Ensemble Recognition in Reproducing Kernel Hilbert Spaces through Aggregated Measurements
This work addresses the challenge of recognizing and clustering ensemble systems in fields like control or biology, but it appears incremental as it builds on existing RKHS and MMD methods.
The paper tackles the problem of learning dynamical properties of ensemble systems from collective behaviors by developing a framework using reproducing kernel Hilbert spaces and maximum mean discrepancy for identification and clustering without prior knowledge of system dynamics. Numerical experiments demonstrate the approach is reliable and robust across different ensemble dynamics.
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.