Updates to the prac

independent_component_analysis/ica_prac.m

@@ -113,9 +113,9 @@ for i = 1:10
     w = randn(d,1); w = w/norm(w)*5; 
     subplot(1,2,1)
     plot(x_w(1,:),x_w(2,:),'o'); hold on
-    axis equal
-    grid on
+    axis equal; grid on
     quiver(0,0,w(1),w(2),'linewidth',2,'color','r'); hold off
+    title(sprintf('%d/10 random projection',i))
     subplot(1,2,2)
     histogram(w'*x_w)
     pause
@@ -151,11 +151,9 @@ grid on
 G0 = @(x)(x.^2);          % quadratic (do not use this!)
 G1 = @(x)(1-exp(-x.^2));    % Gaussian --> integral(x*exp(-x^2/2)
 G2 = @(x)(log(cosh(x)));  % --> integral(tanh)
-G3 = @(x)(x.^3);          % kurtosis
+G3 = @(x)(x.^3);          % skewness
 G4 = @(x)(x.^4);          % tailedness
 G5 = @(x)(sqrt(G1(x)));
-% put your own non-linearity in here!
-G = G3;
 
 % Let's plot these functions
 Gall = {G0, G1, G2, G3, G4};
@@ -178,7 +176,10 @@ end
 angles = linspace(0,2*pi,1000);   % angles to calculate cost function along
 I      = zeros(size(angles));     % Interestingness
 E      = zeros(size(angles));     % Extent (variance)
-G = G4;  % select contrast function
+
+% put your own non-linearity in here!
+G = G4;
+
 for i = 1:length(angles)
     % get vector w along angle 
     [w_x, w_y] = pol2cart(angles(i),1);
@@ -227,19 +228,40 @@ addpath ./utils/FastICA_25
 
 % check the help to see how to change things like the contrast function g
 % note that we are using x (fastica does pre-whitening internally)
-[S, A, W] = fastica(x,'approach', 'symm','g','skew');
+% S = source signals, A = mixing matrix, W = unmixing matrix
+[S, A, W] = fastica(x_c,'approach', 'symm','g','skew');
 
-% I am not sure why I need to do the below
-W = A';
+mixedS = A*S; % mixture of source signals
 
 % plot the results
 figure
+subplot(1,3,1)
+plot(S(1,:),S(2,:),'o'); hold on
+quiver(0,0,A(1,1),A(2,1),'linewidth',3,'color','k')
+quiver(0,0,-A(1,1),-A(2,1),'linewidth',3,'color','k')
+quiver(0,0,A(1,2),A(2,2),'linewidth',3,'color','c')
+quiver(0,0,-A(1,2),-A(2,2),'linewidth',3,'color','c')
+xlim([-5,5]); ylim([-6,6])
+title('Estimated Source')
+
+
+subplot(1,3,2)
+plot(mixedS(1,:),mixedS(2,:),'o'); hold on
+quiver(0,0,A(1,1),A(2,1),'linewidth',3,'color','k')
+quiver(0,0,-A(1,1),-A(2,1),'linewidth',3,'color','k')
+quiver(0,0,A(1,2),A(2,2),'linewidth',3,'color','c')
+quiver(0,0,-A(1,2),-A(2,2),'linewidth',3,'color','c')
+xlim([-4,4]); ylim([-5,5])
+title('Mixed Source')
+
+subplot(1,3,3)
 plot(x_c(1,:),x_c(2,:),'o'); hold on
-quiver(0,0,W(1,1),W(1,2),'linewidth',3,'color','k')
-quiver(0,0,-W(1,1),-W(1,2),'linewidth',3,'color','k')
-quiver(0,0,W(2,1),W(2,2),'linewidth',3,'color','c')
-quiver(0,0,-W(2,1),-W(2,2),'linewidth',3,'color','c')
-axis equal
+quiver(0,0,A(1,1),A(2,1),'linewidth',3,'color','k')
+quiver(0,0,-A(1,1),-A(2,1),'linewidth',3,'color','k')
+quiver(0,0,A(1,2),A(2,2),'linewidth',3,'color','c')
+quiver(0,0,-A(1,2),-A(2,2),'linewidth',3,'color','c')
+xlim([-4,4]); ylim([-5,5])
+title('Original centered data')
 
 
 %% Quick implementation of the FastICA algorithm