Distance measures for hidden Markov models based on Hilbert space embeddings for time series classification

In order to build a classification scheme for sequences based on HMMs, the design of an appropriate distance is critical in both theoretical and practical fields. The Kullback-Leibler (KL) and Hidden Markov Stationary Distance (HSD) measures have been used to build classification schemes for sequences based on HMMs. However, it is well known that the KL measure is not a true metric and the metric HSD is for univariate data. Inspired by the recent emergence of metrics of probability measures in Reproducible Kernel Hilbert Spaces (RKHS), we introduce two new metrics between two stationary HMMs. The difference in the metrics based on RKHS with respect to the HSD metric is that our metrics can be calculated analytically and can be used for multivariate data. We evaluate the performance of the two metrics in the task of time-series classification, using the metrics within a K-Nearest Neighbor (KNN) classifier. The performance of the two metrics is evaluated in the voice database of the Massachusetts Eye and Ear Infirmary Disordered Voice Database from the Kay Elemetrics company. Results show that the proposed metrics provide competitive classification accuracies when compared to the KL, HSD and DTW measure.