There is increasing appetite for analysing populations of network data due to the fast-growing body of applications demanding such methods. While methods exist to provide readily interpretable summaries of heterogeneous network populations, these are often descriptive or ad hoc, lacking any formal justification. In contrast, principled analysis methods often provide results difficult to relate back to the applied problem of interest. Motivated by two complementary applied examples, we develop a Bayesian framework to appropriately model complex heterogeneous network populations, whilst also allowing analysts to gain insights from the data, and make inferences most relevant to their needs. The first application involves a study in Computer Science measuring human movements across a University. The second analyses data from Neuroscience investigating relationships between different regions of the brain. While both applications entail analysis of a heterogeneous population of networks, network sizes vary considerably. We focus on the problem of clustering the elements of a network population, where each cluster is characterised by a network representative. We take advantage of the Bayesian machinery to simultaneously infer the cluster membership, the representatives, and the community structure of the representatives, thus allowing intuitive inferences to be made. The implementation of our method on the human movement study reveals interesting movement patterns of individuals in clusters, readily characterised by their network representative. For the brain networks application, our model reveals a cluster of individuals with different network properties of particular interest in Neuroscience. The performance of our method is additionally validated in extensive simulation studies.

翻译：随着对分析网络数据群体方法的需求快速增长，处理此类问题的应用场景日益增多。尽管现有方法可为异质性网络群体提供易于解释的概要性总结，但这些方法往往是描述性或临时性的，缺乏正式的理论依据。相比之下，基于严格原理的分析方法虽能提供结果，却难以与实际应用问题建立关联。受两个互补性应用实例的启发，我们构建了一个贝叶斯框架以合理建模复杂的异质性网络群体，同时使分析人员能够从数据中获取洞见，并做出最符合其需求的推断。第一个应用案例涉及计算机科学领域中对大学校园内人类移动轨迹的测量研究；第二个案例则分析神经科学中大脑不同区域间的关系数据。尽管这两个应用都需要分析异质性网络群体，但网络规模差异显著。我们聚焦于网络群体元素的聚类问题，其中每个聚类由代表性网络表征。通过利用贝叶斯方法的优势，我们能够同时推断聚类归属、代表性网络及其社区结构，从而得出直观的推论。将该方法应用于人类移动研究后，揭示了聚类中个体的有趣移动模式，这些模式可被其网络代表性轻松表征。在脑网络应用案例中，我们的模型识别出一个具有独特网络属性的个体聚类，这对神经科学具有特殊意义。此外，大量模拟研究进一步验证了该方法的有效性。