Clustering high dimension, low sample size data using the maximal data piling distance

Abstract

We propose a new hierarchical clustering method for high dimension, low sample size (HDLSS) data. The method utilizes the fact that each individ- ual data vector accounts for exactly one dimension in the subspace generated by HDLSS data. The linkage that is used for measuring the distance between clus- ters is the orthogonal distance between affine subspaces generated by each cluster. The ideal implementation would be to consider all possible binary splits of the data and choose the one that maximizes the distance in between. Since this is not computationally feasible in general, we use the singular value decomposition for its approximation. We provide theoretical justification of the method by studying high dimensional asymptotics. Also we obtain the probability distribution of the distance measure under the null hypothesis of no split, which we use to propose a criterion for determining the number of clusters. Simulation and data analysis with microarray data show competitive clustering performance of the proposed method.