Decentralized Eigendecomposition for Online Learning Over Graphs With Applications

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

IEEE Transactions on Signal and Information Processing over Networks Pub Date : 2023-08-07 DOI:10.1109/TSIPN.2023.3302658

Yufan Fan;Minh Trinh-Hoang;Cemil Emre Ardic;Marius Pesavento

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引用次数: 0

Abstract

In this article, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of collecting all information in a fusion center, the proposed algorithm involves only local interactions among adjacent agents. It benefits from the representation of the matrix as a sum of rank-one components which makes the algorithm attractive for online eigenvalue and eigenvector tracking applications. We examine the performance of the proposed algorithm in two types of important application examples: First, we consider the online eigendecomposition of a sample covariance matrix over the network, with application in decentralized Direction-of-Arrival (DoA) estimation and DoA tracking applications. Then, we investigate the online computation of the spectra of the graph Laplacian that is important in, e.g., Graph Fourier Analysis and graph dependent filter design. We apply our proposed algorithm to track the spectra of the graph Laplacian in static and dynamic networks. Simulation results reveal that the proposed algorithm outperforms existing decentralized algorithms both in terms of estimation accuracy as well as communication cost.

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分布式特征分解在图上的在线学习与应用

本文研究了在主成分分析中很重要的一般对称矩阵的分散特征值分解问题，并提出了一种分散在线学习算法。所提出的算法只涉及相邻代理之间的局部交互，而不是在融合中心收集所有信息。它受益于将矩阵表示为秩一分量的和，这使得该算法对在线特征值和特征向量跟踪应用具有吸引力。我们在两类重要应用示例中检验了所提出算法的性能：首先，我们考虑样本协方差矩阵在网络上的在线特征分解，并应用于分散到达方向（DoA）估计和DoA跟踪应用。然后，我们研究了图拉普拉斯算子的谱的在线计算，这在图傅立叶分析和图相关滤波器设计中是重要的。我们将我们提出的算法应用于静态和动态网络中图拉普拉斯算子的谱跟踪。仿真结果表明，该算法在估计精度和通信成本方面均优于现有的分散算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.