Spectral Clustering and Embedding with Hidden Markov Models

Clustering has recently enjoyed progress via spectral methods which group data using only pairwise affinities and avoid parametric assumptions. While spectral clustering of vector inputs is straightforward, extensions to structured data or time-series data remain less explored. This paper proposes a clustering method for time-series data that couples non-parametric spectral clustering with parametric hidden Markov models (HMMs). HMMs add some beneficial structural and parametric assumptions such as Markov properties and hidden state variables which are useful for clustering. This article shows that using probabilistic pairwise kernel estimates between parametric models provides improved experimental results for unsupervised clustering and visualization of real and synthetic datasets. Results are compared with a fully parametric baseline method (a mixture of hidden Markov models) and a non-parametric baseline method (spectral clustering with non-parametric time-series kernels).