利用图形过滤器计算图形傅立叶变换中心性

IF 2.4 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC IEEE open journal of circuits and systems Pub Date : 2024-04-15 DOI:10.1109/OJCAS.2023.3317944
Chien-Cheng Tseng;Su-Ling Lee
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引用次数: 0

摘要

本文介绍了利用图滤波器计算复杂网络的图傅里叶变换中心性(GFTC)。传统的计算方法需要使用图傅里叶变换(GFT)的非稀疏变换矩阵来计算 GFTC 分数。为了降低 GFTC 的计算复杂度,本文采用了一种基于误差矩阵 Frobenius norm 的线性代数方法,将频谱域 GFTC 计算任务转换为顶点域计算任务,从而使 GFTC 可以通过多项式图滤波方法计算。需要研究的图滤波器设计有两种。一种是图感知方法,另一种是图非感知方法。计算复杂度比较和实验结果表明,由于在实现结构中使用了拉普拉斯矩阵的稀疏性,因此所提出的图滤波器方法比传统的 GFT 方法计算效率更高。最后,通过对社交网络、地铁网络和传感器网络的中心性计算,证明了利用图滤波器计算 GFTC 方法的有效性。
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Computation of Graph Fourier Transform Centrality Using Graph Filter
In this paper, the computation of graph Fourier transform centrality (GFTC) of complex network using graph filter is presented. For conventional computation method, it needs to use the non-sparse transform matrix of graph Fourier transform (GFT) to compute GFTC scores. To reduce the computational complexity of GFTC, a linear algebra method based on Frobenius norm of error matrix is applied to convert the spectral-domain GFTC computation task to vertex-domain one such that GFTC can be computed by using polynomial graph filtering method. There are two kinds of designs of graph filters to be studied. One is the graph-aware method; the other is the graph-unaware method. The computational complexity comparison and experimental results show that the proposed graph filter method is more computationally efficient than conventional GFT method because the sparsity of Laplacian matrix is used in the implementation structure. Finally, the centrality computations of social network, metro network and sensor network are used to demonstrate the effectiveness of the proposed GFTC computation method using graph filter.
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