close all; 
clear all; 

%PCA example --------------------------------------------------
x = [1,2;
     3,3;
     3,5;
     5,4;
     5,6;
     6,5;
     8,7;
     9,8]
 
 N = size(x,1);
 D = size(x,2);
 
 subplot(121),scatter(x(:,1),x(:,2),'filled');
 axis([0 10 0 10])
 set(gca,'XTick',0:10);
 set(gca,'YTick',0:10);
 grid on;
 title('Original space')
 
 mu = mean(x);
 s = cov(x);
 
 [u,l,d] = svd (s);
 
 y = (x-repmat(mu,N,1)) * u;
 
 
 % plotting First principal component
 hold on; 
 F = 2;
 h = line(mu(1) + [0 u(1,1)]* F , mu(2) + [0 u(1,2)] * F);
 set(h,'Color', 'r');
 
 % plotting Second principal component
 h = line(mu(1) + [0 u(2,1)]* F , mu(2) + [0 u(2,2)] * F);
 set(h,'Color', 'r');
 hold off; 
 
 subplot(122),scatter(y(:,1),y(:,2),'filled')
 set(gca,'XTick',-6:6);
 set(gca,'YTick',-2:0.5:2);
 grid on;
 title('Projected space')
 
 
 l = diag (l);
 
 l(1)/sum(l)
 l(2)/sum(l)
 
 
 
 %LDA example   ------------------------------------------------
 
 x = [4,1;
      2,4;
      2,3;
      3,6;
      4,4;
      9,10;
      6,8;
      9,5;
      8,7;
      10,8;]
 c = [1,1,1,1,1,2,2,2,2,2]';
 
  N = size(x,1);
[xp, W,lambda] = LDA(x,c);
mu = mean(x);

figure;
subplot(121),gscatter(x(:,1),x(:,2),c);
 axis([0 11 0 11])
 set(gca,'XTick',0:11);
 set(gca,'YTick',0:11);
 grid on;
 legend off; 
 title('Original space')
 
 %plotting Fisher projection
 hold on; 
 F = 5;
 h = line(mu(1) + [0 W(1,1)]* F , mu(2) + [0 W(2,1)] * F);
 set(h,'Color', 'r');
 

subplot(122),gscatter(xp(:,1),zeros(N,1),c);
 axis([0 11 -1 1])
 set(gca,'XTick',0:11);
 set(gca,'YTick',-1:1);
 grid on;
 legend off; 
 title('Projected space')