Contents

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);

Published with MATLAB® R2015a