论文标题
与非白色激发的流式图信号混合模型的在线推断
Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation
论文作者
论文摘要
本文考虑了共同的多刻推理和聚类问题，用于同时推断节点中心性以及图形信号与图形的关联。我们研究了带有非白色和低级激发的过滤低通图信号的混合模型。尽管混合模型是由于实际情况而动机的，但它给先前的图形学习方法带来了重大挑战。作为一种补救措施，我们考虑了一个针对图表的节点中心性的推论问题。我们设计了一种带有独特的低级别和稀疏先验的期望最大化（EM）算法，该算法从低通信号属性中得出。我们提出了一种新颖的在线EM算法，用于推断流数据。例如，我们扩展了在线算法，以检测信号是否是从异常图生成的。我们表明，所提出的算法会收敛到最大A-Posterior（MAP）问题的固定点。数值实验支持我们的分析。
This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with possibly non-white and low-rank excitation. While the mixture model is motivated from practical scenarios, it presents significant challenges to prior graph learning methods. As a remedy, we consider an inference problem focusing on the node centrality of graphs. We design an expectation-maximization (EM) algorithm with a unique low-rank plus sparse prior derived from low pass signal property. We propose a novel online EM algorithm for inference from streaming data. As an example, we extend the online algorithm to detect if the signals are generated from an abnormal graph. We show that the proposed algorithms converge to a stationary point of the maximum-a-posterior (MAP) problem. Numerical experiments support our analysis.
