Online Signed Sampling of Bandlimited Graph Signals

IF 3 3区计算机科学 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2024-01-22 DOI:10.1109/TSIPN.2024.3356794

Wenwei Liu;Hui Feng;Feng Ji;Bo Hu

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Abstract

The theory of sampling and recovery of bandlimited graph signals has been extensively studied. However, in many cases, the observation of a signal is quite coarse. For example, users only provide simple comments such as “like” or “dislike” for a product on an e-commerce platform. This is a particular scenario where only the sign information of a graph signal can be measured. In this paper, we are interested in how to sample based on sign information in an online manner, by which the direction of the original graph signal can be estimated. The online signed sampling problem of a graph signal can be formulated as a Markov decision process in a finite horizon. Unfortunately, it is intractable for large size graphs. We propose a low-complexity greedy signed sampling algorithm (GSS) as well as a stopping criterion. Meanwhile, we prove that the objective function is adaptive monotonic and adaptive submodular, so that the performance is close enough to the global optimum with a lower bound. Finally, we demonstrate the effectiveness of the GSS algorithm by both synthesis and realworld data.

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带限图形信号的在线符号采样

带限图信号的采样和恢复理论已被广泛研究。然而，在许多情况下，对信号的观测是相当粗糙的。例如，在电子商务平台上，用户只提供简单的评论，如对产品的 "喜欢 "或 "不喜欢"。在这种特殊情况下，只能测量图信号的符号信息。在本文中，我们感兴趣的是如何基于符号信息进行在线采样，从而估计出原始图信号的方向。图信号的在线符号采样问题可以表述为有限视界中的马尔可夫决策过程。遗憾的是，对于大尺寸图而言，这个问题难以解决。我们提出了一种低复杂度的贪婪签名采样算法（GSS）以及一种停止准则。同时，我们证明了目标函数是自适应单调性和自适应亚模态的，因此性能足够接近全局最优，并有一个下限。最后，我们通过合成和实际数据证明了 GSS 算法的有效性。

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来源期刊

IEEE Transactions on Signal and Information Processing over Networks Computer Science-Computer Networks and Communications

CiteScore

5.80

自引率

12.50%

发文量

期刊介绍： The IEEE Transactions on Signal and Information Processing over Networks publishes high-quality papers that extend the classical notions of processing of signals defined over vector spaces (e.g. time and space) to processing of signals and information (data) defined over networks, potentially dynamically varying. In signal processing over networks, the topology of the network may define structural relationships in the data, or may constrain processing of the data. Topics include distributed algorithms for filtering, detection, estimation, adaptation and learning, model selection, data fusion, and diffusion or evolution of information over such networks, and applications of distributed signal processing.