Contents

Description

Demonstrates outlier detection methods using dimensionality reduction with kernelized PCA. 9-dimensional City Ratings dataset is projected onto 2 and 3 dimensional spaces.

close all
clear all
f=1;

Outlier detection with Kernel PCA: linear, polynomial, and rbf kernels

load cities.mat
X = ratings;

usage of KPCA with default options

Reduce to 2-dimensions with KPCA

options = struct('maxComponents',2);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot(Xreduced(:,1),Xreduced(:,2),'.');
title('KPCA Projection onto 2-dimensions of cities data (linear kernel)');
fprintf('Click plot to name cities, press any key to continue\n');
gname(names)
grid on
grid minor

% Reduce to 3-dimensions with KPCA
options = struct('maxComponents',3);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot3(Xreduced(:,1),Xreduced(:,2),Xreduced(:,3),'.');
grid on
grid minor
title('KPCA Projection onto 3-dimensions of cities data (linear kernel)');
pause

Number of Components selected: 2
Variance explained by basis: 0.51
Click plot to name cities, press any key to continue
Number of Components selected: 3
Variance explained by basis: 0.64

usage of KPCA with polynomial basis

Reduce to 2-dimensions with KPCA

kernelArgs = struct('bias',0,'order',2);
options = struct('maxComponents',2,'kernelFunc',@ml_kernel_poly,...
                 'kernelArgs',kernelArgs);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot(Xreduced(:,1),Xreduced(:,2),'.');
grid on
grid minor
title('KPCA Projection onto 2-dimensions of cities data (poly kernel)');
fprintf('Click plot to name cities, press any key to continue\n');
gname(names)

% Reduce to 3-dimensions with KPCA
kernelArgs = struct('bias',0,'order',2);
options = struct('maxComponents',3,'kernelFunc',@ml_kernel_poly,...
                 'kernelArgs',kernelArgs);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot3(Xreduced(:,1),Xreduced(:,2),Xreduced(:,3),'.');
grid on
grid minor
title('KPCA Projection onto 3-dimensions of cities data (poly kernel)');
pause

Number of Components selected: 2
Variance explained by basis: 0.71
Click plot to name cities, press any key to continue
Number of Components selected: 3
Variance explained by basis: 0.75

usage of KPCA with rbf basis

Reduce to 2-dimensions with KPCA

kernelArgs = struct('sigma',10);
options = struct('maxComponents',2,'kernelFunc',@ml_kernel_rbf,...
                 'kernelArgs',kernelArgs);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot(Xreduced(:,1),Xreduced(:,2),'.');
grid on
grid minor
title('KPCA Projection onto 2-dimensions of cities data (rbf kernel)');
fprintf('Click plot to name cities, press any key to continue\n');
gname(names)

% Reduce to 3-dimensions with KPCA
kernelArgs = struct('sigma',10);
options = struct('maxComponents',3,'kernelFunc',@ml_kernel_rbf,...
                 'kernelArgs',kernelArgs);
model = ml_unsupervised_dimRedKPCA(X,options);
Xreduced = model.reduceFunc(model,X);
figure(f);f=f+1;
plot3(Xreduced(:,1),Xreduced(:,2),Xreduced(:,3),'.');
grid on
grid minor
title('KPCA Projection onto 3-dimensions of cities data (rbf kernel)');

Number of Components selected: 2
Variance explained by basis: 0.45
Click plot to name cities, press any key to continue
Number of Components selected: 3
Variance explained by basis: 0.58

Published with MATLAB® R2015a