A Novel Curve Clustering Method for Functional Data: Applications to COVID-19 and Financial Data

Abstract

Functional data analysis has significantly enriched the landscape of existing data analysis methodologies, providing a new framework for comprehending data structures and extracting valuable insights. This paper is dedicated to addressing functional data clustering—a pivotal challenge within functional data analysis. Our contribution to this field manifests through the introduction of innovative clustering methodologies tailored specifically to functional curves. Initially, we present a proximity measure algorithm designed for functional curve clustering. This innovative clustering approach offers the flexibility to redefine measurement points on continuous functions, adapting to either equidistant or nonuniform arrangements, as dictated by the demands of the proximity measure. Central to this method is the “proximity threshold”, a critical parameter that governs the cluster count, and its selection is thoroughly explored. Subsequently, we propose a time-shift clustering algorithm designed for time-series data. This approach identifies historical data segments that share patterns similar to those observed in the present. To evaluate the effectiveness of our methodologies, we conduct comparisons with the classic K-means clustering method and apply them to simulated data, yielding encouraging simulation results. Moving beyond simulation, we apply the proposed proximity measure algorithm to COVID-19 data, yielding notable clustering accuracy. Additionally, the time-shift clustering algorithm is employed to analyse NASDAQ Composite data, successfully revealing underlying economic cycles.