Eigenspace-Based Clustering for Personalized System Identification

• URL: http://arxiv.org/abs/2606.20811v1
• Date: Thu, 18 Jun 2026 18:01:12 GMT
• Title: Eigenspace-Based Clustering for Personalized System Identification
• Abstract summary: We propose a one-shot, training-free clustering method that identifies similar systems using the structure of their locally observed data.<n> Numerical experiments demonstrate that the proposed eigenspace-based clustering method effectively identifies systems with shared dynamics.
• Score: 4.1802036269424585
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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