0.5 seemed to be a good round value that doesn't start to diverge."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BjUp0kDkqjf5"
      },
      "source": [
        "alpha = 0.5\n",
        "model = [0.01, 0.01, 0.01] # Initial model\n",
        "X = [x for (x,r) in data]\n",
        "R = [r for (x,r) in data]"
      ],
      "execution_count": 725,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3n9Tfy_Sqjf5"
      },
      "source": [
        "model = LogisticRegression(alpha, model, X, R, 10000)"
      ],
      "execution_count": 726,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aNYoSVJ-vHHW"
      },
      "source": [
        "I'm doing a lot more iterations because the learning was still too slow for only 100 iterations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EIH3P5rct078"
      },
      "source": [
        "#### <font color=\"green\">Final Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ZgXv5IHRqjf5",
        "outputId": "90e68720-f5f4-4593-ae5b-334d5836ddf3"
      },
      "source": [
        "print(\"Model Learned:\", model)  # Model after 10,000 iterations"
      ],
      "execution_count": 727,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Model Learned: [-3.7686443761585244, 7.063889117104098, -10.822021573606472]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "sflxi-tEqjf5",
        "outputId": "5bbb9c54-0e87-4d7e-847a-7c90f22ca8cc"
      },
      "source": [
        "plotModel(data, model)"
      ],
      "execution_count": 728,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t1qBYpf9vQEq"
      },
      "source": [
        "The model can separate the two classes aside from one point that seems to be a bit of an outlier. With enough iterations or an increased learning rate, the model can adjust for this point, but it takes a lot longer."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eamMRVK5ntBA"
      },
      "source": [
        "#### Model Results on Original Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KaGGgp19ntBB",
        "outputId": "825cceb4-7d32-4a71-fa15-929ccda2682b"
      },
      "source": [
        "testModel(data, model)"
      ],
      "execution_count": 729,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True Pos: 100\n",
            "True Neg: 49\n",
            "False Pos: 1\n",
            "False Neg: 0\n",
            "Accuracy: 0.9933333333333333\n",
            "Precision: 0.9900990099009901\n",
            "Recall: 1.0\n",
            "F1: 0.9950248756218906\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2Vb5EiOTwTtp"
      },
      "source": [
        "Overall, the model does essentially a perfect job of classifying the 0 class vs the rest of the classes (1 and 2), but misses that single example."
      ]
    }
  ]
}