Problem
Research questions and friction points this paper is trying to address.
Jointly partition trajectories and learn LDS models
Minimize maximum error across all dynamical models
Determine regularization without predefined state dimension
Joint Problems in Learning Multiple Dynamical Systems
🤖 AI Summary
This paper addresses the joint clustering and linear dynamical system (LDS) modeling of multiple trajectories: given a trajectory set and a prescribed number of clusters, it simultaneously partitions trajectories and learns an LDS model per cluster to minimize the maximum prediction error across all models. Methodologically, we propose a unified optimization framework that does not require pre-specifying the latent state dimension, integrating globally convergent optimization with an EM-inspired heuristic to jointly solve trajectory assignment and LDS parameter estimation. Theoretically, we derive a provably tight upper bound on regularization selection for system identification. Experiments demonstrate robust convergence and high modeling accuracy, significantly outperforming existing sequential baselines on both synthetic and real-world datasets, thereby validating the method’s effectiveness and practicality.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Jointly partitions trajectories and learns LDS models
Globally convergent methods with EM heuristics
No predefined hidden state dimension required
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