maxcanonicalcorrelation.m

a function inside machine learning

function [u, v] = maxCanonicalCorrelation(Xa, Xb)
%A function to find the directions that maximise correlation 

numExamples = size(Xa, 1);
numXaFeatures = size(Xa, 2);
numXbFeatures = size(Xb, 2);

alpha = 0.001;

Caa = Xa'*Xa + eye(numXaFeatures)*alpha; 
Cbb = Xb'*Xb + eye(numXbFeatures)*alpha; 
Cab = Xa'*Xb;
Cba = Cab'; 

Q1 = inv(sqrtm(Caa))*Cab*inv(sqrtm(Cbb)); 
Q2 = inv(sqrtm(Cbb))*Cba*inv(sqrtm(Caa)); 

zeroMatrix1 = zeros(numXaFeatures, numXaFeatures); 
zeroMatrix2 = zeros(numXbFeatures, numXbFeatures); 

Z = [zeroMatrix1, Q1; Q2, zeroMatrix2]; 

[T, D] = eigs(Z, 1); 

u = inv(sqrtm(Caa))*T(1:numXaFeatures, 1); 
v = inv(sqrtm(Cbb))*T(numXaFeatures+1:numXbFeatures+numXaFeatures, 1);

u = u/norm(u);
v = v/norm(v);