01_ML0104EN_Multi-class_Classification__M.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center\">\n",
    "    <a href=\"https://skills.network\" target=\"_blank\">\n",
    "    <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
    "    </a>\n",
    "</p>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  **Softmax Regression, One-vs-All and One-vs-One for Multi-class Classification**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimated time needed: **1** hour\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " In this lab, we will study how to convert a linear classifier into a multi-class classifier, including multinomial logistic regression or softmax regression, One vs. All (One-vs-Rest) and One vs. One.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Objectives**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After completing this lab you will be able to:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*   Understand and apply some theory behind:\n",
    "    *  Softmax regression\n",
    "    *  One vs. All (One-vs-Rest)\n",
    "    * One vs. One\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Introduction**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Multi-class classification, we classify data into multiple class labels. Unlike classification trees and k-nearest neighbor, the concept of multi-class classification for linear classifiers is not as straightforward. We can convert logistic regression to multi-class classification using multinomial logistic regression or softmax regression; this is a generalization of logistic regression, this will not work for support vector machines. One vs. All (One-vs-Rest) and One vs. One are two other multi-class classification techniques can convert any two-class classifier into a multi-class classifier.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Install and Import the required libraries**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this lab, we are going to be using several Python libraries such as scit-learn, numpy, and matplotlib  for visualizations. Some of these libraries might be installed in your lab environment, and others may need to be installed by you by removing the hash signs. The cells below will install these libraries when executed.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting scikit-learn==1.0.2\n",
      "  Downloading scikit_learn-1.0.2-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (24.8 MB)\n",
      "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m24.8/24.8 MB\u001b[0m \u001b[31m60.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m00:01\u001b[0m00:01\u001b[0m\n",
      "\u001b[?25hRequirement already satisfied: numpy>=1.14.6 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from scikit-learn==1.0.2) (1.21.6)\n",
      "Requirement already satisfied: scipy>=1.1.0 in /home/jupyterlab/conda/envs/python/lib/python3.7/site-packages (from scikit-learn==1.0.2) (1.7.3)\n",
      "Collecting joblib>=0.11 (from scikit-learn==1.0.2)\n",
      "  Downloading joblib-1.3.2-py3-none-any.whl (302 kB)\n",
      "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m302.2/302.2 kB\u001b[0m \u001b[31m37.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
      "\u001b[?25hCollecting threadpoolctl>=2.0.0 (from scikit-learn==1.0.2)\n",
      "  Downloading threadpoolctl-3.1.0-py3-none-any.whl (14 kB)\n",
      "Installing collected packages: threadpoolctl, joblib, scikit-learn\n",
      "  Attempting uninstall: scikit-learn\n",
      "    Found existing installation: scikit-learn 0.20.1\n",
      "    Uninstalling scikit-learn-0.20.1:\n",
      "      Successfully uninstalled scikit-learn-0.20.1\n",
      "Successfully installed joblib-1.3.2 scikit-learn-1.0.2 threadpoolctl-3.1.0\n"
     ]
    }
   ],
   "source": [
    "!pip install scikit-learn==1.0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility Function\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function plots a different decision boundary. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_colors = \"ryb\"\n",
    "plot_step = 0.02\n",
    "\n",
    "def decision_boundary (X,y,model,iris, two=None):\n",
    "    x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1\n",
    "    y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, plot_step),\n",
    "                         np.arange(y_min, y_max, plot_step))\n",
    "    plt.tight_layout(h_pad=0.5, w_pad=0.5, pad=2.5)\n",
    "    \n",
    "    Z = model.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    cs = plt.contourf(xx, yy, Z,cmap=plt.cm.RdYlBu)\n",
    "    \n",
    "    if two:\n",
    "        cs = plt.contourf(xx, yy, Z,cmap=plt.cm.RdYlBu)\n",
    "        for i, color in zip(np.unique(y), plot_colors):\n",
    "            \n",
    "            idx = np.where( y== i)\n",
    "            plt.scatter(X[idx, 0], X[idx, 1], label=y,cmap=plt.cm.RdYlBu, s=15)\n",
    "        plt.show()\n",
    "  \n",
    "    else:\n",
    "        set_={0,1,2}\n",
    "        print(set_)\n",
    "        for i, color in zip(range(3), plot_colors):\n",
    "            idx = np.where( y== i)\n",
    "            if np.any(idx):\n",
    "\n",
    "                set_.remove(i)\n",
    "\n",
    "                plt.scatter(X[idx, 0], X[idx, 1], label=y,cmap=plt.cm.RdYlBu, edgecolor='black', s=15)\n",
    "\n",
    "\n",
    "        for  i in set_:\n",
    "            idx = np.where( iris.target== i)\n",
    "            plt.scatter(X[idx, 0], X[idx, 1], marker='x',color='black')\n",
