2023_2024_stumps_trees_forests_SV.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/alixland/GMIC/blob/master/2023_2024_stumps_trees_forests_SV.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qPmhOuVYcG3F"
      },
      "source": [
        "# Stumps, trees and forests\n",
        "\n",
        "** Ecole Centrale Nantes **\n",
        "\n",
        "** Diana Mateus **"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nrw54JTccG3H"
      },
      "source": [
        "PARTICIPANTS: Elisa Bouchut, Alix Landemaine"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "hdy4QirrcG3J"
      },
      "outputs": [],
      "source": [
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6Atthmp5cG3K"
      },
      "source": [
        "## 1. Decision stumps\n",
        "A decision stump is a machine learning model consisting of a one-level decision tree. That is, it is a decision tree with one internal node (the root) which is immediately connected to the terminal nodes (its leaves). A decision stump makes a prediction based on the value of just a single input feature. Sometimes they are also called 1-rules [Wikipedia]\n",
        "\n",
        "***a)*** Run the provided code to generate and plot a toy dataset consisting of 2D points and 4 classes\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "hW4QwWcycG3L",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 490
        },
        "outputId": "c1c1035b-00ca-4a0b-952a-580f0be76407"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-3-257ef14297e9>:8: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.\n",
            "  plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.get_cmap('rainbow', 4));\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "#a) Load and plot dataset, split in train and test sets\n",
        "from sklearn.datasets import make_blobs\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "n_classes = 4\n",
        "X, y = make_blobs(n_samples=300, centers=n_classes,\n",
        "                  random_state=0, cluster_std=1.0)\n",
        "plt.scatter(X[:, 0], X[:, 1], c=y, s=50, cmap=plt.cm.get_cmap('rainbow', 4));\n",
        "plt.colorbar();\n",
        "\n",
        "Xtrain, Xtest, ytrain, ytest = train_test_split(X, y, random_state=0)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LkOD_MbbcG3M"
      },
      "source": [
        "\n",
        "**b)** Observe the functions **stump** and **split**.\n",
        "\n",
        "**stump** is a function that generates the parameters of a random axis-aligned split  according to the number of features of a given dataset. The function receives the data matrix Xtrain and returns\n",
        "    - the index of one randomly chosen feature (one dimension)\n",
        "    - as well as a randomly chosen threshold within the min and max values of the chosen feature.\n",
        "\n",
        "**split**  receives as input:\n",
        "    - A dataset of points\n",
        "    - the parameters generated by the stump function above.\n",
        "The function then partitions the *dataset* in two subsets according to the threshold of the chosen dimension.\n",
        "The output are two arrays, each containing the _indices_ of the points belonging to one or the other subset.\n",
        "\n",
        "**c)** Run the split function **several times**, and display the resulting subsets as 2D scatter plots with circles of different colors for each class. Use the provided plotting functions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "Q2UQmyrdcG3M",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 554
        },
        "outputId": "ef9bced1-1845-4423-e2a6-96dcae70b13b"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Stump parameters 0 3.788152055855357\n",
            "Sizes: original set: 225  left subset: (223,)  right subset: (2,)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-6-b53318550903>:24: MatplotlibDeprecationWarning: The get_cmap function was deprecated in Matplotlib 3.7 and will be removed two minor releases later. Use ``matplotlib.colormaps[name]`` or ``matplotlib.colormaps.get_cmap(obj)`` instead.\n",
            "  plt.scatter(X0_c,X1_c, s=50,alpha=0.5,cmap=plt.cm.get_cmap('rainbow', 4),label=str(c))\n",
            "<ipython-input-6-b53318550903>:24: UserWarning: No data for colormapping provided via 'c'. Parameters 'cmap' will be ignored\n",
