论文标题
基于协方差的功能数据的软聚类基于Wasserstein-Procrustes度量
Covariance-based soft clustering of functional data based on the Wasserstein-Procrustes metric
论文作者
论文摘要
我们根据其协方差结构来考虑聚类功能数据的问题。我们基于Wasserstein-Prorcrustes距离贡献了一种软聚类方法，其中群集变异性与分区矩阵熵成比例的期限惩罚。这样，每个协方差运算符可以部分分为多个组。这种软分类允许簇重叠，并且在所有或某些簇之间的分离之间自然而然地出现。我们还讨论了如何估计组数量并测试任何群集结构的存在。使用模拟和真实数据说明该算法。补充材料中有R实施。
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.
