Quantile-based Clustering for Functional Data via Modelling Functional Principal Components Scores

Abstract

Clustering tasks of functional data arise naturally in many applications, and efficient classification approaches are needed to find groups. The current paper combines the quantile-based model with the principal component analysis of functional data (FPCA). In our proposed procedures, the projection of functional data is first approximated based on (rotated) FPCA. The quantile-based model is then implemented on the space of rotated scores to identify the potential features of underlying clusters. The proposed method overcomes the limitation of using direct basis function expansion such as Fourier, B-spline, or linear fitting, besides representing a nonparametric clustering alternative based on a quantile approach. The proposed method’s performance has been evaluated in a comprehensive simulation study and afterward compared with existing functional and non-functional clustering methods. The simulation study results showed that the proposed method performs well in terms of correct classification rate and computing time average. Finally, a real-world application concerning temporal wind speed data has been analyzed to demonstrate the proposed method’s advantages and usefulness.