A Clustering Framework for Functional Data: Functional Gaussian Process Mixture Model (FunGP)

Abstract

Functional data analysis (FDA) is a rapidly evolving field that focuses on the analysis and interpretation of data where each observation is a function, typically represented by curves or surfaces over a continuum such as time or space. this dissertation presents a novel clustering framework, tailored for functional data, named FunGP. The proposed framework is divided into three layers, including smoother, projector, and clustering. Each layer can be used individually or combined into a complete clustering model process. Such a design aims for flexibility and ease of use, allowing methods and parameters to be adapted to user needs.

To verify the effectiveness of our framework, we conduct comprehensive evaluations using simulated and real data sets, demonstrating that FunGP not only surpasses traditional clustering methods in accuracy but also exhibits significant robustness in different scenarios. Our results highlight the potential of FunGP as a preferred solution for functional data clustering, combining accuracy, flexibility, and user-friendliness to address a wide range of analytical needs.