FishersLDA判别分析_判别分析_fisher判别分析_FishersLDA判别分析_Fisher线性判别_模式判别分析_

function [Lpred, w] = FishersLDA(Dtrain, Ltrain, Dtest) % Binary Classification using Fisher's linear discriminant % 1. Find the optimal data projection direction w using the training dataset % 2. And use Fisher's linear discriminant to make classification for testing dataset % Note: the class labels use 1 and -1 to represent the two classes to be classified. % Inputs: % Dtrain - training dataset % Ltrain - class labels of training patterns % Dtest - testing patterns % Outputs % Lpred - predicted class labels of the testing patterns % w - optimal weight vector for data projection %--------Fisher Linear Discriminant---------% idx1 = find(Ltrain==1); % the index for class 1 idx2 = find(Ltrain==-1); % the index for class -1 Dtrain_c1 = Dtrain(idx1, :); % the training samples of class 1 Dtrain_c2 = Dtrain(idx2, :); % the training samples of class 2 N_c1 = length(idx1); % the number of samples in class 1 N_c2 = length(idx2); % the number of samples in class 2 %---First, obtain the optimal direction w for data projection Y = wTx --------% % Complete the implementation here C = unique(Ltrain); Lpred = []; w = []; for iC = 1:length(C); cl = C(iC); idx = find(Ltrain==cl); data = Dtrain(idx,:); mu = mean(data); sigma = cov(data); % P = length(idx)/length(Ltrain); % Wi = -0.5*inv(sigma); li = inv(sigma)*mu'; w = [w, li]; %wio = (-0.5*mu*li)-0.5*log(det(sigma))+log(P); %for j = 1:size(Dtest,1) % x = Dtest(j,:); % prior = P; % G(iC,j) = x*Wi*x'+li'*x'+wio; % end end m1 = mean(Dtrain_c1); m2 = mean(Dtrain_c2); diff = m1-m2; Sb = diff*diff'; Scat_between = w'*Sb*w; store1 = []; for iC = 1:N_c1; %cl = C(iC); %idx1 = find(Ltrain==cl); xi = Dtrain(iC, :); mult1 = (xi-m1)*(xi-m1)'; store1 = [store1, mult1]; end S1 = sum(store1); for iC = 1:N_c2; cl = C(iC); idx2 = find(Ltrain==-1); xj = Dtrain(idx2, :); mult2 = (xj-m2)*(xj-m2)'; store2 = [store2, mult2]; end S2 = sum(store2); s1sq = w'*S1*w; s2sq = w'*S2*w; Sw = s1sq+s2sq; Scat_within = w'*Sw*w; Jw = Scat_between/Scat_within; wmax = max(Jw); % % % % %---Second, perform Bayesian Classification on Projected Data in 1D Space-----% % Complete the implementation here % % % % % %---------------------------------------------------------------%