update lds_demo. TODO: init with ldsPCA in ldsEM

chapter13/LDS/ldsEm.m

@@ -36,7 +36,13 @@
 model.G = iwishrnd(eye(k),k);
 model.C = randn(d,k);
 model.S = iwishrnd(eye(d),d);
-
+% [A,C,Z] = ldsPca(X,k,3*k);
+% model.mu0 = Z(:,1);
+% model.P0 = ;
+% model.A = A;
+% model.C = C;
+% model.G = ;
+% model.S = ;
 
 function model = maximization(X ,nu, U, Ezz, Ezy)
 n = size(X,2);

demo/ch13/lds_demo.m

@@ -1,21 +1,19 @@
 close all;
-%% generate data
+%% Parameter
 clear; 
 d = 2;
-k = 4;
+k = 2;
 n = 50;
 
-A = [1 0 1 0; 
-     0 1 0 1;
-     0 0 1 0;
-     0 0 0 1]; 
-G = 0.001*eye(k);
+A = [1,1; 
+     0 1];
+G = eye(k)*1e-3;
 
-C = [1 0 0 0;
-     0 1 0 0];
-S = eye(d);
+C = [1 0;
+     0 1];
+S = eye(d)*1e-1;
 
-mu0 = [8; 10; 1; 0];
+mu0 = [0; 0];
 P0 = eye(k);
 
 model.A = A;
@@ -25,43 +23,58 @@
 model.mu0 = mu0;
 model.P0 = P0;
 
-[z,x] = ldsRnd(model, n);
+%% Generate data
+[z,x] = ldsRnd(model,n);
 figure;
 hold on
 plot(x(1,:), x(2,:), 'ro');
 plot(z(1,:), z(2,:), 'b*-');
 legend('observed', 'latent')
+title('Generated Data')
 axis equal
 hold off
-
-%% filter
-[mu, V, llh] = kalmanFilter(model, x);
+%% Kalman filter
+[mu, V, llh] = kalmanFilter(model,x);
 figure
 hold on
 plot(x(1,:), x(2,:), 'ro');
 plot(mu(1,:), mu(2,:), 'b*-');
 legend('observed', 'filtered')
+title('Kalman filter')
 axis equal
 hold off
-
-%% smoother
-[nu, U, llh] = kalmanSmoother(model, x);
+%% Kalman smoother
+[nu, U, llh] = kalmanSmoother(model,x);
 figure
 hold on
 plot(x(1,:), x(2,:), 'ro');
 plot(nu(1,:), nu(2,:), 'b*-');
 legend('observed', 'smoothed')
+title('Kalman smoother')
 axis equal
 hold off
-
-%% EM
-[model, llh] = ldsEm(x,model);
-nu = kalmanSmoother(model, x);
+%% LDS Subspace
+[A,C,z] = ldsPca(x,k,3*k);
+y = C*z;
+t = size(z,2);
+figure;
+hold on
+plot(x(1,1:t), x(2,1:t), 'ro');
+plot(y(1,1:t), y(2,1:t), 'b*-');
+legend('observed', 'projected')
+title('LDS subspace learning')
+axis equal
+hold off
+%% LDS EM
+[model, llh] = ldsEm(x,k);
+nu = kalmanSmoother(model,x);
+y = model.C*nu;
 figure
 hold on
 plot(x(1,:), x(2,:), 'ro');
-plot(nu(1,:), nu(2,:), 'b*-');
-legend('observed', 'smoothed with fitted model')
+plot(y(1,:), y(2,:), 'b*-');
+legend('observed', 'learned')
+title('LDS EM learning')
 axis equal
 hold off
 figure;