通过突击探测中尺度结构
Detecting mesoscale structures by surprise
摘要：
在复杂网络中识别中尺度结构的重要性怎么估计都不过分。到目前为止，很多注意力都集中在二元网络上的社区，二分和核心-外围结构的检测上：这样的努力导致了基于称为惊喜的评分函数的统一框架的定义，即可以分配给无向和有向网络上任何给定节点分区的p值。在这里，我们的目标是更进一步，通过扩展整个框架的加权的情况下：在审查应用程序的基于递归的形式主义检测二进制中尺度结构，我们提出了一个合适的泛化它检测加权中尺度结构，一个主题，已收到少得多的关注。为此，我们分析了惊喜的四种变体;从技术的角度来看，这相当于使用了超几何分布的四种变体：用于检测二元社区的二项分布、用于检测二元社区的多项分布。“双模”结构及其用于检测加权网络上的社区和“双模”结构的负对应物。最重要的是，我们定义了两个“增强”的惊喜的变种，能够编码的二进制和加权约束，其定义取决于两个合适的概括的超几何分布本身。因此，我们提出了一个通用的，基于概率的方法来检测网络上的中尺度结构，通过一个统一的，基于惊喜的框架。为了说明我们的方法的性能，我们首先在各种成熟的合成基准上测试它们，然后将它们应用于几个现实世界的网络，即社会，经济，金融和生态网络。此外，我们在论文中附上了一个Python代码，实现了所有考虑过的惊喜变体。
英文摘要：
The importance of identifying the presence of mesoscale structures in complex networks can be hardly overestimated. So far, much attention has been devoted to the detection of communities, bipartite and core-periphery structures on binary networks: such an effort has led to the definition of a unified framework based upon the score function called surprise, i.e. a p-value that can be assigned to any given partition of nodes, on both undirected and directed networks. Here, we aim at making a step further, by extending the entire framework to the weighted case: after reviewing the application of the surprise-based formalism to the detection of binary mesoscale structures, we present a suitable generalization of it for detecting weighted mesoscale structures, a topic that has received much less attention. To this aim, we analyze four variants of the surprise; from a technical point of view, this amounts at employing four variants of the hypergeometric distribution: the binomial one for the detection of binary communities, the multinomial one for the detection of binary "bimodular" structures and their negative counterparts for the detection of communities and "bimodular" structures on weighted networks. On top of that, we define two "enhanced" variants of surprise, able to encode both binary and weighted constraints and whose definition rests upon two suitable generalizations of the hypergeometric distribution itself. As a result, we present a general, statistically-grounded approach to detect mesoscale structures on networks via a unified, suprise-based framework. To illustrate the performance of our methods, we, first, test them on a variety of well-established, synthetic benchmarks and, then, apply them to several real-world networks, i.e. social, economic, financial and ecological ones. Moreover, we attach to the paper a Python code implementing all the considered variants of surprise.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
