Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination as Compactness. Further, we propose LOCLU to optimize the Compactness score. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

中文翻译：

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将用户的偏好纳入属性图聚类

图聚类已经在普通图和属性图上得到了广泛的研究。然而，所有这些方法都需要对整个图进行分区以找到集群结构。有时，基于领域知识，人们可能有关于图中特定目标区域的信息，只想找到集中在该局部区域的单个集群。这样的任务称为本地聚类。与全局聚类相反，局部聚类旨在仅找到一个专注于给定种子顶点（以及属性图的指定属性）的聚类。目前，很少有方法可以处理此类任务。为此，我们为本地集群提出了两种质量度量：图单峰性（GU）和属性单峰性（AU）。前者衡量图结构的同质性，后者衡量由指定属性组成的子空间的同质性。我们称它们的线性组合为 Compactness。此外，我们建议使用 LOCLU 来优化 Compactness 分数。LOCLU 检测到的局部聚类集中在感兴趣的区域，在图中提供有效的信息流，并在指定属性的子空间中表现出单峰数据分布。