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On the estimation of the latent discriminative subspace in the Fisher-EM algorithm

Abstract : The Fisher-EM algorithm has been recently proposed in [2] for the simultaneous visualization and clustering of high-dimensional data. It is based on a discriminative latent mixture model which fits the data into a latent discriminative subspace with an intrinsic dimension lower than the dimension of the original space. The Fisher-EM algorithm includes an F-step which estimates the projection matrix whose columns span the discriminative latent space. This matrix is estimated via an optimization problem which is solved using a Gram-Schmidt procedure in the original algorithm. Unfortunately, this procedure suffers in some case from numerical instabilities which may result in a deterioration of the visualization quality or the clustering accuracy. Two alternatives for estimating the latent subspace are proposed to overcome this limitation. The optimization problem of the F-step is first recasted as a regression-type problem and then reformulated such that the solution can be approximated with a SVD. Experiments on simulated and real datasets show the improvement of the proposed alternatives for both the visualization and the clustering of data.
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Contributor : Charles Bouveyron <>
Submitted on : Monday, October 17, 2011 - 10:09:26 AM
Last modification on : Sunday, January 19, 2020 - 6:38:32 PM
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  • HAL Id : hal-00632926, version 1


Charles Bouveyron, Camille Brunet. On the estimation of the latent discriminative subspace in the Fisher-EM algorithm. Journal de la Société Française de Statistique, Société Française de Statistique et Société Mathématique de France, 2011, 152 (3), pp.98-115. ⟨hal-00632926⟩



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