Clustering functional data using forward search based on functional spatial ranks with medical applications.

Cluster analysis of functional data is finding increasing application in the field of medical research and statistics. Here we introduce a functional version of the forward search methodology for the purpose of functional data clustering. The proposed forward search algorithm is based on the functional spatial ranks and is a data-driven non-parametric method. It does not require any preprocessing functional data steps, nor does it require any dimension reduction before clustering. The Forward Search Based on Functional Spatial Rank (FSFSR) algorithm identifies the number of clusters in the curves and provides the basis for the accurate assignment of each curve to its cluster. We apply it to three simulated datasets and two real medical datasets, and compare it with six other standard methods. Based on both simulated and real data, the FSFSR algorithm identifies the correct number of clusters. Furthermore, when compared with six standard methods used for clustering and classification, it records the lowest misclassification rate. We conclude that the FSFSR algorithm has the potential to cluster and classify functional data.