            "  plt.scatter(X0_c,X1_c, s=50,alpha=0.5,cmap=plt.cm.get_cmap('rainbow', 4),label=str(c))\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from random import randint, uniform\n",
        "\n",
        "# b) Stumps and Split\n",
        "\n",
        "def stump(X):\n",
        "    f = randint(0, X.shape[1]-1) #randomly select a feature/dimension randint()\n",
        "    t = uniform(np.min(X[:,f]),np.max(X[:,f])) #sample from an uniform() between the min and max values of the feature\n",
        "    return f,t\n",
        "\n",
        "\n",
        "def split(X, f, t):\n",
        "    ind_l, = np.where(X[:,f]<=t)\n",
        "    ind_r, = np.where(X[:,f]>t)\n",
        "    return ind_l, ind_r\n",
        "\n",
        "# c) Plotting a stump\n",
        "\n",
        "def plot_stump (Xtrain,ytrain,feat,th,ind_l,ind_r):\n",
        "    n_classes=np.max(ytrain)+1;\n",
        "    #print(n_classes)\n",
        "    for c in range(n_classes):\n",
        "        X0_c=Xtrain[np.where(ytrain==c), 0] #first coordinate of points belonging to class c\n",
        "        X1_c=Xtrain[np.where(ytrain==c), 1] #second coordinate of points belonging to class c\n",
        "        plt.scatter(X0_c,X1_c, s=50,alpha=0.5,cmap=plt.cm.get_cmap('rainbow', 4),label=str(c))\n",
        "\n",
        "    #plt.axis('equal')\n",
        "\n",
        "    #draw the points on the left and right child as circles around the original training dataset\n",
        "    plt.scatter(Xtrain[ind_l, 0], Xtrain[ind_l, 1], c='none', edgecolor='r')\n",
        "    plt.scatter(Xtrain[ind_r, 0], Xtrain[ind_r, 1], c='none', edgecolor='b')\n",
        "\n",
        "    #draw threshold line\n",
        "    if feat == 0:\n",
        "        plt.plot([th,th],[np.min(Xtrain[:,1]),np.max(Xtrain[:,1])])\n",
        "    elif feat == 1:\n",
        "        plt.plot([np.min(Xtrain[:,0]),np.max(Xtrain[:,0])],[th,th])\n",
        "    leg = plt.legend();\n",
        "\n",
        "\n",
        "feat, th = stump(Xtrain)\n",
        "print('Stump parameters', feat, th)\n",
        "ind_l,ind_r = split(Xtrain, feat, th)\n",
        "print('Sizes: original set:', len(ytrain),\n",
        "      ' left subset:' ,  ind_l.shape,\n",
        "      ' right subset:', ind_r.shape)\n",
        "\n",
        "\n",
        "plot_stump(Xtrain,ytrain,feat,th,ind_l,ind_r)\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "FeDvn9jECgi5"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "26Un2mCecG3N"
      },
      "source": [
        "**d)** Implement a function ***class_distributions*** that given a set of points reaching a node returns the posterior class distribution of the node (approximated as the normalized histogram with #points per class).\n",
        "\n",
        "``` python\n",
        "def class_distributions(ytrain,num_classes):\n",
        "```\n",
        "\n",
        "Compute the class distributions of:\n",
        "    - of the original training set (before the split),\n",
        "    - of each of the 2 subsets resulting from after the split has been applied.\n",
        "\n",
        "Plot the histograms of the children nodes\n",
        "\n",
        "**e)** Create a function to compute the ***information_gain*** of a split. The function should receive the full training dataset (Xtrain and ytrain) and the indices of two subsets resulting from the current split.\n",
        "\n",
        "``` python\n",
        "def information_gain(ytrain,ind_left, ind_right,num_classes):\n",
        "```\n",
        "```Hint: ```  when computing the Entropy, ignore the classes with zero probabilities, and carry on summation using the same equation.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "83El46MxcG3O",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "5c65220e-39e1-439e-c340-5ecaa2f15cfe"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "def class_distributions(ytrain,num_classes):\n",
        "  hist=np.histogram(ytrain, bins=num_classes)\n",
        "  x=np.arange(0, num_classes, 1, dtype=int)\n",
        "\n",
        "  return (x,hist[0]/sum(hist[0]))\n",
        "\n",
        "num_classes=4\n",
        "x,hist=class_distributions(ytrain,num_classes)\n",
        "plt.bar(x,hist,width=0.5)\n",
        "plt.title('ytrain')\n",
        "plt.show()\n",
        "\n",
        "x,hist=class_distributions(ind_l,num_classes)\n",
        "plt.bar(x,hist,width=0.5)\n",
        "plt.title('ind_l')\n",