    "\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function will plot the probability of belonging to each class; each column is the probability of belonging to a class and the row number is the sample number.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_probability_array(X,probability_array):\n",
    "\n",
    "    plot_array=np.zeros((X.shape[0],30))\n",
    "    col_start=0\n",
    "    ones=np.ones((X.shape[0],30))\n",
    "    for class_,col_end in enumerate([10,20,30]):\n",
    "        plot_array[:,col_start:col_end]= np.repeat(probability_array[:,class_].reshape(-1,1), 10,axis=1)\n",
    "        col_start=col_end\n",
    "    plt.imshow(plot_array)\n",
    "    plt.xticks([])\n",
    "    plt.ylabel(\"samples\")\n",
    "    plt.xlabel(\"probability of 3 classes\")\n",
    "    plt.colorbar()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In ths lab we will use the  iris dataset,  it consists of three different types of irises’ (Setosa y=0, Versicolour y=1, and Virginica y=2), petal and sepal length, stored in a 150x4 numpy.ndarray.\n",
    "\n",
    "The rows being the samples and the columns: Sepal Length, Sepal Width, Petal Length and Petal Width.\n",
    "\n",
    "The following plot uses the second two features:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pair=[1, 3]\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:, pair]\n",
    "y = iris.target\n",
    "np.unique(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'petal width')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdYlBu)\n",
    "plt.xlabel(\"sepal width (cm)\")\n",
    "plt.ylabel(\"petal width\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Softmax Regression**  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SoftMax regression is similar to logistic regression, and the softmax function converts the actual distances, that is, dot products of $x$ with each of the parameters $\\theta_i$ for the $K$ classes. This is converted to probabilities using the following: \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$softmax(x,i) = \\frac{e^{ \\theta_i^T \\bf x}}{\\sum_{j=1}^K e^{\\theta_j^T x}} $\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training procedure is almost identical to logistic regression. Consider the three-class example where $y \\in \\{0,1,2\\}$ we would like to classify $x_1$. We can use the softmax function to generate a probability of how likely the sample belongs to each class:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$[softmax(x_1,0),softmax(x_1,1),softmax(x_1,2)]=[0.97,0.2,0.1]$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The index of each probability is the same as the class. We can make a prediction using the argmax function:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{y}=argmax_i  \\{softmax(x,i)\\}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the previous example, we can make a prediction as follows:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\hat{y}=argmax_i  \\{[0.97,0.2,0.1]\\}=0$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The <code>sklearn</code> does this automatically, but we can verify the prediction step, as we fit the model:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LogisticRegression(random_state=0).fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We generate the probability using the method <ocde>predict_proba</code>:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "probability=lr.predict_proba(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the probability of belonging to each class; each column is the probability of belonging to a class and the row number is the sample number.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_probability_array(X,probability)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, is the output for the first sample:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.57671606e-01, 4.22321095e-02, 9.62845517e-05])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probability[0,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see it sums to one.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probability[0,:].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the $argmax$ function.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmax(probability[0,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the $argmax$ function to each sample.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2,\n",
       "       2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_prediction=np.argmax(probability,axis=1)\n",
    "softmax_prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can verify that sklearn does this under the hood by comparing it to the output of the method <code> predict  </code>.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat =lr.predict(X)\n",
    "accuracy_score(yhat,softmax_prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can't use Softmax regression for SVMs, Let's explore two methods of Multi-class Classification that we can apply to SVM.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SVM \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sklean performs Multi-class Classification automatically, we can apply the method and calculate the accuracy. Train a SVM classifier with the `kernel` set to `linear`, `gamma` set to `0.5`, and the `probability` paramter set to `True`, then train the model using the `X` and `y` data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(gamma=0.5, kernel='linear', probability=True)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = SVC(kernel='linear', gamma=.5, probability=True) #ADD CODE\n",
    "\n",
    "#ADD CODE\n",
