  In this paper, we consider clustering based on principal component analysis
(PCA) for high-dimension, low-sample-size (HDLSS) data. We give theoretical
reasons why PCA is effective for clustering HDLSS data. First, we derive a
geometric representation of HDLSS data taken from a two-class mixture model.
With the help of the geometric representation, we give geometric consistency
properties of sample principal component scores in the HDLSS context. We
develop ideas of the geometric representation and geometric consistency
properties to multiclass mixture models. We show that PCA can classify HDLSS
data under certain conditions in a surprisingly explicit way. Finally, we
demonstrate the performance of the clustering by using microarray data sets.