        "plt.show()\n",
        "\n",
        "x,hist=class_distributions(ind_r,num_classes)\n",
        "plt.bar(x,hist,width=0.5)\n",
        "plt.title('ind_r')\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "j1Hh9GtccG3O",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c8dec514-6ab8-46c5-cd99-f5baaeeed208"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.018244845287104905\n"
          ]
        }
      ],
      "source": [
        "def information_gain(ytrain,ind_left, ind_right,num_classes):\n",
        "  x,hist=class_distributions(ytrain,num_classes)\n",
        "  n=len(ytrain)\n",
        "  entropie_x=0\n",
        "  for i in x:\n",
        "    if hist[i]!=0:\n",
        "      entropie_x+=-hist[i]*np.log2(hist[i])\n",
        "  f_l=[]\n",
        "  for i in ind_left:\n",
        "    f_l.append(ytrain[i])\n",
        "  f_r=[]\n",
        "  for i in ind_right:\n",
        "    f_r.append(ytrain[i])\n",
        "  xl,hist_l=class_distributions(f_l,num_classes)\n",
        "  xr,hist_r=class_distributions(f_r,num_classes)\n",
        "  entropie_l=0\n",
        "  for i in xl:\n",
        "    if hist_l[i]!=0:\n",
        "      entropie_l+=-hist_l[i]*np.log2(hist_l[i])\n",
        "  entropie_r=0\n",
        "  for i in xr:\n",
        "    if hist_r[i]!=0:\n",
        "      entropie_r+=-hist_r[i]*np.log2(hist_r[i])\n",
        "\n",
        "  gain=entropie_x-len(f_l)/n*entropie_l-len(f_r)/n*entropie_r\n",
        "  return(gain)\n",
        "\n",
        "\n",
        "\n",
        "f,t=stump(Xtrain)\n",
        "ind_left,ind_right=split(Xtrain,f,t)\n",
        "\n",
        "print(information_gain(ytrain,ind_left,ind_right,4))\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jni23uJ2cG3P"
      },
      "source": [
        "**f)** Create a function ***train*** to perfom a *randomized node optimization*. The function receives as parameters the full training dataset (Xtrain and ytrain) as well as the number of random stumps to try. The function will\n",
        "- generate the desired number of stumps,\n",
        "- split the dataset according to each stump,\n",
        "- evaluate the ***information gain*** for each split\n",
        "- choose and then return the parameters of the best stump.\n",
        "\n",
        "``` python\n",
        "def train_stumps(Xtrain, ytrain, trials):\n",
        "```\n",
        "\n",
        "Print the progress of the information gain during the training process\n",
        "\n",
        "**g)** Make predictions with the trained model and display the restuls"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "QZ4RNQgHcG3P",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d6da23c4-a0d2-494d-dc95-2f0528aebcb7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Trial 1/100, Feature: 1, Threshold: -0.53, Info Gain: 0.0559\n",
            "Trial 2/100, Feature: 0, Threshold: -2.27, Info Gain: 0.1140\n",
            "Trial 3/100, Feature: 1, Threshold: 6.23, Info Gain: 0.6229\n",
            "Trial 4/100, Feature: 1, Threshold: 4.84, Info Gain: 0.6203\n",
            "Trial 5/100, Feature: 0, Threshold: -0.05, Info Gain: 0.6573\n",
            "Trial 6/100, Feature: 0, Threshold: -3.39, Info Gain: 0.0311\n",
            "Trial 7/100, Feature: 1, Threshold: 9.23, Info Gain: 0.0350\n",
            "Trial 8/100, Feature: 1, Threshold: 3.21, Info Gain: 0.6207\n",
            "Trial 9/100, Feature: 1, Threshold: 4.03, Info Gain: 0.6699\n",
            "Trial 10/100, Feature: 1, Threshold: 3.56, Info Gain: 0.6566\n",
            "Trial 11/100, Feature: 0, Threshold: -3.30, Info Gain: 0.0354\n",
            "Trial 12/100, Feature: 0, Threshold: 0.01, Info Gain: 0.6920\n",
            "Trial 13/100, Feature: 1, Threshold: 5.48, Info Gain: 0.6391\n",
            "Trial 14/100, Feature: 0, Threshold: 3.13, Info Gain: 0.0379\n",
            "Trial 15/100, Feature: 1, Threshold: 4.74, Info Gain: 0.6563\n",
            "Trial 16/100, Feature: 0, Threshold: 1.49, Info Gain: 0.3005\n",
            "Trial 17/100, Feature: 0, Threshold: -0.94, Info Gain: 0.4487\n",
            "Trial 18/100, Feature: 1, Threshold: 2.07, Info Gain: 0.5320\n",
            "Trial 19/100, Feature: 0, Threshold: 2.50, Info Gain: 0.1209\n",
            "Trial 20/100, Feature: 1, Threshold: 4.57, Info Gain: 0.6320\n",
            "Trial 21/100, Feature: 1, Threshold: 1.46, Info Gain: 0.4221\n",
