basic help using hmm to clasify a sequence

Question

I am very new to matlab, hidden markov model and machine learning, and am trying to classify a given sequence of signals. Please let me know if the approach I have followed is correct:

1. create a N by N transition matrix and fill with random values which sum to 1for each row. (N will be the number of states)
2. create a N by M emission/observation matrix and fill with random values which sum to 1 for each row

3. convert different instances of the sequence (i.e each instance will be saying the word 'hello' ) into one long stream and feed each stream to the hmm train function such that:

   new_transition_matrix old_transition_matrix = hmmtrain(sequence,old_transition_matrix,old_emission_matrix)

4. give the final transition and emission matrix to hmm decode with an unknown sequence to give the probability i.e [posterior_states logrithmic_probability] = hmmdecode( sequence, final_transition_matrix,final_emission_matris)

Answer 1

1. and 2. are correct. You have to be careful that your initial transition and emission matrices are not completely uniform, they should be slightly randomized for the training to work.

3. I would just feed in the 'Hello' sequences separately rather than concatenating them to form a single long sequence.

Let's say this is the sequence for Hello: [1,0,1,1,0,0]. If you form one long sequence from 3 'Hello' sequences, you would get:

data = [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]

This is not ideal, instead you should feed the sequences in separately like:

data = [1,0,1,1,0,0; 1,0,1,1,0,0; 1,0,1,1,0,0].

Since you are using MatLab, I would recommend using the HMM toolbox by Murphy. It has a demo on how you can train an HMM with multiple observation sequences:

M = 3;
N  = 2;

% "true" parameters
prior0 = normalise(rand(N ,1));
transmat0 = mk_stochastic(rand(N ,N ));
obsmat0 = mk_stochastic(rand(N ,M));

% training data: a 5*6 matrix, e.g. 5 different 'Hello' sequences of length 6
number_of_seq = 5;
seq_len= 6;
data = dhmm_sample(prior0, transmat0, obsmat0, number_of_seq, seq_len);

% initial guess of parameters
prior1 = normalise(rand(N ,1));
transmat1 = mk_stochastic(rand(N ,N ));
obsmat1 = mk_stochastic(rand(N ,M));

% improve guess of parameters using EM
[LL, prior2, transmat2, obsmat2] = dhmm_em(data, prior1, transmat1, obsmat1, 'max_iter', 5);
LL

4. What you say is correct, below is how you calculate the log probaility in the HMM toolbox:

% use model to compute log[P(Obs|model)]
loglik = dhmm_logprob(data, prior2, transmat2, obsmat2)

Finally: Have a look at this paper by Rabiner on how the mathematics work if anything is unclear.

Hope this helps.