Functional Data Clustering Based on Weighted Functional Spatial Ranks With Clinical Applications

Abstract

Functional data analysis is receiving increasing attention in several scientific disciplines. However, identifying and classifying clusters of data that are essentially curves that map into an infinite dimensional space poses a significant challenge for existing methods. Here, we introduce weighted functional spatial ranks (WFSRs) as part of a nonparametric clustering approach for functional data analysis. A two-stage or filtering method is used to approximate the curves into some basis functions and reduce the dimension of the data using functional principle components analysis (FPCA). The curves are then ranked based on WFSRs to create a contour map. This allows the visualization of the cluster structure and the size and content of each cluster to be ascertained. The effectiveness of the methods in functional data analysis is evaluated using numerical examples from simulated and two real medical datasets. Compared with several other cluster methods, the WFSR algorithm records the lowest misclassification rates over the two real datasets.