Contents

Description

Demonstration of logistic regression with different bases on three synthetic datasets with distinct patterns to the class labels

clear all
close all
generateData_vert

usage of logistic regression (vert dataset)

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

Averaged absolute test error with Logistic Regression is: 0.124

usage of logistic regression with polynomial basis (vert dataset)

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

Averaged absolute test error with Binary Classification under Basis Change, Polynomial Kernel is: 0.302

usage of logistic regression with RBF basis (vert dataset)

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

Averaged absolute test error with Binary Classification under Basis Change, RBF Kernel is: 0.551

figure;
plot2DClassifier(Xtrain, ytrain, model_lg);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs1);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs2);

generateData_circular

usage of logistic regression (circular dataset)

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

Averaged absolute test error with Logistic Regression is: 0.782

usage of logistic regression with polynomial basis (circular dataset)

options_bs1 = [];
options_bs1.basisFunc = @ml_kernel_poly;
options_bs1.basisOptions.bias = 0;
options_bs1.basisOptions.order = 2;
options_bs1.subModel = @ml_binaryclass_logistic;
options_bs1.subOptions.addBias = 1;
model_bs1 = ml_binaryclass_basis(Xtrain, ytrain, options_bs1);
yhat_bs1 = model_bs1.predict(model_bs1, Xtest);
testError_bs1 = mean(abs(yhat_bs1 - ytest));
fprintf('Averaged absolute test error with %s is: %.3f\n', ...
    model_bs1.name, testError_bs1);

Averaged absolute test error with Binary Classification under Basis Change, Polynomial Kernel is: 0.178

usage of logistic regression with RBF basis (circular dataset)

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

Averaged absolute test error with Binary Classification under Basis Change, RBF Kernel is: 0.462

figure;
plot2DClassifier(Xtrain, ytrain, model_lg);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs1);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs2);

generateData_curved

usage of logistic regression (curved dataset)

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

Averaged absolute test error with Logistic Regression is: 0.169

usage of logistic regression with polynomial basis (curved dataset)

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

Averaged absolute test error with Binary Classification under Basis Change, Polynomial Kernel is: 0.196

usage of logistic regression with RBF basis (curved dataset)

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

Averaged absolute test error with Binary Classification under Basis Change, RBF Kernel is: 0.009

figure;
plot2DClassifier(Xtrain, ytrain, model_lg);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs1);
figure;
plot2DClassifier(Xtrain, ytrain, model_bs2);

Published with MATLAB® R2015a