A Novel Entropy Algorithm for State Sequence of Bakis Hidden Markov Model

Hidden Markov model (HMM) can be categorised as an ergodic model or a left-to-right model. The categorization is subject to its state transition. An ergodic Hidden Markov model has full state transitions but a left-to-right hidden Markov model has partial state transitions. A Bakis Hidden Markov model (BHMM) is a special type of the left-to-right Hidden Markov model. State sequence for a BHMM is invisible but this research is able to track the most likelihood state sequence using Viterbi algorithm. However, while tracking the optimal state sequence for BHMM, the conventional algorithm does not provide a measure of uncertainty which is present in the solution. This issue can be overcome by the proposed novel algorithm, namely, BHMM entropy-based forward algorithm (BHMM-EFA) for computing state entropy of a BHMM. This algorithm is based on a decreasing-ladder trellis structure which provides a clear picture on how the entropy associated with the optimal state sequence is determined. Therefore, the novel algorithm requires O(TN) calculations for tracking the optimal state sequence of a first-order BHMM where T is the length of the observational sequence and N is the number of hidden states.