新的图形表示矩阵系列:图形和信号分类的应用

IF 3.2 2区 工程技术 Q2 ENGINEERING, ELECTRICAL & ELECTRONIC
T. Averty;A. O. Boudraa;D. Daré-Emzivat
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引用次数: 0

摘要

包含图形信息的最自然矩阵是邻接矩阵和拉普拉斯矩阵。这些代数表示法是图信号处理的基本概念和工具,尽管它们揭示信息的方式各不相同。此外,在谱图分类中,可能会出现共谱性问题,而这些矩阵并不能很好地解决这一问题。因此,寻找最佳图表示矩阵的问题依然存在。在这封信中,我们介绍了一个新的表示族,它能很好地捕捉图的信息,还能找到标准表示矩阵。这个统一矩阵族能很好地捕捉图形信息,并扩展了近期的文献成果。研究证明了两个特性,即其正半定性和特征值的单调性。报告的谱图分类实验结果凸显了这一新矩阵族的潜力和附加值,并证明最佳表示取决于底层图的结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A New Family of Graph Representation Matrices: Application to Graph and Signal Classification
Most natural matrices that incorporate information about a graph are the adjacency and the Laplacian matrices. These algebraic representations govern the fundamental concepts and tools in graph signal processing even though they reveal information in different ways. Furthermore, in the context of spectral graph classification, the problem of cospectrality may arise and it is not well handled by these matrices. Thus, the question of finding the best graph representation matrix still stands. In this letter, a new family of representations that well captures information about graphs and also allows to find the standard representation matrices, is introduced. This family of unified matrices well captures the graph information and extends the recent works of the literature. Two properties are proven, namely its positive semidefiniteness and the monotonicity of their eigenvalues. Reported experimental results of spectral graph classification highlight the potential and the added value of this new family of matrices, and evidence that the best representation depends upon the structure of the underlying graph.
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来源期刊
IEEE Signal Processing Letters
IEEE Signal Processing Letters 工程技术-工程:电子与电气
CiteScore
7.40
自引率
12.80%
发文量
339
审稿时长
2.8 months
期刊介绍: The IEEE Signal Processing Letters is a monthly, archival publication designed to provide rapid dissemination of original, cutting-edge ideas and timely, significant contributions in signal, image, speech, language and audio processing. Papers published in the Letters can be presented within one year of their appearance in signal processing conferences such as ICASSP, GlobalSIP and ICIP, and also in several workshop organized by the Signal Processing Society.
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