# Ensemble Recognition in Reproducing Kernel Hilbert Spaces through Aggregated Measurements

arXiv: https://arxiv.org/abs/2112.14307 · HTML: https://mlsanity.com/paper/2112.14307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 28 Dec 2021.

## Builds on (most cited first, 7 of 7)

- [Controllability of ensembles of linear dynamical systems](https://mlsanity.com/paper/1504.06167/) (2015)
- [Fixed-Endpoint Optimal Control of Bilinear Ensemble Systems](https://mlsanity.com/paper/1601.03329/) (2016)
- [Free-Endpoint Optimal Control of Inhomogeneous Bilinear Ensemble Systems](https://mlsanity.com/paper/1612.00090/) (2016)
- [Structure Theory for Ensemble Controllability, Observability, and Duality](https://mlsanity.com/paper/1804.10882/) (2018)
- [Uniform and Lq-Ensemble Reachability of Parameter-dependent Linear Systems](https://mlsanity.com/paper/1810.09117/) (2018)
- [On Separating Points for Ensemble Controllability](https://mlsanity.com/paper/1908.05323/) (2019)
- [A Convex-Geometric Approach to Ensemble Control Analysis and Design in a Hilbert Space](https://mlsanity.com/paper/2003.09987/) (2020)

## Abstract (arXiv)

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.