空间相关噪声下的拓扑辨识
Topology Identification under Spatially Correlated Noise
AI总结：
针对空间相关外源噪声下的线性动态网络拓扑辨识问题，本文将相关噪声转化为含隐节点的扩展网络，并基于IPSDM虚部的稀疏加低秩分解恢复相关图。
摘要：
本文研究如何仅依据时间序列测量，重构通过线性动力学相互作用的智能体网络拓扑，而这些智能体同时受到可能在不同智能体之间相关的外源随机源激励。文中表明，在相关性本质上为仿射的假设下，这种节点交互网络等价于一个增加了智能体的网络，这些增加的智能体由隐节点表示，且没有相应的时间序列测量可用；然而，在该扩展网络中，所有外源激励在空间上（即跨智能体）互不相关。文中进一步将仿射相关性推广，表明在多项式相关性下，扩展网络中的隐节点可由噪声源簇激励，而这些簇彼此互不相关。如果允许隐节点具有非线性交互，则这些簇可以用单个噪声源替代。最后，利用时间序列数据的逆功率谱密度矩阵（IPSDM）虚部的稀疏加低秩矩阵分解，重构网络拓扑。在非保守假设下，相关图得以恢复。
英文摘要：
This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series measurements alone. It is shown, under the assumption that the correlations are affine in nature, such network of nodal interactions is equivalent to a network with added agents, represented by nodes that are latent, where no corresponding time-series measurements are available; however, here all exogenous excitements are spatially (that is, across agents) uncorrelated. Generalizing affine correlations, it is shown that, under polynomial correlations, the latent nodes in the expanded networks can be excited by clusters of noise sources, where the clusters are uncorrelated with each other. The clusters can be replaced with a single noise source if the latent nodes are allowed to have non-linear interactions. Finally, using the sparse plus low-rank matrix decomposition of the imaginary part of the inverse power spectral density matrix (IPSDM) of the time-series data, the topology of the network is reconstructed. Under non conservative assumptions, the correlation graph is retrieved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
