pca

Principal component analysis (PCA)

Contents

Syntax

Description

data2=pca(data) returns the results of PCA (principal component analysis)

• data: a data matrix, where each column is a data vector, or a dataset object
• data2: output data matrix after projection, or output dataset object

data2=pca(data, eigVecNum) uses the specified no. of eigenvectors for PCA

• eigVecNum: No. of selected eigenvectors, or the percentage of total variance explained

[data2, eigVec, eigValue]=pca(...) returns extra info:

• eigVec: Each column of this matrix is a eigenvector of dataMat*dataMat', sorted by decending order of the corresponding eigenvalues
• eigValue: Eigenvalues of (dataMat*dataMat') corresponding to eigVec

Example

Demo for 2D data

dataNum=1000;
j=sqrt(-1);
data=randn(1,dataNum)+j*randn(1,dataNum)/3;
data=data*exp(j*pi/6);		% Rotate 30 degress
data=data-mean(data);		% Zero mean'ed
plot(real(data), imag(data), '.'); axis image;
data=[real(data); imag(data)];
[data2, v, eigValue]=pca(data);
v1=v(:, 1);
v2=v(:, 2);
arrow=[-1 0 nan -0.1 0 -0.1]+1+j*[0 0 nan 0.1 0 -0.1];
arrow1=2*arrow*(v1(1)+j*v1(2))*eigValue(1)/dataNum;
arrow2=2*arrow*(v2(1)+j*v2(2))*eigValue(2)/dataNum;
line(real(arrow1), imag(arrow1), 'color', 'r', 'linewidth', 4);
line(real(arrow2), imag(arrow2), 'color', 'm', 'linewidth', 4);
title('Axes for PCA');

Demo for the iris dataset

DS=prData('iris');
dataNum=size(DS.input, 2);
DS2=pca(DS);
figure;
subplot(1,2,1); dsScatterPlot(DS2); title('IRIS projected on the first 2D of LDA');
DS2.input=DS2.input(3:4, :);
subplot(1,2,2); dsScatterPlot(DS2); title('IRIS projected on the last 2D of LDA');

Warning: data dim is larger than 2. The plot is based on the first 2 dimensions

Published with MATLAB® R2018a