Jeub Lucas G S, Sporns Olaf, Fortunato Santo
School of Informatics, Computing and Engineering, Indiana University, Indiana, United States.
Department of Psychological and Brain Sciences, Indiana University, Indiana, United States.
Sci Rep. 2018 Feb 19;8(1):3259. doi: 10.1038/s41598-018-21352-7.
Networks often exhibit structure at disparate scales. We propose a method for identifying community structure at different scales based on multiresolution modularity and consensus clustering. Our contribution consists of two parts. First, we propose a strategy for sampling the entire range of possible resolutions for the multiresolution modularity quality function. Our approach is directly based on the properties of modularity and, in particular, provides a natural way of avoiding the need to increase the resolution parameter by several orders of magnitude to break a few remaining small communities, necessitating the introduction of ad-hoc limits to the resolution range with standard sampling approaches. Second, we propose a hierarchical consensus clustering procedure, based on a modified modularity, that allows one to construct a hierarchical consensus structure given a set of input partitions. While here we are interested in its application to partitions sampled using multiresolution modularity, this consensus clustering procedure can be applied to the output of any clustering algorithm. As such, we see many potential applications of the individual parts of our multiresolution consensus clustering procedure in addition to using the procedure itself to identify hierarchical structure in networks.
网络通常在不同尺度上呈现出结构。我们提出了一种基于多分辨率模块度和一致性聚类来识别不同尺度上社区结构的方法。我们的贡献包括两个部分。首先，我们提出了一种对多分辨率模块度质量函数的整个可能分辨率范围进行采样的策略。我们的方法直接基于模块度的属性，特别是提供了一种自然的方式，避免了为打破少数剩余的小社区而将分辨率参数提高几个数量级的需要，而使用标准采样方法时需要对分辨率范围引入临时限制。其次，我们基于一种改进的模块度提出了一种层次一致性聚类过程，该过程允许在给定一组输入划分的情况下构建层次一致性结构。虽然在这里我们感兴趣的是其在使用多分辨率模块度采样的划分上的应用，但这种一致性聚类过程可以应用于任何聚类算法的输出。因此，除了使用该过程本身来识别网络中的层次结构外，我们还看到了我们的多分辨率一致性聚类过程的各个部分的许多潜在应用。
