标题： 基于递归二元分割的近似完美聚类方法使用最大MMD 显示英文标题

标题： Near-perfect Clustering Based on Recursive Binary Splitting Using Max-MMD

摘要： 我们开发了新的聚类算法，用于当聚类数量$K$未知时以及当其固定时的功能数据。 这些算法是基于两组观测之间的最大均值差异（MMD）度量开发的。 这些算法递归地使用二元分割策略，将数据集划分为两个子组，使得它们在适当的加权MMD度量方面尽可能分离。 当$K$未知时，所提出的聚类算法有一个额外的步骤，用于检查通过二元分割技术获得的一组观测是否来自单一总体。 我们还使用该算法获得了$K$的一个真实估计量。 当$K$固定时，提出了一种对前一种算法的修改，该修改包括一个额外的步骤，即合并在加权MMD距离方面相似的子组。 在需要知道不同总体观测经验分布的oracle场景中，研究了所提出算法的理论性质。 在这种情况下，我们证明了当$K$未知时提出的算法实现了完美的聚类，而当$K$固定时提出的算法具有完美顺序保持（POP）属性。 使用具有位置差异以及尺度差异的各种模型进行的大量真实和模拟数据分析表明，两种算法都表现出接近完美的聚类性能，并优于功能数据的最新聚类方法。 显示英文摘要

摘要： We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of observations. The algorithms recursively use a binary splitting strategy to partition the dataset into two subgroups such that they are maximally separated in terms of an appropriate weighted MMD measure. When $K$ is unknown, the proposed clustering algorithm has an additional step to check whether a group of observations obtained by the binary splitting technique consists of observations from a single population. We also obtain a bonafide estimator of $K$ using this algorithm. When $K$ is prefixed, a modification of the previous algorithm is proposed which consists of an additional step of merging subgroups which are similar in terms of the weighted MMD distance. The theoretical properties of the proposed algorithms are investigated in an oracle scenario that requires the knowledge of the empirical distributions of the observations from different populations involved. In this setting, we prove that the algorithm proposed when $K$ is unknown achieves perfect clustering while the algorithm proposed when $K$ is prefixed has the perfect order preserving (POP) property. Extensive real and simulated data analyses using a variety of models having location difference as well as scale difference show near-perfect clustering performance of both the algorithms which improve upon the state-of-the-art clustering methods for functional data.