Near-Optimal Clustering in Mixture of Markov Chains

Junghyun Lee; Yassir Jedra; Alexandre Proutière; Se-Young Yun

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arXiv · 2506.01324

Near-Optimal Clustering in Mixture of Markov Chains

Junghyun Lee·Yassir Jedra·Alexandre Proutière·Se-Young Yun

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Abstract

We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the clustering error rate, governed by the stationary-weighted KL divergence between transition kernels. We then propose a two-stage algorithm: Stage I applies spectral clustering via a new injective Euclidean embedding for ergodic Markov chains, a contribution of independent interest enabling sharp concentration results; Stage II refines clusters with a single likelihood-based reassignment step. We prove that our algorithm achieves near-optimal clustering error with high probability under reasonable requirements on $T$ and $H$. Preliminary experiments support our approach, and we conclude with discussions of its limitations and extensions.

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BibTeX RIS

Junghyun Lee, Yassir Jedra, Alexandre Proutière, Se-Young Yun. 2025-06-02. Near-Optimal Clustering in Mixture of Markov Chains. https://arxiv.org/abs/2506.01324

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