Joint Problems in Learning Multiple Dynamical Systems

TL;DR

This paper introduces a novel method for jointly clustering time series data and learning multiple linear dynamical systems without predefined hidden state dimensions, with proven convergence and practical heuristics.

Contribution

It presents globally convergent algorithms and EM heuristics for joint clustering and LDS learning, providing an upper bound on hidden state dimension and guidance for regularization.

Findings

Algorithms are globally convergent.

Heuristics show promising computational results.

Method does not require predefined hidden state dimension.

Abstract

Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results. The key highlight of this method is that it does not require a predefined hidden state dimension but instead provides an upper bound. Additionally, it offers guidance for determining regularization in the system identification.