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Chapitre D'ouvrage Année : 2008

Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit

Résumé

Auto-associative models have been introduced as a new tool for building nonlinear Principal component analysis (PCA) methods. Such models rely on successive approximations of a dataset by manifolds of increasing dimensions. In this chapter, we propose a precise theoretical comparison between PCA and autoassociative models. We also highlight the links between auto-associative models, projection pursuit algorithms, and some neural network approaches. Numerical results are presented on simulated and real datasets.

Dates et versions

hal-00383137 , version 1 (12-05-2009)

Identifiants

Citer

Stéphane Girard, Serge Iovleff. Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit. Alexander N. Gorban, Balázs Kégl, Donald C. Wunsch, and Andrei Y. Zinovyev. Principal Manifolds for Data Visualisation and Dimension Reduction, Springer-Verlag, pp.202-218, 2008, Lecture Notes in Computational Science and Engineering, 978-3-540-73749-0. ⟨10.1007/978-3-540-73750-6_8⟩. ⟨hal-00383137⟩
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