Function File: vpath = hmmviterbi (sequence, transprob, outprob)

Function File: hmmviterbi (..., 'symbols', symbols)

Function File: hmmviterbi (..., 'statenames', statenames)

Use the Viterbi algorithm to find the Viterbi path of a hidden Markov model given a sequence of outputs. The model assumes that the generation starts in state 1 at step 0 but does not include step 0 in the generated states and sequence.

Arguments

• sequence is the vector of length len of given outputs. The outputs must be integers ranging from 1 to columns (outprob).
• transprob is the matrix of transition probabilities of the states. transprob(i, j) is the probability of a transition to state j given state i.
• outprob is the matrix of output probabilities. outprob(i, j) is the probability of generating output j given state i.

Return values

• vpath is the vector of the same length as sequence of the estimated hidden states. The states are integers ranging from 1 to columns (transprob).

If 'symbols' is specified, then sequence is expected to be a sequence of the elements of symbols instead of integers ranging from 1 to columns (outprob). symbols can be a cell array.

If 'statenames' is specified, then the elements of statenames are used for the states in vpath instead of integers ranging from 1 to columns (transprob). statenames can be a cell array.

Examples

          transprob = [0.8, 0.2; 0.4, 0.6];
          outprob = [0.2, 0.4, 0.4; 0.7, 0.2, 0.1];
          [sequence, states] = hmmgenerate (25, transprob, outprob)
          vpath = hmmviterbi (sequence, transprob, outprob)
          
          symbols = {'A', 'B', 'C'};
          statenames = {'One', 'Two'};
          [sequence, states] = hmmgenerate (25, transprob, outprob,
                               'symbols', symbols, 'statenames', statenames)
          vpath = hmmviterbi (sequence, transprob, outprob,
                  'symbols', symbols, 'statenames', statenames)

References

1. Wendy L. Martinez and Angel R. Martinez. Computational Statistics Handbook with MATLAB. Appendix E, pages 547-557, Chapman & Hall/CRC, 2001.
2. Lawrence R. Rabiner. A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE, 77(2), pages 257-286, February 1989.