Clustering for Bivariate Functional Data

• Published in: Acta Mathematicae Applicatae Sinica Vol. 40; no. 3; pp. 613 - 629
• Main Authors: Cao, Shi-yun, Zhou, Yan-qiu, Wan, Yan-ling, Zhang, Tao
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Edition: English series
• Subjects: Applications of Mathematics; Bivariate analysis; Clustering; Empirical analysis; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Principal components analysis; Theoretical; partial derivative function; bivariate functional data; functional principal component analysis; 62J99; centres surface clustering; 62E20
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-024-1116-5

In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k -centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, k -centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data.