Functional hierarchical clustering using shape distance

A functional clustering analysis is a crucial machine learning technique in functional data analysis.Many functional clustering methods have been developed to enhance clustering performance.Moreover, due to the phase variability between functions, elastic functional clustering methods, such as applying the Fisher-Rao metric, which can manage phase variation during clustering, have been developed to improve model performance.However, aligning functions without considering the phase variation can distort functional information because phase variation can be a natural characteristic of functions.Hence, we propose a state-of-the-art functional hierarchical clustering that can manage phase and amplitude variations of functional data.This approach is based on the phase and amplitude separation method using the norm-preserving time warping of functions.Due to its invariance property, this representation provides robust variability for phase and amplitude components of functions and improves clustering performance compared to conventional functional hierarchical clustering models.We demonstrate this framework using simulated and real data.