            "Trial 22/100, Feature: 0, Threshold: 2.55, Info Gain: 0.1116\n",
            "Trial 23/100, Feature: 0, Threshold: -1.92, Info Gain: 0.1989\n",
            "Trial 24/100, Feature: 0, Threshold: 3.78, Info Gain: 0.0182\n",
            "Trial 25/100, Feature: 0, Threshold: -0.85, Info Gain: 0.4852\n",
            "Trial 26/100, Feature: 1, Threshold: 1.41, Info Gain: 0.4221\n",
            "Trial 27/100, Feature: 1, Threshold: 4.30, Info Gain: 0.6428\n",
            "Trial 28/100, Feature: 0, Threshold: -3.11, Info Gain: 0.0496\n",
            "Trial 29/100, Feature: 1, Threshold: 2.88, Info Gain: 0.6009\n",
            "Trial 30/100, Feature: 0, Threshold: 3.58, Info Gain: 0.0182\n",
            "Trial 31/100, Feature: 1, Threshold: 0.41, Info Gain: 0.1112\n",
            "Trial 32/100, Feature: 0, Threshold: -1.78, Info Gain: 0.2357\n",
            "Trial 33/100, Feature: 1, Threshold: 0.88, Info Gain: 0.2311\n",
            "Trial 34/100, Feature: 1, Threshold: 3.64, Info Gain: 0.6592\n",
            "Trial 35/100, Feature: 1, Threshold: 4.88, Info Gain: 0.6203\n",
            "Trial 36/100, Feature: 0, Threshold: 0.74, Info Gain: 0.5448\n",
            "Trial 37/100, Feature: 0, Threshold: 0.11, Info Gain: 0.6453\n",
            "Trial 38/100, Feature: 1, Threshold: 5.26, Info Gain: 0.6483\n",
            "Trial 39/100, Feature: 0, Threshold: 0.86, Info Gain: 0.5147\n",
            "Trial 40/100, Feature: 0, Threshold: -4.11, Info Gain: 0.0090\n",
            "Trial 41/100, Feature: 0, Threshold: -1.50, Info Gain: 0.2960\n",
            "Trial 42/100, Feature: 0, Threshold: 2.92, Info Gain: 0.0640\n",
            "Trial 43/100, Feature: 1, Threshold: 0.09, Info Gain: 0.0851\n",
            "Trial 44/100, Feature: 0, Threshold: -2.97, Info Gain: 0.0496\n",
            "Trial 45/100, Feature: 0, Threshold: 1.43, Info Gain: 0.2890\n",
            "Trial 46/100, Feature: 1, Threshold: -0.27, Info Gain: 0.0753\n",
            "Trial 47/100, Feature: 0, Threshold: 1.77, Info Gain: 0.2027\n",
            "Trial 48/100, Feature: 1, Threshold: 10.21, Info Gain: 0.0086\n",
            "Trial 49/100, Feature: 1, Threshold: 1.37, Info Gain: 0.4068\n",
            "Trial 50/100, Feature: 0, Threshold: -3.57, Info Gain: 0.0227\n",
            "Trial 51/100, Feature: 1, Threshold: 7.25, Info Gain: 0.4522\n",
            "Trial 52/100, Feature: 1, Threshold: 5.23, Info Gain: 0.6456\n",
            "Trial 53/100, Feature: 0, Threshold: 3.08, Info Gain: 0.0379\n",
            "Trial 54/100, Feature: 0, Threshold: -1.63, Info Gain: 0.2809\n",
            "Trial 55/100, Feature: 1, Threshold: 0.46, Info Gain: 0.1313\n",
            "Trial 56/100, Feature: 1, Threshold: 4.86, Info Gain: 0.6203\n",
            "Trial 57/100, Feature: 0, Threshold: -2.32, Info Gain: 0.1007\n",
            "Trial 58/100, Feature: 0, Threshold: -1.47, Info Gain: 0.3099\n",
            "Trial 59/100, Feature: 0, Threshold: 2.43, Info Gain: 0.1282\n",
            "Trial 60/100, Feature: 0, Threshold: -0.29, Info Gain: 0.6071\n",
            "Trial 61/100, Feature: 1, Threshold: 6.12, Info Gain: 0.6002\n",
            "Trial 62/100, Feature: 1, Threshold: 7.79, Info Gain: 0.2803\n",
            "Trial 63/100, Feature: 1, Threshold: 1.16, Info Gain: 0.3176\n",
            "Trial 64/100, Feature: 1, Threshold: 6.23, Info Gain: 0.6229\n",
            "Trial 65/100, Feature: 1, Threshold: 6.14, Info Gain: 0.6002\n",
            "Trial 66/100, Feature: 0, Threshold: 3.30, Info Gain: 0.0221\n",
            "Trial 67/100, Feature: 1, Threshold: 4.06, Info Gain: 0.6699\n",
            "Trial 68/100, Feature: 0, Threshold: 1.86, Info Gain: 0.2022\n",
            "Trial 69/100, Feature: 0, Threshold: -0.34, Info Gain: 0.5984\n",
            "Trial 70/100, Feature: 0, Threshold: 2.18, Info Gain: 0.1568\n",
            "Trial 71/100, Feature: 0, Threshold: 0.70, Info Gain: 0.5637\n",
            "Trial 72/100, Feature: 1, Threshold: 3.65, Info Gain: 0.6515\n",
            "Trial 73/100, Feature: 1, Threshold: 1.48, Info Gain: 0.4295\n",
            "Trial 74/100, Feature: 1, Threshold: -0.32, Info Gain: 0.0753\n",
            "Trial 75/100, Feature: 1, Threshold: 6.34, Info Gain: 0.6422\n",
            "Trial 76/100, Feature: 0, Threshold: -3.02, Info Gain: 0.0496\n",
            "Trial 77/100, Feature: 1, Threshold: 4.81, Info Gain: 0.6203\n",
            "Trial 78/100, Feature: 0, Threshold: -2.70, Info Gain: 0.0638\n",
