  In several application domains, high-dimensional observations are collected
and then analysed in search for naturally occurring data clusters which might
provide further insights about the nature of the problem. In this paper we
describe a new approach for partitioning such high-dimensional data. Our
assumption is that, within each cluster, the data can be approximated well by a
linear subspace estimated by means of a principal component analysis (PCA). The
proposed algorithm, Predictive Subspace Clustering (PSC) partitions the data
into clusters while simultaneously estimating cluster-wise PCA parameters. The
algorithm minimises an objective function that depends upon a new measure of
influence for PCA models. A penalised version of the algorithm is also
described for carrying our simultaneous subspace clustering and variable
selection. The convergence of PSC is discussed in detail, and extensive
simulation results and comparisons to competing methods are presented. The
comparative performance of PSC has been assessed on six real gene expression
data sets for which PSC often provides state-of-art results.

Machine Learning