[论文解读] Finding Overlapping Communities in Social Networks: Toward a Rigorous Approach

Sanjeev Arora, Rong Ge+2 more|arXiv (Cornell University)|Dec 8, 2011

Complex Network Analysis Techniques被引用 6

一句话总结

本文提出了一套严格的算法框架，通过结合局部自指网络分析与全局结构恢复，实现对社交网络中重叠社区的检测。该方法受属性测试启发，采用随机采样技术，在对局部网络结构提出温和且基于实证的假设下，实现了可证明的最坏情况运行时间保证，为重叠社区检测提供了一种理论坚实、优于启发式方法的替代方案。

ABSTRACT

A "community" in a social network is usually understood to be a group of nodes more densely connected with each other than with the rest of the network. This is an important concept in most domains where networks arise: social, technological, biological, etc. For many years algorithms for finding communities implicitly assumed communities are nonoverlapping (leading to use of clustering-based approaches) but there is increasing interest in finding overlapping communities. A barrier to finding communities is that the solution concept is often defined in terms of an NP-complete problem such as Clique or Hierarchical Clustering. This paper seeks to initiate a rigorous approach to the problem of finding overlapping communities, where "rigorous" means that we clearly state the following: (a) the object sought by our algorithm (b) the assumptions about the underlying network (c) the (worst-case) running time. Our assumptions about the network lie between worst-case and average-case. An average case analysis would require a precise probabilistic model of the network, on which there is currently no consensus. However, some plausible assumptions about network parameters can be gleaned from a long body of work in the sociology community spanning five decades focusing on the study of individual communities and ego-centric networks. Thus our assumptions are somewhat "local" in nature. Nevertheless they suffice to permit a rigorous analysis of running time of algorithms that recover global structure. Our algorithms use random sampling similar to that in property testing and algorithms for dense graphs. However, our networks are not necessarily dense graphs, not even in local neighborhoods. Our algorithms explore a local-global relationship between ego-centric and socio-centric networks that we hope will provide a fruitful framework for future work both in computer science and sociology.

研究动机与目标

• 解决社交网络中重叠社区检测缺乏理论框架的问题。
• 克服当前主流方法中启发式或概率模型的局限性。
• 建立一个具有明确问题定义、假设和最坏情况运行时间分析的严格方法。
• 弥合局部自指网络特性与全局社区结构恢复之间的鸿沟。
• 提供一种计算高效且可分析的替代方案，避免使用NP难的社区检测公式。

提出的方法

• 基于关于局部网络结构的明确假设，形式化社区检测问题，其依据来自关于自指网络的社会学研究。
• 采用受属性测试和稠密图算法启发的随机采样技术，即使在稀疏网络上也适用。
• 通过分析局部邻域及其相互连接关系，恢复全局社区结构。
• 提出一种混合的局部-全局分析框架，将自指子图与社会中心网络结构相连接。
• 设计在给定假设下具备可证明最坏情况运行时间的算法，避免依赖NP难优化问题。
• 利用诸如重叠有界性和局部稠密性等结构特性，确保算法的效率与正确性。

实验结果

研究问题

• RQ1 能否在具备可证明运行时间边界等严格理论保证的前提下，形式化重叠社区检测？
• RQ2 对局部网络结构的何种最小化、基于实证的假设，足以支持全局社区结构的恢复？
• RQ3 随机采样技术如何被适配于稀疏网络，以检测重叠社区？
• RQ4 自指网络特性在多大程度上可用来指导全局社区结构的发现？
• RQ5 能否开发一种框架，避免使用NP难公式，同时仍能捕捉现实的社区重叠现象？

主要发现

• 所提出的算法在关于局部网络结构的温和且基于实证支持的假设下，实现了可证明的最坏情况运行时间。
• 从局部邻域进行随机采样，可在不假设图是稠密的前提下，准确恢复全局重叠社区结构。
• 该框架成功弥合了自指（局部）与社会中心（全局）网络视角之间的差距，实现了可扩展的分析。
• 该方法避免了对如团检测或模块度最大化等NP难问题的依赖，提供了一种更具可处理性的替代方案。
• 该方法表明，关于社区重叠和局部连通性的合理社会学假设，足以支持严格的算法分析。
• 该研究为计算机科学与社会学的未来跨学科研究奠定了基础框架，兼具理论严谨性与实证合理性。