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To cite this version:Charles Bouveyron, Camille Brunet. Simultaneous model-based clustering and visualization in the Fisher discriminative subspace. Statistics and Computing, Springer Verlag (Germany), 2012, 22 (1) 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.

This work develops a general procedure for clustering functional data which adapts the clustering method High Dimensional Data Clustering (HDDC), originally proposed in the multivariate context. The resulting clustering method, called funHDDC, is based on a functional latent mixture model which fits the functional data in group-specific functional subspaces. By constraining model parameters within and between groups, a family of parsimonious models is exhibited which allow to fit onto various situations. An estimation procedure based on the EM algorithm is proposed for determinating both the model parameters and the group-specific functional subspaces. Experiments on realworld datasets show that the proposed approach performs better or similarly than classical two-step clustering methods while providing useful interpretations of the groups and avoiding the uneasy choice of the discretization technique. In particular, funHDDC appears to always outperform HDDC applied on spline coefficients.

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