Distinguishability of graphs: a case for quantum-inspired measures

A. Polychronopoulou, Jumanah Alshehri, Z. Obradovic
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引用次数: 1

Abstract

The question of graph similarity or graph distinguishability arises often in natural systems and their analysis over graphical networks. In many domains, graph similarity is used for graph classification, outlier detection or the identification of distinguished interaction patterns. Several methods have been proposed on how to address this topic, but graph comparison still presents many challenges. Recently, information physics has emerged as a promising theoretical foundation for complex networks. In many applications, it has been demonstrated that natural complex systems exhibit features that can be described and interpreted by measures typically applied in quantum mechanical systems. Therefore, a natural starting point for the identification of network similarity measures is information physics and a series of measures of distance for quantum states. In this work, we report experiments on synthetic and real-world data sets, and compare quantum-inspired measures to a series of state-of-the-art and well-established methods of graph distinguishability. We show that quantum-inspired methods satisfy the mathematical and intuitive requirements for graph similarities, while offering high interpretability.
图的可分辨性:量子启发测度的一个例子
图的相似性或图的可分辨性的问题经常出现在自然系统和他们的分析图形网络。在许多领域,图相似度被用于图分类、离群点检测或区分交互模式的识别。关于如何解决这个问题,已经提出了几种方法,但是图形比较仍然存在许多挑战。最近,信息物理学已经成为复杂网络的一个有前途的理论基础。在许多应用中,已经证明自然复杂系统表现出可以用量子力学系统中典型应用的测量来描述和解释的特征。因此,识别网络相似性度量的自然起点是信息物理学和量子态的一系列距离度量。在这项工作中,我们报告了合成和现实世界数据集的实验,并将量子启发的措施与一系列最先进和完善的图形可分辨性方法进行了比较。我们证明了量子启发的方法满足图相似度的数学和直观要求,同时提供了很高的可解释性。
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