modify ldsEm to use ldsPca as initialization

Author: sth4nth

chapter13/LDS/ldsEm.m

@@ -17,7 +17,7 @@
     model = init(X,m);
 end
 tol = 1e-4;
-maxIter = 1000;
+maxIter = 2000;
 llh = -inf(1,maxIter);
 for iter = 2:maxIter
 %     E-step
@@ -29,20 +29,23 @@
 llh = llh(2:iter);
 
 function model = init(X, k)
-d = size(X,1);
-model.mu0 = randn(k,1);
-model.P0 = iwishrnd(eye(k),k);
-model.A = randn(k,k);
-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 = ;
+% d = size(X,1);
+% model.mu0 = randn(k,1);
+% model.P0 = iwishrnd(eye(k),k);
+% model.A = randn(k,k);
+% 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);
+E = Z(:,1:end-1)-Z(:,2:end);
+model.P0 = (dot(E(:),E(:))/(k*size(E,2)))*eye(k);
+model.A = A;
+E = A*Z(:,1:end-1)-Z(:,2:end);
+model.G = E*E'/size(E,2);
+model.C = C;
+E = C*Z-X(:,1:size(Z,2));
+model.S = E*E'/size(E,2);
 
 function model = maximization(X ,nu, U, Ezz, Ezy)
 n = size(X,2);

demo/ch13/lds_demo.m

@@ -1,19 +1,20 @@
 close all;
-%% Parameter
+% Parameter
 clear; 
 d = 2;
-k = 2;
-n = 50;
+k = 3;
+n = 100;
 
-A = [1,1; 
-     0 1];
+A = [1,0,1; 
+     0 1,0;
+     0,0,1];
 G = eye(k)*1e-3;
 
-C = [1 0;
-     0 1];
+C = [1,0,0;
+     0 1,0];
 S = eye(d)*1e-1;
 
-mu0 = [0; 0];
+mu0 = [0;0;0];
 P0 = eye(k);
 
 model.A = A;
@@ -54,9 +55,9 @@
 axis equal
 hold off
 %% LDS Subspace
-[A,C,z] = ldsPca(x,k,3*k);
-y = C*z;
-t = size(z,2);
+[A,C,nu] = ldsPca(x,k,3*k);
+y = C*nu;
+t = size(y,2);
 figure;
 hold on
 plot(x(1,1:t), x(2,1:t), 'ro');
@@ -66,9 +67,9 @@
 axis equal
 hold off
 %% LDS EM
-[model, llh] = ldsEm(x,k);
-nu = kalmanSmoother(model,x);
-y = model.C*nu;
+[tmodel, llh] = ldsEm(x,k);
+nu = kalmanSmoother(tmodel,x);
+y = tmodel.C*nu;
 figure
 hold on
 plot(x(1,:), x(2,:), 'ro');