            "Trial 79/100, Feature: 1, Threshold: 5.10, Info Gain: 0.6410\n",
            "Trial 80/100, Feature: 1, Threshold: 10.12, Info Gain: 0.0086\n",
            "Trial 81/100, Feature: 1, Threshold: 3.61, Info Gain: 0.6674\n",
            "Trial 82/100, Feature: 0, Threshold: -1.10, Info Gain: 0.3743\n",
            "Trial 83/100, Feature: 1, Threshold: -0.36, Info Gain: 0.0753\n",
            "Trial 84/100, Feature: 0, Threshold: 2.94, Info Gain: 0.0640\n",
            "Trial 85/100, Feature: 1, Threshold: 6.96, Info Gain: 0.5312\n",
            "Trial 86/100, Feature: 0, Threshold: -2.79, Info Gain: 0.0638\n",
            "Trial 87/100, Feature: 1, Threshold: 8.48, Info Gain: 0.1093\n",
            "Trial 88/100, Feature: 1, Threshold: 2.40, Info Gain: 0.5260\n",
            "Trial 89/100, Feature: 0, Threshold: 2.51, Info Gain: 0.1209\n",
            "Trial 90/100, Feature: 0, Threshold: -4.08, Info Gain: 0.0090\n",
            "Trial 91/100, Feature: 1, Threshold: 0.28, Info Gain: 0.1014\n",
            "Trial 92/100, Feature: 1, Threshold: 7.15, Info Gain: 0.4827\n",
            "Trial 93/100, Feature: 0, Threshold: 2.00, Info Gain: 0.1826\n",
            "Trial 94/100, Feature: 1, Threshold: -0.16, Info Gain: 0.0851\n",
            "Trial 95/100, Feature: 1, Threshold: 1.76, Info Gain: 0.5088\n",
            "Trial 96/100, Feature: 0, Threshold: -0.64, Info Gain: 0.5422\n",
            "Trial 97/100, Feature: 1, Threshold: 8.32, Info Gain: 0.1490\n",
            "Trial 98/100, Feature: 1, Threshold: 5.15, Info Gain: 0.6410\n",
            "Trial 99/100, Feature: 1, Threshold: 8.01, Info Gain: 0.2230\n",
            "Trial 100/100, Feature: 0, Threshold: 2.82, Info Gain: 0.0767\n",
            "Best Stump: (0, 0.005223170220544304)\n",
            "Predictions on test data: [1 1 1 1 0 0 1 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1\n",
            " 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 1 0 0 0 1 1\n",
            " 1]\n"
          ]
        }
      ],
      "source": [
        "def train_stumps(Xtrain, ytrain, trials):\n",
        "    best_gain = -1\n",
        "    best_stump = None\n",
        "\n",
        "    for i in range(trials):\n",
        "\n",
        "        # Randomly select a feature and a threshold\n",
        "        feature_index = np.random.randint(Xtrain.shape[1])\n",
        "        threshold = np.random.uniform(np.min(Xtrain[:, feature_index]), np.max(Xtrain[:, feature_index]))\n",
        "\n",
        "        # Split the dataset\n",
        "        left_indices = Xtrain[:, feature_index] <= threshold\n",
        "        right_indices = ~left_indices\n",
        "\n",
        "        # Calculate information gain\n",
        "        gain = information_gain(ytrain, left_indices, right_indices)\n",
        "\n",
        "        # Print the progress of the information gain\n",
        "        print(f\"Trial {i+1}/{trials}, Feature: {feature_index}, Threshold: {threshold:.2f}, Info Gain: {gain:.4f}\")\n",
        "\n",
        "        # Update best stump if needed\n",
        "        if gain > best_gain:\n",
        "            best_gain = gain\n",
        "            best_stump = (feature_index, threshold)\n",
        "\n",
        "    return best_stump\n",
        "\n",
        "def information_gain(y, left_indices, right_indices):\n",
        "\n",
        "    # Calculate the entropy before the split\n",
        "    initial_entropy = stats.entropy(np.bincount(y), base=2)\n",
        "\n",
        "    # Calculate the weighted entropy after the split\n",
        "    left_entropy = stats.entropy(np.bincount(y[left_indices]), base=2)\n",
        "    right_entropy = stats.entropy(np.bincount(y[right_indices]), base=2)\n",
        "    weighted_entropy = (np.sum(left_indices) / len(y)) * left_entropy + (np.sum(right_indices) / len(y)) * right_entropy\n",
        "\n",
        "    # Information gain is the reduction in entropy\n",
        "    return initial_entropy - weighted_entropy\n",
        "\n",
        "def predict(X, stump):\n",
        "    feature_index, threshold = stump\n",
        "    predictions = np.where(X[:, feature_index] <= threshold, 0, 1)\n",
        "    return predictions\n",
        "\n",
        "\n",
        "# Train the Model\n",
        "best_stump = train_stumps(Xtrain, ytrain, 100)  # Let's say 100 trials\n",
