Mode Clustering for Markov Jump Systems

TL;DR

This paper introduces a novel method for mode clustering in Markov jump systems, enabling the identification of system modes and reduced-rank models solely from observational data.

Contribution

The paper proposes a new approach combining SVD and k-means for mode clustering and reduced-rank Markov chain estimation, with theoretical error bounds and practical validation.

Findings

Clustering error can be bounded under certain conditions.

Reduced-rank Markov chain approximates the original effectively.

Method demonstrates success in simulations and real-world data.

Abstract

In this work, we consider the problem of mode clustering in Markov jump models. This model class consists of multiple dynamical modes with a switching sequence that determines how the system switches between them over time. Under different active modes, the observations can have different characteristics. Given the observations only and without knowing the mode sequence, the goal is to cluster the modes based on their transition distributions in the Markov chain to find a reduced-rank Markov matrix that is embedded in the original Markov chain. Our approach involves mode sequence estimation, mode clustering and reduced-rank model estimation, where mode clustering is achieved by applying the singular value decomposition and k-means. We show that, under certain conditions, the clustering error can be bounded, and the reduced-rank Markov chain is a good approximation to the original Markov chain. Through simulations, we show the efficacy of our approach and the application of our approach to real world scenarios.