The matlab code below is taken from the previous paper.

%number of examples N=size(X,2); %dimension of each example M=size(X,1); %mean meanX=mean(X,2); %centering the data Xm=X-meanX*ones(1,N); %covariance matrix C=(Xm*Xm')/N; %computing the eigenspace: [U D]=eig(C); %projecting the centered data over the eigenspace P=U'*Xm;

Helpful lecture video

Download JAMA package

Java code:

import Jama.*; public class KLTransform { //Matrix x[i,j]= jth feature in ith example public Matrix k_lTransform(Matrix x) { x = x.transpose(); int nExample = x.getColumnDimension(); //calculate mean Matrix mean = getMean(x); double[][] oneD = new double[1][nExample]; for(int i = 0; i < nExample; i++) oneD[0][i] = 1; Matrix ones = new Matrix(oneD); //center the data Matrix xm = x.minus(mean.times(ones)); //Calculate covariance matrix Matrix cov = xm.times(xm.transpose()); /* In the matlab code, the covariance matrix is divided with N (nExample). Now cov and cov/nExample have the same eigenvectors but different eigenvalues. In this code, the division doesn't make any difference as we are only considering the eigenvectors. But there are some cases, like in Kaiser-Guttman stopping rule where only the eigenvectors with eigenvalue > 1 are chosen, division might make a difference. */ cov = cov.times(1.0/nExample); //compute eigen vectors Matrix eigenVectors = cov.eig().getV(); //compute pca Matrix pca = eigenVectors.transpose().times(xm); return pca; } public Matrix getMean(Matrix x) { int nExample = x.getColumnDimension(); int nFeature = x.getRowDimension(); double[][] meanD = new double[nFeature][1]; Matrix mean = new Matrix(meanD); for(int i = 0; i < nFeature; i++) { double avg = 0.0; for(int j = 0; j < nExample; j++) { avg+=x.get( i,j); } mean.set(i, 0, avg/nExample); } return mean; } //test public static void main(String[] args) { KLTransform kl = new KLTransform(); double [][] d = new double[][]{{1, 2, 3},{4,5,6}}; Matrix x = new Matrix(d); Matrix pc = kl.k_lTransform(x); pc.print(pc.getRowDimension(), 2); } }

Note that in the matlab code, number of examples is the number of columns that is each column is an example. But the java code assumes each row is an example. So the matrix X in matlab is the transpose of matrix X in java.

To test the java and matlab code:

run java with :

X=

[1 2 3]

[4 5 6]

run matlab with: X = [1, 4; 2, 5; 3, 6]

syntax highlighting tutorial

## 1 comment:

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A little suggestion: could you please embed the comment form at the end of your posts? It's really bothering to open up a new window to post the comment. Hope you will think about it.

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Eid Mubarak. :)

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