demgausshmm_traj.m

VARHMMBOX, version 1.1, Iead Rezek, Oxford University, MAR 2002 Matlab toolbox for Hidden Markov Mo

% A demonstration of the HMM software using a Gaussian observation
% model on trajectory in 2-D space
clear
load demgauss_traj
T=size(data,1);

% data  original time series

figure
plot3(data(:,1),data(:,2),1:T);
title('Original data');
disp('The data forms a trajectory in a 2-D space. It is composed of 2');
disp(' sinusoidal waves with added gaussian random noise');

disp('We will train an HMM model to trace the trajectory, ');
disp('practically quantising the sequence');
disp(' ');
disp('Press a key to continue');
pause

% Train up GMM on this data
hmm.K=12;
hmm=hmminit(data,hmm,'full');

% Emphasis is on a smooth trajectory in space
hmm.priors.Dir2d_alpha=ones(hmm.K)+2*eye(hmm.K);

hmm.train.cyc=30;
hmm.obsmodel='Gauss';
hmm.train.obsupdate=ones(1,hmm.K);    % update observation models ?
hmm.train.init=1;         % Yes, we've already done initialisation

hmm=hmmtrain(data,T,hmm);

[block]=hmmdecode(data,T,hmm);

% sorting the labels s.t. lowest starts frist
block.sq_star=ones(size(block.q_star));
l=block.q_star(1);
for i=1:hmm.K
  ndx=find(~ismember(block.q_star,l));
  block.sq_star(ndx(:))=block.sq_star(ndx(:))+ones(1,length(ndx));
  if isempty(ndx), break; else l=[l block.q_star(ndx(1))]; end;
end;
  
subplot(211),plot(data),title('Original data sequence'),axis off;
subplot(212),plot(block.sq_star),
title('Estimated and Sorted State sequence'),axis off;