Use PCA in Machine Learning

Matlab Code

% Source

% http://www.dcs.gla.ac.uk/~srogers/firstcourseml/matlab/chapter7/pcaexample.html#2

clear all;close all;
% Generate the data
Y = [randn(20,2);randn(20,2)+5;randn(20,2)-5];
% Add 5 random dimensions
N = size(Y,1);
Y = [Y randn(N,5)];

% labels - just used for plotting
t = [repmat(1,20,1);repmat(2,20,1);repmat(3,20,1)];

% Plot the original data
symbs = {'ro','gs','b^'};
figure(1);hold off
for k = 1:3
    pos = find(t==k);
    plot(Y(pos,1),Y(pos,2),symbs{k});
    hold on
end

% Do the PCA
% Subtract the means

Y = Y - repmat(mean(Y,1),N,1);
% Compute covariance matrix
C = (1/N)*Y'*Y;
% Find the eigen-vectors/values
% columns of w correspond to the projection directions
[w,lam] = eig(C);

% Plot the first two components on to the original data
figure;
hold off
for k = 1:3
    pos = find(t==k);
    plot(Y(pos,1),Y(pos,2),symbs{k});
    hold on
end

xl = xlim;
for k = 1:2
    plot(xl,xl*w(1,k)/w(2,k),'k');
end

% Bar plot of the eigenvalues
figure;
hold off
bar(diag(lam));
xlabel('Projection dimension');

% Plot the data projected into the first two dimensions

X = Y*w(:,1:2);
figure;
hold off
for k = 1:3
    pos = find(t==k);
    plot(X(pos,1),X(pos,2),symbs{k});
    hold on
end
ylabel('Variance');

Outputs