In order to investigate exchanges between objects, a clustering model for skew-symmetric data is proposed, which relies on the between-cluster effects of the skew-symmetries that represent the imbalances of the observed exchanges between pairs of objects. The aim is to detect clusters of objects that share the same behaviour of exchange so that origin and destination clusters are identified. The proposed model is based on the decomposition of the skew-symmetric matrix pertaining to the imbalances between clusters into a sum of a number of off-diagonal block matrices. Each matrix can be approximated by a skew-symmetric matrix by using a truncated Singular Value Decomposition (SVD) which exploits the properties of the skew-symmetric matrices. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is provided. Finally, in order to show the potentiality of the model and the features of the resulting clusters, an extensive simulation study and an illustrative application to real data are presented.

为了研究对象之间的交换，提出了一种倾斜对称数据的聚类模型，该模型依赖于倾斜对称性的簇间效应，该效应代表了观察到的对象对之间交换的不平衡性。目的是检测具有相同交换行为的对象集群，以便识别源集群和目标集群。所提出的模型基于将与簇之间不平衡有关的斜对称矩阵分解为多个非对角块矩阵的总和。每个矩阵都可以通过使用截断奇异值分解 (SVD) 来近似为斜对称矩阵，该分解利用了斜对称矩阵的属性。该模型适合最小二乘框架，并提供有效的交替最小二乘算法。最后，为了展示模型的潜力和所得集群的特征，提出了广泛的模拟研究和对实际数据的说明性应用。