寻找内生形成的社区
Finding Endogenously Formed Communities
摘要：
电子商务中的一个核心问题是在没有外部标识或标记的情况下确定个人或对象之间的重叠社区。我们通过引入一个框架来解决这个问题，该框架捕获了由其成员之间的相对亲和力决定的社区或集群的概念。为此，我们定义了我们所谓的亲和系统，它是一组元素，每个元素都有一个向量来表征它对集合中所有其他元素的偏好。我们在亲和系统中定义了一个自然的（可能重叠的）社区概念，在这个系统中，给定社区的成员集体地彼此偏好，而不是社区之外的任何其他人。因此，这些社区是在亲和系统中内生形成的，并由其成员“自我决定”或“自我证明”。我们提供了一个严格的多项式约束作为社区的鲁棒性的函数的自我决定的社区的数量。我们提出了一个多项式时间算法来枚举这些社区。此外，我们得到了一个本地算法具有很强的随机性能保证，可以找到一个社区的时间近似线性的大小社区。社交网络特别自然地适合于亲和系统框架--如果我们能够从社交网络中相对稀疏但丰富的信息中适当地提取亲和度，那么我们的分析就会产生一组用于枚举社交网络中的自我决定社区的有效算法。在社交网络的背景下，我们还将我们的分析与有关$(α,β)$的结果联系起来--Mishra、Schreiber、Stanton和Tarjan \cite{msst}提出的聚类。与我们在亲和系统模型中证明的社区数的多项式界相反，我们证明了存在一族具有超多项式数目的$(α,β)$ -簇的网络。
英文摘要：
A central problem in e-commerce is determining overlapping communities among individuals or objects in the absence of external identification or tagging. We address this problem by introducing a framework that captures the notion of communities or clusters determined by the relative affinities among their members. To this end we define what we call an affinity system, which is a set of elements, each with a vector characterizing its preference for all other elements in the set. We define a natural notion of (potentially overlapping) communities in an affinity system, in which the members of a given community collectively prefer each other to anyone else outside the community. Thus these communities are endogenously formed in the affinity system and are "self-determined" or "self-certified" by its members. We provide a tight polynomial bound on the number of self-determined communities as a function of the robustness of the community. We present a polynomial-time algorithm for enumerating these communities. Moreover, we obtain a local algorithm with a strong stochastic performance guarantee that can find a community in time nearly linear in the of size the community. Social networks fit particularly naturally within the affinity system framework -- if we can appropriately extract the affinities from the relatively sparse yet rich information from social networks, our analysis then yields a set of efficient algorithms for enumerating self-determined communities in social networks. In the context of social networks we also connect our analysis with results about $(α,β)$-clusters introduced by Mishra, Schreiber, Stanton, and Tarjan \cite{msst}. In contrast with the polynomial bound we prove on the number of communities in the affinity system model, we show that there exists a family of networks with superpolynomial number of $(α,β)$-clusters.
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