A new distance measure for hidden Markov models

Hidden Markov model (HMM) has been found useful in modeling complex time series in various applications. An appropriate distance measure between two HMMs is of theoretical interests and it is also important in HMM-based applications. Kullback–Leibler (KL) and modified KL are usually used as distance measures between two HMMs. However, these measures do not satisfy the necessary properties of a distance measure, such as the triangle inequality. A novel distance measure, which is based on the HMM stationary cumulative distribution function, is proposed to discriminate two HMMs. It is proved that the measure can fulfill the properties requirements. The distance measure is evaluated by making comparisons to KL distance in experiments on a series of models. Also clustering on both synthesized data and real world data is performed with the new distance and KL distance, respectively. The results show that the proposed distance is more effective and reasonable in discriminating HMMs.