Covariance‐based soft clustering of functional data based on the Wasserstein–Procrustes metric
提出一种基于Wasserstein-Procrustes距离的软聚类方法，用于按协方差结构对函数数据进行聚类，允许协方差算子部分属于多个组，并讨论了组数估计和聚类结构检验。
Abstract 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 penalized 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 Appendix .