Auto-Associative Models and Generalized ...
Document type :
Article dans une revue scientifique: Article original
Title :
Auto-Associative Models and Generalized Principal Component Analysis
Author(s) :
Girard, Stéphane [Auteur]
Modelling and Inference of Complex and Structured Stochastic Systems [?-2006] [MISTIS [?-2006]]
Iovleff, Serge [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Modelling and Inference of Complex and Structured Stochastic Systems [?-2006] [MISTIS [?-2006]]
Iovleff, Serge [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Journal title :
Journal of Multivariate Analysis
Pages :
21-39
Publisher :
Elsevier
Publication date :
2005
ISSN :
0047-259X
HAL domain(s) :
Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]
Statistiques [stat]/Théorie [stat.TH]
English abstract : [en]
In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation ...
Show more >In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatter-plot by a differentiable manifold. In this paper, they are interpreted as Projection pursuit models adapted to the auto-associative case. Their theoretical properties are established and are shown to extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.Show less >
Show more >In this paper, we propose auto-associative (AA) models to generalize Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatter-plot by a differentiable manifold. In this paper, they are interpreted as Projection pursuit models adapted to the auto-associative case. Their theoretical properties are established and are shown to extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.Show less >
Language :
Anglais
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
Collections :
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