使用渐近Surprise检测社区
Detecting communities using asymptotical Surprise
摘要：
现实世界网络中的节点被反复观察到形成密集的集群，通常被称为社区。检测这些节点组的方法通常最大化目标函数，该目标函数隐含地包含社区的定义。我们在这里分析了最近提出的一种称为惊喜的措施，它评估了网络划分为社区的质量。以其目前的形式，出其不意的提法相当难以分析。因此，我们在这里开发一个精确的渐近近似。这使得开发一种有效的算法来优化惊喜。顺便说一句，这导致了对加权图的惊讶的直接扩展。此外，这种近似可以更密切地分析突袭，并将其与其他方法进行比较，特别是模块化。我们发现，惊喜是（几乎）不受众所周知的分辨率限制，模块化的一个特殊问题。然而，惊喜可能会高估社区的数量，而他们可能被低估的模块化。简而言之，惊喜在许多小社区的限制下运作良好，而模块化在少数大社区的限制下运作得更好。从这个意义上说，惊奇比模块化更具区分性，并且可能发现模块化无法识别任何结构的社区。
英文摘要：
Nodes in real-world networks are repeatedly observed to form dense clusters, often referred to as communities. Methods to detect these groups of nodes usually maximize an objective function, which implicitly contains the definition of a community. We here analyze a recently proposed measure called surprise, which assesses the quality of the partition of a network into communities. In its current form, the formulation of surprise is rather difficult to analyze. We here therefore develop an accurate asymptotic approximation. This allows for the development of an efficient algorithm for optimizing surprise. Incidentally, this leads to a straightforward extension of surprise to weighted graphs. Additionally, the approximation makes it possible to analyze surprise more closely and compare it to other methods, especially modularity. We show that surprise is (nearly) unaffected by the well known resolution limit, a particular problem for modularity. However, surprise may tend to overestimate the number of communities, whereas they may be underestimated by modularity. In short, surprise works well in the limit of many small communities, whereas modularity works better in the limit of few large communities. In this sense, surprise is more discriminative than modularity, and may find communities where modularity fails to discern any structure.
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