Online Graph Learning under Smoothness Priors
Online Graph Learning under Smoothness Priors
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DOI：
10.23919/eusipco54536.2021.9616123
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
S. S. Saboksayr-S.;G. Mateos;M. Çetin
中科院分区：
文献类型：
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作者：
S. S. Saboksayr-S.;G. Mateos;M. Çetin
图形信号处理（GSP）方法的日益成功在很大程度上依赖于网络数据承认某些规律性的图形的先验识别。然而，适应日益动态的环境以及实时处理流数据的需求为此提出了重大挑战。在这种情况下，我们开发新的算法在线网络拓扑推理流观测假设是光滑的寻求图。与现有的批处理算法不同，我们的目标是跟踪（可能）随时间变化的网络拓扑结构，同时通过按顺序处理图形信号来保持内存和计算成本。为了以在线方式恢复图形，我们利用邻近梯度（PG）方法来解决明智的平滑正则化时变优化问题。在温和的技术条件下，我们建立了在线图学习算法收敛到的邻域内（即，它跟踪）最佳时变批量解决方案。使用合成和真实的金融市场数据的计算机模拟说明了所提出的算法在适应流信号跟踪缓慢变化的网络连接的有效性。
The growing success of graph signal processing (GSP) approaches relies heavily on prior identification of a graph over which network data admit certain regularity. However, adaptation to increasingly dynamic environments as well as demands for real-time processing of streaming data pose major challenges to this end. In this context, we develop novel algorithms for online network topology inference given streaming observations assumed to be smooth on the sought graph. Unlike existing batch algorithms, our goal is to track the (possibly) time-varying network topology while maintaining the memory and computational costs in check by processing graph signals sequentially-in-time. To recover the graph in an online fashion, we leverage proximal gradient (PG) methods to solve a judicious smoothness-regularized, time-varying optimization problem. Under mild technical conditions, we establish that the online graph learning algorithm converges to within a neighborhood of (i.e., it tracks) the optimal time-varying batch solution. Computer simulations using both synthetic and real financial market data illustrate the effectiveness of the proposed algorithm in adapting to streaming signals to track slowly-varying network connectivity.