Eigenspace-Based Clustering for Personalized System Identification
It addresses the problem of clustering heterogeneous dynamical systems for personalized modeling, offering a more robust alternative to iterative training-based methods.
This paper introduces a one-shot, training-free clustering method for personalized system identification that uses eigenspace alignment of local state covariance matrices to group systems with similar dynamics, achieving lower estimation error than training-based clustering and non-clustered baselines.
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.