Clustering hidden Markov models with variational HEM

TL;DR

This paper introduces a variational hierarchical EM algorithm for clustering hidden Markov models, enabling efficient grouping and representative modeling of sequential data with improved scalability and robustness.

Contribution

The paper presents a novel variational HEM algorithm for clustering HMMs, addressing intractable inference and demonstrating improved performance on time-series data tasks.

Findings

Effective hierarchical clustering of motion capture sequences

Improved annotation and retrieval of music and handwriting data

Reduced learning times and enhanced model robustness

Abstract

The hidden Markov model (HMM) is a widely-used generative model that copes with sequential data, assuming that each observation is conditioned on the state of a hidden Markov chain. In this paper, we derive a novel algorithm to cluster HMMs based on the hierarchical EM (HEM) algorithm. The proposed algorithm i) clusters a given collection of HMMs into groups of HMMs that are similar, in terms of the distributions they represent, and ii) characterizes each group by a "cluster center", i.e., a novel HMM that is representative for the group, in a manner that is consistent with the underlying generative model of the HMM. To cope with intractable inference in the E-step, the HEM algorithm is formulated as a variational optimization problem, and efficiently solved for the HMM case by leveraging an appropriate variational approximation. The benefits of the proposed algorithm, which we call variational HEM (VHEM), are demonstrated on several tasks involving time-series data, such as hierarchical clustering of motion capture sequences, and automatic annotation and retrieval of music and of online hand-writing data, showing improvements over current methods. In particular, our variational HEM algorithm effectively leverages large amounts of data when learning annotation models by using an efficient hierarchical estimation procedure, which reduces learning times and memory requirements, while improving model robustness through better regularization.