inria-00176283, version 1
High-Dimensional Discriminant Analysis
Charles Bouveyron 1, 2Stephane Girard
1, 2Cordelia Schmid 2, 3
Communication in Statistics- Theory and Methods / Communications in Statistics Theory and Methods 36, 14 (2007) 2607 – 2623
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.
- 1: MISTIS (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
- INRIA – Laboratoire Jean Kuntzmann
- 2: Laboratoire Jean Kuntzmann (LJK)
- CNRS : UMR5224 – Université Joseph Fourier - Grenoble I – Université Pierre Mendès-France - Grenoble II – Institut Polytechnique de Grenoble - Grenoble Institute of Technology
- 3: LEAR (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
- CNRS : FR71 – CNRS : UMR5527 – INRIA – Laboratoire Jean Kuntzmann – Université Joseph Fourier - Grenoble I – Institut National Polytechnique de Grenoble (INPG)
- Keywords : Class-specific subspaces – Discriminant analysis – High-dimensional data – Regularization
- inria-00176283, version 1
- http://hal.inria.fr/inria-00176283
- oai:hal.inria.fr:inria-00176283
- From: Stephane Girard
- Submitted on: Wednesday, 3 October 2007 10:39:50
- Updated on: Monday, 20 December 2010 10:42:33
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