        "print(\"Best Stump:\", best_stump)\n",
        "\n",
        "# Make Predictions\n",
        "predictions = predict(Xtest, best_stump)\n",
        "\n",
        "# Display Results\n",
        "print(\"Predictions on test data:\", predictions)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x2sn16_dcG3Q"
      },
      "source": [
        "## 3. Comparing classifiers on the Caltech 101 dataset\n",
        "\n",
        "Compare the performances of an SVM, a Decision Tree and Random Forest classifiers on the 10 classes subset of the **Caltech 101** dataset.\n",
        "Focus here on the **multi-class** classification task (e.g. 5 classes).\n",
        "Reuse the `loadImagesAndLabels()` and `buildDataset()` functions from the SVM lab course.\n",
        "\n",
        "\n",
        "**a)** Load and split the dataset\n",
        "\n",
        "**b)** Train three classification models on the train dataset\n",
        "- a Logistic Regression\n",
        "- an SVM\n",
        "- a single decision tree ``sklearn.tree.DecisionTree``\n",
        "- a Random Forest ``sklearn.ensemble.RandomForestClassifier``\n",
        "\n",
        "Question: Which among these are natively multi-class classifiers?\n",
        "\n",
        "Print the accuracy on the train and test sets for each model. ``from sklearn import metrics``\n",
        "\n",
        "**c)** Can we use ROC curves directly in this case? How ?\n",
        "\n",
        "**d)** Do a gridsearch with a 5-fold crossvalidation varying the hyperparameters of each model (e.g., for the SVM the ``kernel``, the ``gamma`` and ``c``, and for the tree-based models  ``max_depth``, ``max_features``, ``min_samples_leaf``, and ``n_estimators``).\n",
        "\n",
        "``from sklearn.model_selection import GridSearchCV``\n",
        "\n",
        "**Hint**\n",
        "```\n",
        "tuned_parameters = [{'max_depth': [1, 5, 10],\n",
        "                     'max_features': [1, 15, 30, 45, 60],\n",
        "                     'n_estimators': [1, 25, 50, 75, 100],\n",
        "                     'min_samples_leaf': [3,5,10]}]\n",
        "                     \n",
        "```\n",
        "- What are the best parameters found to maximize the area under the curve in each case?\n",
        "\n",
        "**e)** Discuss the results and curves."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import random\n",
        "import os\n",
        "import skimage\n",
        "\n",
        "#Keep4students\n",
        "def loadImagesAndLabels(IMDIR):\n",
        "  #This function glances through all subdirectories in IMDIR,\n",
        "  #and creates a list of the subdirectory names, which will be\n",
        "  #used as labels for all the images within.The function returns\n",
        "  #the list of labels\n",
        "  #\n",
        "  #If the function returns an empty list, it is likely that IMDIR\n",
        "  #is not defined correctly. In that case uncomment the lines below\n",
        "  #to check the files that are actually being read.\n",
        "\n",
        "  labelNamesAll = []\n",
        "\n",
        "  for root, dirnames, filenames in os.walk(IMDIR):\n",
        "      labelNamesAll.append(dirnames)\n",
        "      #uncomment to check if the folder contains images\n",
        "      #for filename in filenames:\n",
        "      #   f = os.path.join(root, filename)\n",
        "      #   if f.endswith(('.png', '.jpg', '.jpeg','.JPG', '.tif', '.gif')):\n",
        "      #       print(f)\n",
        "\n",
        "  labelNamesAll = labelNamesAll[0]\n",
        "  return labelNamesAll\n",
        "\n",
        "#Call the function and\n",
        "#print the list of all labels/subdirectories\n",
        "\n",
        "#Keep4students\n",
        "def buildDataset (IMDIR,labelNamesAll,K=2,N=100,imHeight=100,imWidth=100,seed=50):\n",
        "    #This function builds the data matrix from (a subset) of the label list.\n",
        "    #Images are read using a composition of the path and the label list.\n",
        "    #Parameters of this functions are:\n",
        "    # K : the number of classes to consider\n",
        "    # N : the maximum number of images to read from each category (the number\n",
        "    #    of images per label is variable).\n",
        "    # imHeight,imWidth: define the size of the target image. All read images\n",
        "    #                  are resized to imHeight x imWidth\n",
