Spectral Clustering via Adaptive Layer Aggregation for Multi-Layer Networks
Spectral Clustering via Adaptive Layer Aggregation for Multi-Layer Networks
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DOI：
10.1080/10618600.2022.2134874
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发表时间：
2020-12
影响因子：
2.4
通讯作者：
Sihan Huang;Haolei Weng;Yang Feng
中科院分区：
文献类型：
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作者：
Sihan Huang;Haolei Weng;Yang Feng
网络分析中的一个基本问题是在多层网络中发现社区结构，其中每一层代表节点之间的一种边信息。我们提出了基于有效凸层聚合的综合谱聚类方法。我们的聚合方法是强烈的动机加权邻接矩阵的谱嵌入和下游的k-均值聚类，在一个具有挑战性的制度，社区检测一致性是不可能的一个微妙的渐近分析。事实上，该方法被证明是为了估计最优凸聚集，这使得在某些特定的多层网络模型下的误聚类误差最小化。我们的分析进一步表明，使用高斯混合模型的聚类一般优于常用的k-均值谱聚类上级。大量的数值研究表明，我们的自适应聚合技术，再加上高斯混合模型聚类，使新的谱聚类显着的竞争力相比，几个常用的方法。本文的补充材料可在网上查阅。
Abstract 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 misclustering 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. Supplementary materials for this article are available online.