The normalized Laplacian tensor of hypergraphs has a wide range of applications in multi class clustering problems involving hypergraph models. In this paper, we prove that if is a connected general hypergraph with rank ()=, then the spectrum of the adjacency tensor of is symmetric if and only if is even and is odd-colorable. Furthermore, we give a characterization of the general hypergraphs with the normalized Laplace spectral radius 2 in terms of the odd-colorability of general hypergraphs.
给定一组对象,划分是为了某些目的将项目分为几个组。它是分析或解决科学、技术、人文、医学和工程问题的有用工具。通过机器对非结构化数据进行划分是降低噪声、提取有意义信息和选择关键组件的有效方法。聚类在许多领域都有广泛的应用,例如图像分割,生物信息学,对象识别,数据挖掘,空间数据分析等。作为一类重要的分割聚类方法,谱聚类方法基于谱图理论对项目进行聚类。它们在计算机视觉、VLSI(Very Large Scale Integration)设计等领域很受欢迎。
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