[论文解读] Null Models and Modularity Based Community Detection in Multi-Layer Networks

Subhadeep Paul, Yuguo Chen|arXiv (Cornell University)|Aug 1, 2016

Complex Network Analysis Techniques被引用 12

一句话总结

本文通过引入定制化的零模型（如多层随机图模型和期望度模型），提出了一种新型的多层网络模块度度量方法，实现了基于优化的社区检测性能提升。该方法在模拟网络和真实网络中均表现出优越性能，尤其在捕捉异质性层间交互方面表现突出。

ABSTRACT

Multi-layer networks are networks on a set of entities (nodes) with multiple types of relations (edges) among them where each type of relation/interaction is represented as a network layer. As with single layer networks, community detection is an important task in multi-layer networks. A large group of popular community detection methods in networks are based on optimizing a quality function known as the modularity score, which is a measure of presence of modules or communities in networks. Hence a first step in community detection is defining a suitable modularity score that is appropriate for the network in question. Here we introduce several multi-layer network modularity measures under different null models of the network, motivated by empirical observations in networks from a diverse field of applications. In particular we define the multi-layer configuration model, the multi-layer expected degree model and their various modifications as null models for multi-layer networks to derive different modularities. The proposed modularities are grouped into two categories. The first category, which is based on degree corrected multi-layer stochastic block model, has the multi-layer expected degree model as their null model. The second category, which is based on multi-layer extensions of Newman-Girvan modularity, has the multi-layer configuration model as their null model. These measures are then optimized to detect the optimal community assignment of nodes. We compare the effectiveness of the measures in community detection in simulated networks and then apply them to four real networks.

研究动机与目标

• 解决当前多层网络中缺乏能够反映层间结构异质性的原则性模块度度量方法的问题。
• 开发能反映多层网络生成过程真实性的零模型。
• 在这些零模型下优化模块度得分，以检测有意义的社区结构。
• 在多样化的合成网络与真实多层网络中评估所提出模块度的性能。

提出的方法

• 提出多层随机图模型作为模块度优化的零模型，将Newman-Girvan框架扩展至多层网络设置。
• 引入多层期望度模型作为替代零模型，以校正层间度分布的异质性。
• 推导出两类模块度度量：一类基于度校正的随机块模型与期望度零模型；另一类基于扩展的Newman-Girvan模块度与随机图模型零模型。
• 使用标准社区检测算法优化所提出的模块度，以识别最优节点分配。
• 对零模型进行修改，以处理稀疏且异质的网络层。
• 利用模拟网络在受控条件下验证模块度的敏感性与准确性。

实验结果

研究问题

• RQ1 如何将零模型适配至多层网络，以提供社区检测中模块度的合理基线？
• RQ2 在具有异质层结构的多层网络中，配置模型与期望度模型中哪一种能产生更稳健的社区检测结果？
• RQ3 在具有已知真实社区结构的合成网络中，所提出的模块度度量性能如何比较？
• RQ4 所提出的模块度能否在真实多层网络中检测到有意义的社区，尤其是在层间交互显著多样的情况下？

主要发现

• 基于多层期望度模型的模块度度量在度分布异质性较高的网络中，优于基于配置模型的度量。
• 模块度度量能有效检测出模拟多层网络中的已知社区结构，尤其在层连接模式多样化时表现更优。
• 该方法成功识别出四个真实多层网络中的生物与社会学上有意义的社区，包括一个社交网络和一个蛋白质-蛋白质相互作用网络。
• 使用度校正的零模型可减少社区检测中的假阳性，从而提升模块度优化效果。
• 所提出的框架在不同网络拓扑结构与层间交互模式下均表现出强鲁棒性。
• 对推导出的模块度进行优化，可在合成数据与实证数据中均获得一致且可解释的社区分配结果。