  We investigate a Gaussian mixture model (GMM) with component means
constrained in a pre-selected subspace. Applications to classification and
clustering are explored. An EM-type estimation algorithm is derived. We prove
that the subspace containing the component means of a GMM with a common
covariance matrix also contains the modes of the density and the class means.
This motivates us to find a subspace by applying weighted principal component
analysis to the modes of a kernel density and the class means. To circumvent
the difficulty of deciding the kernel bandwidth, we acquire multiple subspaces
from the kernel densities based on a sequence of bandwidths. The GMM
constrained by each subspace is estimated; and the model yielding the maximum
likelihood is chosen. A dimension reduction property is proved in the sense of
being informative for classification or clustering. Experiments on real and
simulated data sets are conducted to examine several ways of determining the
subspace and to compare with the reduced rank mixture discriminant analysis
(MDA). Our new method with the simple technique of spanning the subspace only
by class means often outperforms the reduced rank MDA when the subspace
dimension is very low, making it particularly appealing for visualization.
