## Contents

- Description of demo_multiclass_basis.m
- usage of multi-class logistic regression (4grid data)
- usage of multi-class logistic regression with polynomial basis (4grid data)
- usage of multi-class logistic regression with RBF basis (4grid data)
- usage of multi-class logistic regression (5grid data)
- usage of multi-class logistic regression with polynomial basis (5grid data)
- usage of multi-class logistic regression with RBF basis (5grid data)
- usage of multi-class logistic regression (gridMulti data)
- usage of multi-class logistic regression with polynomial basis (gridMulti data)
- usage of multi-class logistic regression with RBF basis (gridMulti data)

## Description of demo_multiclass_basis.m

Demonstrates multiclass logistic regression in a variety of different bases and on synthetic datasets with particular structures

    clear all
    close all
    generateData_4grid

## usage of multi-class logistic regression (4grid data)

    options_lg = [];
    model_lg = ml_multiclass_logistic(Xtrain, ytrain, options_lg);
    yhat_lg = model_lg.predict(model_lg, Xtest);
    testError_lg = mean(yhat_lg ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_lg.name, testError_lg);

    Averaged misclassification test error with Multiclass Logistic Classification is: 0.062

## usage of multi-class logistic regression with polynomial basis (4grid data)

    options_bs1 = [];
    options_bs1.basisFunc = @ml_kernel_poly;
    options_bs1.basisOptions.bias = 0;
    options_bs1.basisOptions.order = 3;
    options_bs1.subModel = @ml_multiclass_logistic;
    options_bs1.subOptions.addBias = 1;
    model_bs1 = ml_multiclass_basis(Xtrain, ytrain, options_bs1);
    yhat_bs1 = model_bs1.predict(model_bs1, Xtest);
    testError_bs1 = mean(yhat_bs1 ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs1.name, testError_bs1);

    Averaged misclassification test error with Classification under Basis Change with: Polynomial Kernel is: 0.138

## usage of multi-class logistic regression with RBF basis (4grid data)

    options_bs2 = [];
    options_bs2.basisFunc = @ml_kernel_rbf;
    options_bs2.basisOptions.sigma = 1;
    options_bs2.subModel = @ml_multiclass_logistic;
    options_bs2.subOptions.addBias = 1;
    model_bs2 = ml_multiclass_basis(Xtrain, ytrain, options_bs2);
    yhat_bs2 = model_bs2.predict(model_bs2, Xtest);
    testError_bs2 = mean(yhat_bs2 ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs2.name, testError_bs2);

    Averaged misclassification test error with Classification under Basis Change with: RBF Kernel is: 0.191

    figure;
    plotClassifier(Xtrain, ytrain, model_lg);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs1);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs2);

    generateData_5grid

## usage of multi-class logistic regression (5grid data)

    options_lg = [];
    model_lg = ml_multiclass_logistic(Xtrain, ytrain, options_lg);
    yhat_lg = model_lg.predict(model_lg, Xtest);
    testError_lg = mean(yhat_lg ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_lg.name, testError_lg);

    Averaged misclassification test error with Multiclass Logistic Classification is: 0.084

## usage of multi-class logistic regression with polynomial basis (5grid data)

    options_bs1 = [];
    options_bs1.basisFunc = @ml_kernel_poly;
    options_bs1.basisOptions.bias = 3;
    options_bs1.basisOptions.order = 2;
    options_bs1.subModel = @ml_multiclass_logistic;
    options_bs1.subOptions.addBias = 1;
    model_bs1 = ml_multiclass_basis(Xtrain, ytrain, options_bs1);
    yhat_bs1 = model_bs1.predict(model_bs1, Xtest);
    testError_bs1 = mean(yhat_bs1 ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs1.name, testError_bs1);

    Averaged misclassification test error with Classification under Basis Change with: Polynomial Kernel is: 0.080

## usage of multi-class logistic regression with RBF basis (5grid data)

    options_bs2 = [];
    options_bs2.basisFunc = @ml_kernel_rbf;
    options_bs2.basisOptions.sigma = 1;
    options_bs2.subModel = @ml_multiclass_logistic;
    options_bs2.subOptions.addBias = 1;
    model_bs2 = ml_multiclass_basis(Xtrain, ytrain, options_bs2);
    yhat_bs2 = model_bs2.predict(model_bs2, Xtest);
    testError_bs2 = mean(yhat_bs2 ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs2.name, testError_bs2);

    Averaged misclassification test error with Classification under Basis Change with: RBF Kernel is: 0.164

    figure;
    plotClassifier(Xtrain, ytrain, model_lg);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs1);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs2);

    generateData_gridMulti

## usage of multi-class logistic regression (gridMulti data)

    options_lg = [];
    model_lg = ml_multiclass_logistic(Xtrain, ytrain, options_lg);
    yhat_lg = model_lg.predict(model_lg, Xtest);
    testError_lg = mean(yhat_lg ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_lg.name, testError_lg);

    Averaged misclassification test error with Multiclass Logistic Classification is: 0.298

## usage of multi-class logistic regression with polynomial basis (gridMulti data)

    options_bs1 = [];
    options_bs1.basisFunc = @ml_kernel_poly;
    options_bs1.basisOptions.bias = 3;
    options_bs1.basisOptions.order = 2;
    options_bs1.subModel = @ml_multiclass_logistic;
    options_bs1.subOptions.addBias = 1;
    model_bs1 = ml_multiclass_basis(Xtrain, ytrain, options_bs1);
    yhat_bs1 = model_bs1.predict(model_bs1, Xtest);
    testError_bs1 = mean(yhat_bs1 ~= ytest);
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs1.name, testError_bs1);

    Averaged misclassification test error with Classification under Basis Change with: Polynomial Kernel is: 0.227

## usage of multi-class logistic regression with RBF basis (gridMulti data)

    options_bs2 = [];
    options_bs2.basisFunc = @ml_kernel_rbf;
    options_bs2.basisOptions.sigma = 1;
    options_bs2.subModel = @ml_multiclass_logistic;
    options_bs2.subOptions.addBias = 1;
    model_bs2 = ml_multiclass_basis(Xtrain, ytrain, options_bs2);
    yhat_bs2 = model_bs2.predict(model_bs2, Xtest);
    testError_bs2 = mean(abs(yhat_bs2 ~= ytest));
    fprintf('Averaged misclassification test error with %s is: %.3f\n', ...
            model_bs2.name, testError_bs2);

    Averaged misclassification test error with Classification under Basis Change with: RBF Kernel is: 0.489

    figure;
    plotClassifier(Xtrain, ytrain, model_lg);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs1);
    figure;
    plotClassifier(Xtrain, ytrain, model_bs2);