  Clustering in high-dimensional spaces is a difficult problem which is
recurrent in many domains, for example in image analysis. The difficulty is due
to the fact that high-dimensional data usually live in different
low-dimensional subspaces hidden in the original space. This paper presents a
family of Gaussian mixture models designed for high-dimensional data which
combine the ideas of dimension reduction and parsimonious modeling. These
models give rise to a clustering method based on the Expectation-Maximization
algorithm which is called High-Dimensional Data Clustering (HDDC). In order to
correctly fit the data, HDDC estimates the specific subspace and the intrinsic
dimension of each group. Our experiments on artificial and real datasets show
that HDDC outperforms existing methods for clustering high-dimensional data