        "    # seed : fixes the random seed to be able to reproduce the results.\n",
        "    # The function returns the data matrix X and the label vector Y.\n",
        "    # Ideally, the X matrix will be of size (KxN)x(ImHeight x ImWidth) but\n",
        "    # the number of rows will be less if there number of images in a given\n",
        "    # category is smaller than N\n",
        "\n",
        "    X = np.zeros([K*N,imHeight*imWidth]) #data matrix, one image per row\n",
        "    Y = -np.ones([K*N,1]) #label indices initiallized to -1\n",
        "    labelNames = [] #list of retained categories\n",
        "\n",
        "    random.seed(a=seed) #comment to make each run random\n",
        "\n",
        "    globalCount = 0 #counts the actual number of images copied to the datamatrix\n",
        "\n",
        "    # Iterate over the number of classes\n",
        "    for i in range(K):\n",
        "        #Randomly choose a new category\n",
        "        while True:\n",
        "            lab = random.randint(0,len(labelNamesAll)-1)\n",
        "            if lab not in labelNames:\n",
        "                break\n",
        "\n",
        "        #define the path to read the images of the chosen label.\n",
        "        #folders are named after the class label, print the chosen label\n",
        "        filedir = os.path.join(IMDIR,labelNamesAll[lab])\n",
        "        print('The chosen label ',i, ' is ',labelNamesAll[lab])\n",
        "        print('It will be read in',filedir)\n",
        "\n",
        "        #save the name of the class in labelNames\n",
        "        labelNames.append(labelNamesAll[lab])\n",
        "\n",
        "        #walk through the files of the label folder,\n",
        "        #read images in grayscale and resize them\n",
        "        #flatten the images to a vector\n",
        "        #copy each image to one row of the data matrix\n",
        "        #use classCount to retain at most N images per class\n",
        "        #use globalCount to keep track of the total number of images\n",
        "        classCount = 0\n",
        "        for filename in os.listdir(filedir):\n",
        "            f = os.path.join(filedir, filename)\n",
        "            if f.endswith(('.jpg')) and (classCount < N):\n",
        "                image = skimage.io.imread(f, as_gray=True)\n",
        "                image = skimage.transform.resize(image, [imHeight,imWidth],mode='constant')#,anti_aliasing=True)\n",
        "                X[globalCount,:] = image.flatten()\n",
        "                Y[globalCount,:] = i\n",
        "                globalCount += 1\n",
        "                classCount += 1\n",
        "\n",
        "    #Remove the unused entries of X and Y\n",
        "    print(\"Total number of samples\",globalCount)\n",
        "    X = X[:globalCount,:]\n",
        "    Y = Y[:globalCount,:]\n",
        "\n",
        "    return X,Y,labelNames\n",
        "\n"
      ],
      "metadata": {
        "id": "YeyXBoD9db_8"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "2SeKPtZucG3R",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "outputId": "ef6f0a0c-bfa9-46ea-dbbe-0fe782486363"
      },
      "outputs": [
        {
          "output_type": "error",
          "ename": "IndexError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-22-a40450d906ef>\u001b[0m in \u001b[0;36m<cell line: 14>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[0mIMDIR\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'C:/Users/alixl/Desktop/EI2/APSTA/caltech-101/101_ObjectCategories/101_ObjectCategories'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m \u001b[0mlabelNamesAll\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mloadImagesAndLabels\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mIMDIR\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabelNames\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbuildDataset\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mIMDIR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabelNamesAll\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mK\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mN\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mimHeight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mimWidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mseed\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mX_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my_test\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrain_test_split\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtest_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrandom_state\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-18-5fbcc50374e6>\u001b[0m