Ensemble Recognition in Reproducing Kernel Hilbert Spaces through Aggregated Measurements

TL;DR

This paper introduces a novel RKHS-based framework for recognizing and clustering ensemble systems from aggregated measurements, without prior knowledge of their dynamics, using statistical and gradient flow methods.

Contribution

It presents a new approach combining MMD and aggregated Markov parameters for system recognition and clustering in RKHS, extending to unknown ensembles.

Findings

Method reliably recognizes ensemble systems with diverse dynamics.

Approach effectively clusters multiple unknown ensembles.

Numerical experiments confirm robustness and accuracy.

Abstract

In this paper, we study the problem of learning dynamical properties of ensemble systems from their collective behaviors using statistical approaches in reproducing kernel Hilbert space (RKHS). Specifically, we provide a framework to identify and cluster multiple ensemble systems through computing the maximum mean discrepancy (MMD) between their aggregated measurements in an RKHS, without any prior knowledge of the system dynamics of ensembles. Then, leveraging the gradient flow of the newly proposed notion of aggregated Markov parameters, we present a systematic framework to recognize and identify an ensemble systems using their linear approximations. Finally, we demonstrate that the proposed approaches can be extended to cluster multiple unknown ensembles in RKHS using their aggregated measurements. Numerical experiments show that our approach is reliable and robust to ensembles with different types of system dynamics.