    "\n",
    "model.fit(X,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python    \n",
    "model = SVC(kernel='linear', gamma=.5, probability=True)\n",
    "\n",
    "model.fit(X,y)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the `accuracy_score` on the training data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat = model.predict(X)\n",
    "\n",
    "accuracy_score(y,yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<details><summary>Click here for the solution</summary>\n",
    "\n",
    "```python    \n",
    "yhat = model.predict(X)\n",
    "\n",
    "accuracy_score(y,yhat)\n",
    "\n",
    "```\n",
    "\n",
    "</details>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the decision_boundary.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "decision_boundary (X,y,model,iris)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's implement One vs. All and One vs One:\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One vs. All (One-vs-Rest) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For one-vs-all classification, if we have K classes, we use K two-class classifier models. The number of class labels present in the dataset is equal to the number of generated classifiers. First, we create an artificial class we will call this \"dummy\" class. For each classifier, we split the data into two classes. We take the class samples we would like to classify, the rest of the samples will be labelled as a dummy class. We repeat the process for each class. To make a  classification, we use the classifier with the highest probability, disregarding the dummy class.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train Each Classifier\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we train three classifiers and place them in the list <code>my_models</code>. For each class we take the class samples we would like to classify, and the rest will be labelled as a dummy class. We repeat the process for each class. For each classifier, we plot the decision regions. The class we are interested in is in red, and the dummy class is in blue. Similarly, the class samples are marked in blue, and the dummy samples are marked with a black x. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0, 1, 2}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#dummy class\n",
    "dummy_class=y.max()+1\n",
    "#list used for classifiers \n",
    "my_models=[]\n",
    "#iterate through each class\n",
    "for class_ in np.unique(y):\n",
    "    #select the index of our  class\n",
    "    select=(y==class_)\n",
    "    temp_y=np.zeros(y.shape)\n",
    "    #class, we are trying to classify \n",
    "    temp_y[y==class_]=class_\n",
    "    #set other samples  to a dummy class \n",
    "    temp_y[y!=class_]=dummy_class\n",
    "    #Train model and add to list \n",
    "    model=SVC(kernel='linear', gamma=.5, probability=True)    \n",
    "    my_models.append(model.fit(X,temp_y))\n",
    "    #plot decision boundary \n",
    "    decision_boundary (X,temp_y,model,iris)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " For each sample we calculate the  probability of belonging to each class, not including the dummy class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "probability_array=np.zeros((X.shape[0],3))\n",
    "for j,model in enumerate(my_models):\n",
    "\n",
    "    real_class=np.where(np.array(model.classes_)!=3)[0]\n",
    "\n",
    "    probability_array[:,j]=model.predict_proba(X)[:,real_class][:,0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, is the probability of belonging to each class for the first sample.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9.91455258e-01, 1.22019983e-01, 1.18287770e-11])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probability_array[0,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As each is the probability of belonging to the actual class and not the dummy class, it does not sum to one. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.113475241065618"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "probability_array[0,:].sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the probability of belonging to the class. The row number is the sample number.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_probability_array(X,probability_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply the $argmax$ function to each sample to find the class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_vs_all=np.argmax(probability_array,axis=1)\n",
    "one_vs_all"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can calculate the accuracy. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9466666666666667"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y,one_vs_all)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see the accuracy is less than the one obtained by sklearn, and this is because for SVM, sklearn uses one vs one; let's verify it by comparing the outputs. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9733333333333334"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(one_vs_all,yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the outputs are different, now lets implement one vs one.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One vs One \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "In One-vs-One classification, we split up the data into each class, and then train a two-class classifier on each pair of classes. For example, if we have class 0,1,2, we would train one classifier on the samples that are class 0 and class 1, a second classifier on samples that are of class 0 and class 2, and a final classifier on samples of class 1 and class 2.\n",
