  Clustering in high-dimensional spaces is nowadays a recurrent problem in many
scientific domains but remains a difficult task from both the clustering
accuracy and the result understanding points of view. This paper presents a
discriminative latent mixture (DLM) model which fits the data in a latent
orthonormal discriminative subspace with an intrinsic dimension lower than the
dimension of the original space. By constraining model parameters within and
between groups, a family of 12 parsimonious DLM models is exhibited which
allows to fit onto various situations. An estimation algorithm, called the
Fisher-EM algorithm, is also proposed for estimating both the mixture
parameters and the discriminative subspace. Experiments on simulated and real
datasets show that the proposed approach performs better than existing
clustering methods while providing a useful representation of the clustered
data. The method is as well applied to the clustering of mass spectrometry
data.
