Clustering of Functional Data by Band Depth

Abstract

The notion of data depth is a generalization of order statistics, ranks, and medians in one-dimensional space to multi-dimensional space. Band depth is a depth measure of functional data. A few articles in the literature emerged in recent years that used band depth to analyze functional data. The present work is the first attempt to develop a non-parametric clustering method based on band depth. Three definitions of band depth are compared, a few combinations of clustering strategies are employed, and band depth clustering is applied to DNA microarray data of yeast cell cycle. The results show that band depth clustering is efficient and robust.