论文标题
多层网络的自适应层聚集光谱聚类
Spectral clustering via adaptive layer aggregation for multi-layer networks
论文作者
论文摘要
网络分析中的基本问题之一是检测多层网络中的社区结构，其中每一层代表节点之间的一种边缘信息。我们提出了基于有效凸层聚集的集成光谱聚类方法。我们的聚合方法是由对加权邻接矩阵的光谱嵌入和下游$ k $ - 均值聚类的微妙渐近分析的强烈动机，这是在不可能的社区检测一致性的挑战性方面。实际上，这些方法被证明可以估计最佳凸聚集，从而最大程度地减少了一些专业的多层网络模型下的错误群集误差。我们的分析进一步表明，使用高斯混合物模型的聚类通常优于光谱聚类中常用的$ k $均值。广泛的数值研究表明，我们的自适应聚集技术与高斯混合模型聚类一起使新的光谱聚类与几种常用的方法相比非常有竞争力。
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream $k$-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the mis-clustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used $k$-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods.
