  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.

Systems and Control;Systems and Control;Signal Processing