TY - JOUR
A2 - Su, Steve
AU - Chan, Jason Chin-Tiong
AU - Ong, Hong Choon
PY - 2018
DA - 2018/05/02
TI - A Novel Entropy-Based Decoding Algorithm for a Generalized High-Order Discrete Hidden Markov Model
SP - 8068196
VL - 2018
AB - The optimal state sequence of a generalized High-Order Hidden Markov Model (HHMM) is tracked from a given observational sequence using the classical Viterbi algorithm. This classical algorithm is based on maximum likelihood criterion. We introduce an entropy-based Viterbi algorithm for tracking the optimal state sequence of a HHMM. The entropy of a state sequence is a useful quantity, providing a measure of the uncertainty of a HHMM. There will be no uncertainty if there is only one possible optimal state sequence for HHMM. This entropy-based decoding algorithm can be formulated in an extended or a reduction approach. We extend the entropy-based algorithm for computing the optimal state sequence that was developed from a first-order to a generalized HHMM with a single observational sequence. This extended algorithm performs the computation exponentially with respect to the order of HMM. The computational complexity of this extended algorithm is due to the growth of the model parameters. We introduce an efficient entropy-based decoding algorithm that used reduction approach, namely, entropy-based order-transformation forward algorithm (EOTFA) to compute the optimal state sequence of any generalized HHMM. This EOTFA algorithm involves a transformation of a generalized high-order HMM into an equivalent first-order HMM and an entropy-based decoding algorithm is developed based on the equivalent first-order HMM. This algorithm performs the computation based on the observational sequence and it requires OTN~2 calculations, where N~ is the number of states in an equivalent first-order model and T is the length of observational sequence.
SN - 1687-952X
UR - https://doi.org/10.1155/2018/8068196
DO - 10.1155/2018/8068196
JF - Journal of Probability and Statistics
PB - Hindawi
KW -
ER -