We consider the problem of clustering functional data according to their covariance structure. We contribute a soft clustering methodology based on the Wasserstein-Procrustes distance, where the in-between cluster variability is penalised by a term proportional to the entropy of the partition matrix. In this way, each covariance operator can be partially classified into more than one group. Such soft classification allows for clusters to overlap, and arises naturally in situations where the separation between all or some of the clusters is not well-defined. We also discuss how to estimate the number of groups and to test for the presence of any cluster structure. The algorithm is illustrated using simulated and real data. An R implementation is available in the Supplementary materials.
翻译:我们根据功能数据的共变结构来考虑将功能数据分组的问题。我们根据瓦塞斯坦-普罗克鲁斯特距离提出软组合方法,即组群内部的变异性受到与分区矩阵的正方位成比例的术语的处罚。这样,每个共变操作者可以部分地分为一个以上组。这种软分类允许组群重叠,并在所有组群或某些组群之间的分离没有明确界定的情况下自然产生。我们还讨论如何估计组群数量并测试是否存在任何组群结构。算法使用模拟和实际数据加以说明。补充材料中有R的落实情况。