Abstract

In this paper we propose a novel clustering method for functional data based on the principal curve clustering approach. By this method functional data are approximated using functional principal component analysis (FPCA) and the principal curve clustering is then performed on the principal scores. The proposed method makes use of the nonparametric principal curves to summarize the features of the principal scores extracted from the original functional data, and a probabilistic model combined with Bayesian Information Criterion is employed to automatically and simultaneously find the appropriate number of features, the optimal degree of smoothing and the corresponding cluster members. The simulation studies show that the proposed method outperforms the existing functional clustering approaches considered. The capability of this method is also demonstrated by the applications in the human mortality and fertility data.

摘要

在本文中，我们提出了一种基于主曲线聚类方法的功能数据聚类方法。通过这种方法，使用功能主成分分析 (FPCA) 来近似功能数据，然后对主分数执行主曲线聚类。该方法利用非参数主曲线对从原始功能数据中提取的主分数的特征进行概括，并采用概率模型结合贝叶斯信息准则，自动同时找到合适数量的特征，最优度的平滑和相应的集群成员。仿真研究表明，所提出的方法优于现有的功能聚类方法。