Network data often represent multiple types of relations, which can also denote exchanged quantities, and are typically encompassed in a weighted multiplex. Such data frequently exhibit clustering structures, however, traditional clustering methods are not well-suited for multiplex networks. Additionally, standard methods treat edge weights in their raw form, potentially biasing clustering towards a node's total weight capacity rather than reflecting cluster-related interaction patterns. To address this, we propose transforming edge weights into a compositional format, enabling the analysis of connection strengths in relative terms and removing the impact of nodes' total weights. We introduce a multiplex Dirichlet stochastic block model designed for multiplex networks with compositional layers. This model accounts for sparse compositional networks and enables joint clustering across different types of interactions. We validate the model through a simulation study and apply it to the international export data from the Food and Agriculture Organization of the United Nations.

翻译：网络数据通常表示多种类型的关系，这些关系也可表示交换量，并通常包含在加权多重网络中。此类数据常呈现聚类结构，然而传统聚类方法并不适用于多重网络。此外，标准方法以原始形式处理边权重，可能导致聚类偏向节点的总权重容量，而非反映与聚类相关的交互模式。为解决这一问题，我们提出将边权重转换为成分格式，从而能够以相对方式分析连接强度，并消除节点总权重的影响。我们引入了一种专为具有成分层的多重网络设计的多重狄利克雷随机块模型。该模型考虑了稀疏成分网络，并支持跨不同类型交互的联合聚类。我们通过模拟研究验证了该模型，并将其应用于联合国粮食及农业组织的国际出口数据。