in \u001b[0;36mloadImagesAndLabels\u001b[0;34m(IMDIR)\u001b[0m\n\u001b[1;32m     24\u001b[0m       \u001b[0;31m#       print(f)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 26\u001b[0;31m   \u001b[0mlabelNamesAll\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlabelNamesAll\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     27\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mlabelNamesAll\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mIndexError\u001b[0m: list index out of range"
          ]
        }
      ],
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.svm import SVC\n",
        "from sklearn.tree import DecisionTreeClassifier\n",
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn.model_selection import GridSearchCV\n",
        "\n",
        "\n",
        "    ##Load and split the dataset\n",
        "#----------------------------------------------------------------------------------------\n",
        "\n",
        "IMDIR = 'C:/Users/alixl/Desktop/EI2/APSTA/caltech-101/101_ObjectCategories/101_ObjectCategories'\n",
        "labelNamesAll = loadImagesAndLabels(IMDIR)\n",
        "X, y, labelNames = buildDataset(IMDIR, labelNamesAll, K=5, N=100, imHeight=100, imWidth=100, seed=50)\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n",
        "\n",
        "\n",
        "\n",
        "    ##Train 3 classification modes\n",
        "#----------------------------------------------------------------------------------------\n",
        "\n",
        "# Initialize models\n",
        "log_reg = LogisticRegression()\n",
        "svm_model = SVC()\n",
        "decision_tree = DecisionTreeClassifier()\n",
        "random_forest = RandomForestClassifier()\n",
        "\n",
        "# Train models and print accuracies\n",
        "for model in [log_reg, svm_model, decision_tree, random_forest]:\n",
        "    model.fit(X_train, y_train)\n",
        "    train_acc = accuracy_score(y_train, model.predict(X_train))\n",
        "    test_acc = accuracy_score(y_test, model.predict(X_test))\n",
        "    print(f\"{model.__class__.__name__} - Train Accuracy: {train_acc}, Test Accuracy: {test_acc}\")\n",
        "\n",
        "\n",
        "    ##Grid search\n",
        "#----------------------------------------------------------------------------------------\n",
        "\n",
        "# Define parameter grids\n",
        "param_grid_svm = {'C': [0.1, 1, 10], 'gamma': [0.01, 0.1, 1], 'kernel': ['rbf', 'linear']}\n",
        "param_grid_tree = {'max_depth': [1, 5, 10], 'max_features': [1, 15, 30], 'min_samples_leaf': [3, 5, 10]}\n",
        "param_grid_forest = {'max_depth': [1, 5, 10], 'max_features': [1, 15, 30], 'n_estimators': [1, 25, 50], 'min_samples_leaf': [3, 5, 10]}\n",
        "\n",
        "# Perform grid search\n",
        "for model, param_grid in zip([SVC(), DecisionTreeClassifier(), RandomForestClassifier()], [param_grid_svm, param_grid_tree, param_grid_forest]):\n",
        "    grid_search = GridSearchCV(model, param_grid, cv=5, scoring='roc_auc_ovr')\n",
        "    grid_search.fit(X_train, y_train)\n",
        "    print(f\"Best parameters for {model.__class__.__name__}: {grid_search.best_params_}\")\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Answers to the questions**\n",
        "\n",
        "**b)** Out of these, Logistic Regression, Decision Tree, and Random Forest are natively multi-class classifiers.\n",
        "\n",
        "**c)**\n",
        "ROC curves are typically used for binary classification tasks. For multi-class classification, you can either convert the problem into a binary classification problem using strategies like One-vs-Rest or One-vs-One, or you can compute the ROC curve for each class against all others and then average them.\n",
        "\n"
      ],
      "metadata": {
        "id": "HeSCXcBsQCuY"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "zRITVo2rThnC"
      },
      "execution_count": null,
      "outputs": []
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