Question

I am trying to implement fisher’s linear discriminant function in matlab for K(Class) > 2, I am not really sure the algorithm for the K > 2 scenario. I know Matlab has inbuilt functions but I want to implement this without using them.

It will be great if someone could clear the algorithm.

Answer 1

Here is some sample pseudo code:

N = number of cases
c= number of classes
Priors = vector of prior probabilities for each case per class
Target = Target labels for each case per class
dimension of Data = Features x Cases.

Get target labels for each data point:

T = Targets(:,Cases);      % Target labels for each case 

Calculate the mean vector per class and the common covariance matrix:

classifier.u = [mean(Data(:,(T(1,:)==1)),2),mean_nan(Data(:,(T(2,:)==1)),2),....,mean_nan(Data(:,(T(2,:)==c)),2];   % Matrix of data means
classifier.invCV = cov(Data');

Get discriminant value using class mean vectors and common covariance matrix:

A1=classifier.u;
B1=classifier.invCV;
D = A1'*B1*Data-0.5*(A1'*B1.*A1')*ones(d,N)+log(Priors(:,Cases));

Function will produce c discriminant values. The case is then assigned to the class with the largest discriminant value.