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 on a 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.

翻译：在本文中,我们研究从集体行为中学习混合系统动态特性的问题,使用统计方法复制核心Hilbert空间(RKHS)。具体地说,我们提供了一个框架,通过计算其在核心Hilbert空间(RKHS)中汇总测量结果之间的最大平均差异(MMD)来识别和组合多个混合系统,而没有事先了解集合系统的动态。然后,利用新提出的组合Markov参数概念的梯度流,我们提出了一个系统框架,以便利用它们线性近似值来识别和识别混合系统。 最后,我们证明,拟议的方法可以推广到利用综合测量结果在核心Hilbert空间(RKHS)中组合多个未知的集合。 数字实验表明,我们的方法可靠而有力,可以将不同类型的系统动态聚合在一起。