Data-free metrics for Dirichlet and generalized Dirichlet mixture-based HMMs - A practical study

Approaches to design metrics between hidden Markov models (HMM) can be divided into two classes: data-based and parameter-based. The latter has the clear advantage of being deterministic and faster but only a very few similarity measures that can be applied to mixture-based HMMs have been proposed so far. Most of these metrics apply to the discrete or Gaussian HMMs and no comparative study have been led to the best of our knowledge. With the recent development of HMMs based on the Dirichlet and generalized Dirichlet distributions for proportional data modeling, we propose to design three new parametric similarity measures between these HMMs. Extensive experiments on synthetic data show the reliability of these new measures where the existing ones fail at giving expected results when some parameters vary. Illustration on real data show the clustering capability of these measures and their potential applications.