daniele@193: function SMALL_DL_test
daniele@193: clear, clc, close all
daniele@193: % Create a 2-dimensional dataset of points that are oriented in 3
daniele@193: % directions on a x-y plane
daniele@193: nData = 10000;						%number of data
daniele@193: theta = [pi/6 pi/3 4*pi/6];			%angles
daniele@193: m     = length(theta);
daniele@193: Q	  = [cos(theta); sin(theta)];	%rotation matrix
daniele@193: X	  = Q*randmog(m,nData);
daniele@193: 
daniele@193: % find principal directions using PCA and plot them
daniele@193: XXt = X*X';
daniele@193: [U ~] = svd(XXt);
daniele@193: scale = 3;
daniele@193: subplot(1,2,1), hold on
daniele@193: title('Principal Component Analysis')
daniele@193: scatter(X(1,:), X(2,:),'.');
daniele@193: O = zeros(size(U));
daniele@193: quiver(O(1,1:2),O(2,1:2),scale*U(1,:),scale*U(2,:),'LineWidth',2,'Color','k')
daniele@193: axis equal
daniele@193: 
daniele@193: subplot(1,2,2), hold on
daniele@193: title('K-SVD Dictionary')
daniele@193: scatter(X(1,:), X(2,:),'.');
daniele@193: axis equal
daniele@193: nAtoms   = 3;
daniele@193: initDict = randn(2,nAtoms);
daniele@193: nIter = 10;
daniele@193: O = zeros(size(initDict));
daniele@193: % apply dictionary learning algorithm
daniele@193: ksvd_params = struct('data',X,...		%training data
daniele@193: 					 'Tdata',1,...		%sparsity level
daniele@193: 					 'dictsize',nAtoms,...	%number of atoms
daniele@193: 					 'initdict',initDict,...
daniele@193: 					 'iternum',10);		%number of iterations
daniele@193: DL = SMALL_init_DL('ksvd','ksvd',ksvd_params);
daniele@193: DL.D = initDict;
daniele@193: xdata = DL.D(1,:);
daniele@193: ydata = DL.D(2,:);
daniele@193: qPlot = quiver(O(1,:),O(2,:),scale*initDict(1,:),scale*initDict(2,:),...
daniele@193: 	'LineWidth',2,'Color','k','XDataSource','xdata','YDataSource','ydata');
daniele@193: problem = struct('b',X);				%training data
daniele@193: 
daniele@193: %plot dictionary and learn
daniele@193: for iIter=1:nIter
daniele@193: 	DL.ksvd_params.initdict = DL.D;
daniele@193: 	DL = SMALL_learn(problem,DL);			%learn dictionary
daniele@193: 	xdata = DL.D(1,:);	
daniele@193: 	ydata = DL.D(2,:);
daniele@193: 	pause
daniele@193: 	refreshdata(gcf,'caller');
daniele@193: 	%quiver(O(1,:),O(2,:),scale*DL.D(1,:),scale*DL.D(2,:),'LineWidth',2,'Color','k');
daniele@193: end
daniele@193: 
daniele@193: 
daniele@193: function X = randmog(m, n)
daniele@193: % RANDMOG - Generate mixture of Gaussians
daniele@193: s = [0.2 2];
daniele@193: % Choose which Gaussian
daniele@193: G1 = (rand(m, n) < 0.9);
daniele@193: % Make them
daniele@193: X = (G1.*s(1) + (1-G1).*s(2)) .* randn(m,n);