Eigenspace-Based Clustering for Personalized System Identification

2026-06-18

AI Summary

This work addresses the limitations of traditional system identification methods in heterogeneous environments, which rely on iterative clustering and are thus sensitive to model initialization and learning uncertainty. The authors propose a training-free, one-shot clustering approach that quantifies dynamic similarity among systems by measuring the alignment of principal subspaces derived from state covariance matrices estimated using local observational data. By leveraging the intrinsic subspace structure of these covariance matrices, the method circumvents iterative optimization and provides theoretical guarantees on clustering success under finite-sample regimes. Experimental results demonstrate that the proposed approach effectively identifies systems sharing common dynamics, significantly reduces estimation error for personalized models, and outperforms both training-based clustering and non-clustering baselines.

Abstract

We study the problem of system identification in heterogeneous settings, where different systems may follow distinct underlying dynamics. Existing clustered system identification approaches often rely on iterative training-based cluster assignment, which can be sensitive to learning uncertainty and model initialization. In contrast, we propose a one-shot, training-free clustering method that identifies similar systems using the structure of their locally observed data. Specifically, each system estimates a local state covariance matrix, and cluster identities are inferred by measuring the alignment between the leading covariance eigenspaces of different systems. We provide a mathematical interpretation of the proposed similarity score and develop a finite-sample analysis that characterizes how covariance estimation error induces eigenspace perturbations in terms of the underlying system dynamics. We then derive a probability bound for pairwise false merges and a global clustering success guarantee. Numerical experiments demonstrate that the proposed eigenspace-based clustering method effectively identifies systems with shared dynamics, leading to lower personalized model-estimation error compared with training-based clustering and non-clustered baselines.

Problem

• system identification
• heterogeneous systems
• clustering
• personalized modeling
• dynamics

Innovation

• eigenspace alignment
• training-free clustering
• system identification
• covariance estimation
• heterogeneous dynamics