How to get the transition matrix and radiation from a multiple sequence for HMM in MATLAB?

Question

I am performing the class classification task in MATLAB using HMM. I have 13 sequences and their respective classes. As I understand it, hmmestimate () returns a transition and radiation matrix for one sequence and its class. But I need the final transition and emission matrix calculated from all these 13 sequences. How can i do this?

Answer 1

What should you do ...

A sincere, completely unscrupulous suggestion is to write a for pair to count all the transitions and state-radiation pairs present in the sequences, then normalize the rows in the two matrices received (transition and emission) so that they add 1. This is what does hmmestimate at the end, and this is probably how you should do it.

However, let it go ahead and force the square snap into the round hole ...

and what could you do

If you combined your sequences together, then this can be run through hmmestimate . This will give the correct emission matrix, but transitions between adjacent sequences will be random with transition probabilities. The trick around this is to increase each sequence with a new unique state and corresponding emission. Thus, all information about concatenations will be assigned to a subset of the output matrix that you can discard.

Example

Let some data be generated, so the input is clear.

 % true transitions and emission probabilities tr = [0.9 0.1; 0.05 0.95]; em = [0.9 0.1; 0.2 0.8]; num_seqs = 100; seq_len = 100; seqs = zeros(num_seqs,seq_len); states = zeros(num_seqs,seq_len); % generate some sequences for i = 1:num_seqs [seqs(i,:), states(i,:)] = hmmgenerate(seq_len,tr,em); end 

Using hmmestimate to evaluate

Note that MATLAB represents its states as consecutive integers, so we need to use the following integer for our token separator. In the sample example, we use '3'.

 % augment the sequences seqs_aug = [3*ones(num_seqs,1) seqs]; states_aug = [3*ones(num_seqs,1) states]; % concatenate the rows, and estimate % credit: http://stackoverflow.com/a/2731032/570918 [tr_aug,em_aug] = hmmestimate(reshape(seqs_aug.',1,[]),reshape(states_aug.',1,[])); % subset the good parts tr_hat = tr_aug(1:2,1:2); em_hat = em_aug(1:2,1:2); % renormalize tr_hat = tr_hat./sum(tr_hat,2); % NB: em_hat is already normalized 

Using rng(1) before creating the data above, this gives

 tr_hat % [0.9008 0.0992; 0.0490 0.9510] em_hat % [0.9090 0.0910; 0.1950 0.8050]