A Novel Low-Complexity HMM Similarity Measure

In this letter, we propose a novel similarity measure for comparing Hidden Markov models (HMMs) and an efficient scheme for its computation. In the proposed approach, we probabilistically evaluate the correspondence, or goodness of match, between every pair of states in the respective HMMs, based on the concept of semi-Markov random walk. We show that this correspondence score reflects the contribution of a given state pair to the overall similarity between the two HMMs. For similar HMMs, each state in one HMM is expected to have only a few matching states in the other HMM, resulting in a sparse state correspondence score matrix. This allows us to measure the similarity between HMMs by evaluating the sparsity of the state correspondence matrix. Estimation of the proposed similarity score does not require time-consuming Monte-Carlo simulations, hence it can be computed much more efficiently compared to the Kullback-Leibler divergence (KLD) thas has been widely used. We demonstrate the effectiveness of the proposed measure through several examples.