学习网络集合中的共同结构：在食物网中的应用
Learning common structures in a collection of networks. An application to food webs
AI总结：
本文扩展SBM以联合建模网络集合，利用变分EM和惩罚似然准则识别共同拓扑结构并聚类网络，在67个食物网中发现五种中尺度结构。
摘要：
设一个网络集合表示若干（社会或生态）系统内的相互作用。我们追求两个目标：识别不同网络之间共同具有的拓扑结构相似性，以及将该集合聚类为结构同质网络的子集合。我们采用基于概率模型的方法来处理这两个问题。我们提出了随机块模型（Stochastic Block Model，SBM）的一种扩展，使其适用于网络集合的联合建模。该集合中的网络被假定为SBM的独立实现。共同连接结构通过某些参数相等来施加。模型参数使用变分期望最大化（Expectation-Maximization，EM）算法进行估计。我们推导了一个专门的惩罚似然准则，用于选择块的数量，并评估在不同网络结构之间发现的共识是否充分。同一准则还可用于根据网络的连接结构对网络进行聚类。因此，它将该集合划分为若干结构同质网络的子集。我们在两个生态网络集合上评估了所提方法的相关性。首先，对三个溪流食物网的应用揭示了它们结构的同质性，以及不同生态系统中发挥等价生态作用的物种类群之间的对应关系。此外，联合分析能够对较小网络的结构进行更细致的分析。其次，我们根据连接结构对67个食物网进行聚类，并证明五种中尺度结构足以描述该集合。
英文摘要：
Let a collection of networks represent interactions within several (social or ecological) systems. We pursue two objectives: identifying similarities in the topological structures that are held in common between the networks and clustering the collection into sub-collections of structurally homogeneous networks. We tackle these two questions with a probabilistic model based approach. We propose an extension of the Stochastic Block Model (SBM) adapted to the joint modeling of a collection of networks. The networks in the collection are assumed to be independent realizations of SBMs. The common connectivity structure is imposed through the equality of some parameters. The model parameters are estimated with a variational Expectation-Maximization (EM) algorithm. We derive an ad-hoc penalized likelihood criterion to select the number of blocks and to assess the adequacy of the consensus found between the structures of the different networks. This same criterion can also be used to cluster networks on the basis of their connectivity structure. It thus provides a partition of the collection into subsets of structurally homogeneous networks. The relevance of our proposition is assessed on two collections of ecological networks. First, an application to three stream food webs reveals the homogeneity of their structures and the correspondence between groups of species in different ecosystems playing equivalent ecological roles. Moreover, the joint analysis allows a finer analysis of the structure of smaller networks. Second, we cluster 67 food webs according to their connectivity structures and demonstrate that five mesoscale structures are sufficient to describe this collection.
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