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High-Dimensional Discriminant Analysis

Charles Bouveyron 1 Stephane Girard 1 Cordelia Schmid 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
2 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : We propose a new discriminant analysis method for high-dimensional data, called High-Dimensional Discriminant Analysis (HDDA). Our approach is based on the assumption that high-dimensional data live in different subspaces with low dimensionality. We therefore propose a new parameterization of the Gaussian model which combines the ideas of dimension reduction and constraints on the model. This parameterization takes into account the specific subspace and the intrinsic dimension of each class to limit the number of parameters to estimate. In addition, it is possible to make additional assumptions on the model to further limit the number of parameters. Our experiments on artificial and real datasets highlight that HDDA is more efficient than classical methods in high-dimensional spaces and with small learning datasets.
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https://hal.inria.fr/inria-00176283
Contributor : Stephane Girard <>
Submitted on : Wednesday, October 3, 2007 - 10:39:50 AM
Last modification on : Tuesday, February 9, 2021 - 3:20:20 PM

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Charles Bouveyron, Stephane Girard, Cordelia Schmid. High-Dimensional Discriminant Analysis. Communications in Statistics - Theory and Methods, Taylor & Francis, 2007, 36 (14), pp.2607-2623. ⟨10.1080/03610920701271095⟩. ⟨inria-00176283⟩

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