  Thanks to their dependency structure, non-parametric Hidden Markov Models
(HMMs) are able to handle model-based clustering without specifying group
distributions. The aim of this work is to study the Bayes risk of clustering
when using HMMs and to propose associated clustering procedures. We first give
a result linking the Bayes risk of classification and the Bayes risk of
clustering, which we use to identify the key quantity determining the
difficulty of the clustering task. We also give a proof of this result in the
i.i.d. framework, which might be of independent interest. Then we study the
excess risk of the plugin classifier. All these results are shown to remain
valid in the online setting where observations are clustered sequentially.
Simulations illustrate our findings.
