现实大规模复杂网络的多级层次核谱聚类
Multilevel Hierarchical Kernel Spectral Clustering for Real-Life Large Scale Complex Networks
摘要：
核谱聚类对应于约束优化框架下的加权核主成分分析问题。原始配方导致的特征分解的中心拉普拉斯矩阵的对偶水平。对偶公式允许在训练阶段在大规模网络的代表性子图上建立模型，并且在验证阶段估计模型参数。KSC模型具有强大的样本外扩展属性，该属性允许大型数据网中不可见的节点加入集群。在本文中，我们利用结构的特征空间中的投影在验证阶段自动确定一组增加的距离阈值。我们在测试阶段使用这些距离阈值来获得大规模网络的多层层次结构。网络中的分层结构以自下而上的方式确定。我们的经验表明，现实世界的网络有多级层次的组织，不能有效地检测到几个国家的最先进的大规模分层社区发现技术，如Louvain，OSLOM和Infomap方法。我们展示了我们所提出的方法的一个主要优势，即能够在7个现实生活中的网络上使用内部集群质量指标在较粗和较细的层次结构中找到高质量的集群。
英文摘要：
Kernel spectral clustering corresponds to a weighted kernel principal component analysis problem in a constrained optimization framework. The primal formulation leads to an eigen-decomposition of a centered Laplacian matrix at the dual level. The dual formulation allows to build a model on a representative subgraph of the large scale network in the training phase and the model parameters are estimated in the validation stage. The KSC model has a powerful out-of-sample extension property which allows cluster affiliation for the unseen nodes of the big data network. In this paper we exploit the structure of the projections in the eigenspace during the validation stage to automatically determine a set of increasing distance thresholds. We use these distance thresholds in the test phase to obtain multiple levels of hierarchy for the large scale network. The hierarchical structure in the network is determined in a bottom-up fashion. We empirically showcase that real-world networks have multilevel hierarchical organization which cannot be detected efficiently by several state-of-the-art large scale hierarchical community detection techniques like the Louvain, OSLOM and Infomap methods. We show a major advantage our proposed approach i.e. the ability to locate good quality clusters at both the coarser and finer levels of hierarchy using internal cluster quality metrics on 7 real-life networks.
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