    "\n",
    "For $K$ classes, we have to train $K(K-1)/2$ classifiers. So, if $K=3$, we have $(3x2)/2=3 $classes.\n",
    "\n",
    "To perform classification on a sample, we perform a majority vote and select the class with the most predictions. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we list each class.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0, 1, 2}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "classes_=set(np.unique(y))\n",
    "classes_\n",
    "   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine the number of classifiers:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K=len(classes_)\n",
    "K*(K-1)/2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then train a two-class classifier on each pair of classes. We plot the different training points for each of the two classes. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "class 0 vs class 1 \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "class 0 vs class 2 \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "class 1 vs class 2 \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairs=[]\n",
    "left_overs=classes_.copy()\n",
    "#list used for classifiers \n",
    "my_models=[]\n",
    "#iterate through each class\n",
    "for class_ in classes_:\n",
    "    #remove class we have seen before \n",
    "    left_overs.remove(class_)\n",
    "    #the second class in the pair\n",
    "    for second_class in left_overs:\n",
    "        pairs.append(str(class_)+' and '+str(second_class))\n",
    "        print(\"class {} vs class {} \".format(class_,second_class) )\n",
    "        temp_y=np.zeros(y.shape)\n",
    "        #find classes in pair \n",
    "        select=np.logical_or(y==class_ , y==second_class)\n",
    "        #train model \n",
    "        model=SVC(kernel='linear', gamma=.5, probability=True)  \n",
    "        model.fit(X[select,:],y[select])\n",
    "        my_models.append(model)\n",
    "        #Plot decision boundary for each pair and corresponding Training samples. \n",
    "        decision_boundary (X[select,:],y[select],model,iris,two=True)\n",
    "   \n",
    "        \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['0 and 1', '0 and 2', '1 and 2']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pairs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, our data is left-skewed, containing more \"5\" star reviews. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we are plotting the distribution of text length.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "pairs\n",
    "majority_vote_array=np.zeros((X.shape[0],3))\n",
    "majority_vote_dict={}\n",
    "for j,(model,pair) in enumerate(zip(my_models,pairs)):\n",
    "\n",
    "    majority_vote_dict[pair]=model.predict(X)\n",
    "    majority_vote_array[:,j]=model.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following table, each column is the output of a classifier for each pair of classes and the output is the prediction:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0 and 1</th>\n",
       "      <th>0 and 2</th>\n",
       "      <th>1 and 2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   0 and 1  0 and 2  1 and 2\n",
       "0        0        0        1\n",
       "1        0        0        1\n",
       "2        0        0        1\n",
       "3        0        0        1\n",
       "4        0        0        1\n",
       "5        0        0        1\n",
       "6        0        0        1\n",
       "7        0        0        1\n",
       "8        0        0        1\n",
       "9        0        0        1"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(majority_vote_dict).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform classification on a sample, we perform a majority vote, that is, select the class with the most predictions. We repeat the process for each sample. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2,\n",
       "       2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_vs_one=np.array([np.bincount(sample.astype(int)).argmax() for sample  in majority_vote_array]) \n",
    "one_vs_one\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We calculate the accuracy:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.96"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y,one_vs_one)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we compare it to `sklearn`, it's the same! \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(yhat,one_vs_one)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Author\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkML0101ENSkillsNetwork20718538-2021-01-01\" target=\"_blank\">Joseph Santarcangelo</a>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other Contributors\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Azim Hirjani\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Copyright © 2020 IBM Corporation. All rights reserved.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!--\n",
    "## Change Log\n",
    "| Date (YYYY-MM-DD) | Version | Changed By | Change Description      |\n",
    "| ----------------- | ------- | ---------- | ----------------------- |\n",
    "| 2020-07-20        | 0.2     | Azim       | Modified Multiple Areas |\n",
    "| 2020-07-17        | 0.1     | Azim       | Created Lab Template    |\n",
    "| 2022-08-31        | 0.3     | Steve Hord | QA pass edits           |\n",
    "--!>\n"
   ]
  }
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