[论文解读] Local community detection by seed expansion: from conductance to weighted kernel 1-mean optimization.

Twan van Laarhoven, Elena Marchiori|arXiv (Cornell University)|Jan 21, 2016

Complex Network Analysis Techniques参考文献 33被引用 3

一句话总结

本文提出了一种导通率的连续松弛方法，称为σ-导通率，通过加权核1-均值优化实现局部社区检测。通过引入可调参数σ，该方法避免了刚性邻域假设，并借助EMc和PGDc算法实现高质量、局部化的社区结构，具有理论保证，并在合成网络和真实网络中表现出优越性能。

ABSTRACT

In local community detection by seed expansion a single cluster concentrated around few given query nodes in a graph is discovered in a localized way. Conductance is a popular objective function used in many algorithms for local community detection. Algorithms that directly optimize conductance usually add or remove one node at a time to find a local optimum. This amounts to fix a specific neighborhood structure over clusters. A natural way to avoid the problem of choosing a specific neighborhood structure is to use a continuous relaxation of conductance. This paper studies such a continuous relaxation of conductance. We show that in this setting continuous optimization leads to hard clusters. We investigate the relation of conductance with weighted kernel k-means for a single cluster, which leads to the introduction of a weighted kernel 1-mean objective function, called \sigma-conductance, where {\sigma} is a parameter which influences the size of the community. Conductance is obtained by setting {\sigma} to 0. Two algorithms for local optimization of \sigma-conductance based on the expectation maximization and the projected gradient descend method are developed, called EMc and PGDc, respectively. We show that for \sigma=0 EMc corresponds to gradient descend with an infinite step size at each iteration. We design a procedure to automatically select a value for {\sigma}. Performance guarantee for these algorithms is proven for a class of dense communities centered around the seeds and well separated from the rest of the network. On this class we also prove that our algorithms stay localized. A comparative experimental analysis on networks with ground-truth communities is performed using state-of-the-art algorithms based on the graph diffusion method. Our experiments indicate that EMc and PGDc stay localized and produce communities most similar to the ground.

研究动机与目标

• 解决传统种子扩展算法在优化导通率时对固定邻域结构的依赖问题。
• 开发导通率的连续松弛方法，避免在局部社区检测中对邻域结构的任意假设。
• 建立导通率与加权核k-均值在单簇优化中的联系。
• 设计高效的优化算法——EMc和PGDc——以优化所提出的σ-导通率目标。
• 为密集且分离良好的社区提供关于定位性和性能的理论保证。

提出的方法

• 提出σ-导通率作为导通率的连续松弛，其中σ控制社区大小，并在σ=0时推广标准导通率。
• 将局部社区检测重新表述为加权核1-均值优化问题，以实现平滑、连续的聚类分配。
• 开发EMc和PGDc算法，利用期望最大化和投影梯度下降来优化σ-导通率。
• 证明当σ=0时，EMc等价于无限步长的梯度下降，建立与现有方法的理论联系。
• 引入自动σ选择程序，基于种子节点的接近程度和网络结构自适应调节社区大小。
• 通过理论分析证明，对于密集且分离良好的社区，EMc和PGDc均能保持定位性并实现良好性能。

实验结果

研究问题

• RQ1 如何对导通率进行连续松弛，以避免在局部社区检测中对离散邻域结构的依赖？
• RQ2 在单簇优化背景下，导通率与加权核k-均值之间存在何种关系？
• RQ3 对σ-导通率进行连续优化是否能比基于离散导通率的方法实现更好的定位性和准确性？
• RQ4 EMc和PGDc算法在收敛性、定位性和与真实社区的相似性方面表现如何？
• RQ5 如何设计一种有效的σ参数自动选择策略，以在社区大小与质量之间取得平衡？

主要发现

• EMc和PGDc在社区检测精度方面表现优异，在对比实验中生成的聚类与真实社区最为相似。
• 这些算法保持了良好的定位性，即使在网络规模较大时，也不会过度扩展至种子节点周围区域之外。
• 当σ=0时，EMc退化为无限步长的梯度下降，建立了与现有基于导通率方法的理论联系。
• 理论保证证实，EMc和PGDc均能保持定位性，并在密集且分离良好的社区中实现良好性能。
• 自动σ选择程序能有效调节社区大小而无需先验知识，显著提升了方法的鲁棒性。
• 实证结果表明，σ-导通率在社区质量和定位性方面优于当前最先进的图扩散基算法。