# Eigenspace-Based Clustering for Personalized System Identification

arXiv: https://arxiv.org/abs/2606.20811 · HTML: https://mlsanity.com/paper/2606.20811/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 12 of 12)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [FINE Samples for Learning with Noisy Labels](https://mlsanity.com/paper/2102.11628/) (2021)
- [Fundamentals of Task-Agnostic Data Valuation](https://mlsanity.com/paper/2208.12354/) (2022)
- [FedSysID: A Federated Approach to Sample-Efficient System Identification](https://mlsanity.com/paper/2211.14393/) (2022)
- [Learning Personalized Models with Clustered System Identification](https://mlsanity.com/paper/2304.01395/) (2023)
- [Data Similarity-Based One-Shot Clustering for Multi-Task Hierarchical Federated Learning](https://mlsanity.com/paper/2410.02733/) (2024)
- [RCC-PFL: Robust Client Clustering under Noisy Labels in Personalized Federated Learning](https://mlsanity.com/paper/2503.19886/) (2025)
- [Perturbation Analysis of Singular Values in Concatenated Matrices](https://mlsanity.com/paper/2505.01427/) (2025)
- [Redefining Clustered Federated Learning for System Identification: The Path of ClusterCraft](https://mlsanity.com/paper/2505.16857/) (2025)
- [FB-NLL: A Feature-Based Approach to Tackle Noisy Labels in Personalized Federated Learning](https://mlsanity.com/paper/2604.19729/) (2026)
- [Age-Aware Edge-Blind Federated Learning via Over-the-Air Aggregation](https://mlsanity.com/paper/2602.02469/) (2026)
- [Transmit or Idle: Efficient AoI Optimal Transmission Policy for Gossiping Receivers](https://mlsanity.com/paper/2602.12264/) (2026)

## Abstract (arXiv)

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 bound the probability of pairwise false eigenspace alignment and establish sufficient conditions for uniform inter-cluster eigenspace separation with high probability. 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.