In my thesis I'm using to classify data the Matlab 'classify' function with linear discrimination. To see what the math behind it is, I looked into the code and found this:
===================================================== % Pooled estimate of covariance [Q,R] = qr(training - gmeans(gindex,:), 0); R = R / sqrt(n - ngroups); % SigmaHat = R'*R s = svd(R); if any(s <= eps^(3/4)*max(s)) error('The pooled covariance matrix of TRAINING must be positive definite.'); end
% MVN relative log posterior density, by group, for each sample for k = 1:ngroups A = (sample - repmat(gmeans(k,:), mm, 1)) / R; D(:,k) = log(prior(k)) - .5*sum(A .* A, 2); end ======================================================
I dont know exactly, was is going on there. I expected to see something like a multivariate Gauss distribution, like:
or something similar to this. Could somebody verify this or explain what kind of magic the programmer used (why qr decomposition?). I'm also very interested how 'D' is calculated since I use this value to show the distances of a sample to the different classes. Shouldn't this be the probability density function of x for the different classes?