基于谱图小波的时态网络多尺度社区检测
Multi-scale Community Detection in Temporal Networks Using Spectral Graph Wavelets
摘要：
谱图小波在网络中引入了尺度的概念，因此用于从每个节点获得网络的局部视图。通过对这些小波构造一个小波滤波函数，已经发展出了一种多尺度的单一网络社团检测方法。这种构造利用了网络拉普拉斯算子的划分特性。在本文中，我们阐述了一种新的方法，使用谱图小波检测多尺度社区的时间网络。为了做到这一点，我们通过采用多层框架扩展谱图小波的定义到时间网络。我们使用参数扰动理论研究超拉普拉斯矩阵的谱特性，用于时间网络的聚类目的。利用这些属性，我们构建了一个新的小波滤波函数，它衰减的影响，无信息的特征值和中心的过滤器周围的特征值，其中包含信息的粗略描述的流行的社区结构随着时间的推移。我们使用谱图小波作为特征向量的连通性约束聚类过程中检测多尺度社区在不同的尺度，并将这种方法称为时间多尺度社区检测（TMSCD）。我们验证的性能TMSCD和竞争的方法在各种基准。TMSCD的优点是自动选择应寻求社区的相关尺度。
英文摘要：
Spectral graph wavelets introduce a notion of scale in networks, and are thus used to obtain a local view of the network from each node. By carefully constructing a wavelet filter function for these wavelets, a multi-scale community detection method for monoplex networks has already been developed. This construction takes advantage of the partitioning properties of the network Laplacian. In this paper we elaborate on a novel method which uses spectral graph wavelets to detect multi-scale communities in temporal networks. To do this we extend the definition of spectral graph wavelets to temporal networks by adopting a multilayer framework. We use arguments from Perturbation Theory to investigate the spectral properties of the supra-Laplacian matrix for clustering purposes in temporal networks. Using these properties, we construct a new wavelet filter function, which attenuates the influence of uninformative eigenvalues and centres the filter around eigenvalues which contain information on the coarsest description of prevalent community structures over time. We use the spectral graph wavelets as feature vectors in a connectivity-constrained clustering procedure to detect multi-scale communities at different scales, and refer to this method as Temporal Multi-Scale Community Detection (TMSCD). We validate the performance of TMSCD and a competing methodology on various benchmarks. The advantage of TMSCD is the automated selection of relevant scales at which communities should be sought.
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