A Comparison of Hierarchical Methods for Clustering Functional Data

Key Words: cluster analysis; cluster sizes; misspecification; periodic functions. Functional data analysis (FDA) — the analysis of data that can be considered a set of observed continuous functions — is an increasingly common class of statistical analysis. One of the most widely used FDA methods is the cluster analysis of functional data; however, little work has been done to compare the performance of clustering methods on functional data. In this paper a simulation study compares the performance of four major hierarchical methods for clustering functional data. The simulated data varied in three ways: the nature of the signal functions (periodic, non-periodic, or mixed), the amount of noise added to the signal functions, and the pattern of the true cluster sizes. The Rand index was used to compare the performance of each clustering method. As a secondary goal, clustering methods were also compared when the number of clusters has been misspecified. To illustrate the results, a real set of functional data was clustered where the true clustering structure is believed to be known. Comparing the clustering methods for the real data set confirmed the findings of the simulation. This study yields concrete suggestions to future researchers to determine the best method for clustering their functional data. 1.