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Auto-Associative Models and Generalized Principal Component Analysis

Stéphane Girard 1 Serge Iovleff 2
1 IS2 - Statistical Inference for Industry and Health
Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive - UMR 5558
Abstract : In this paper, we propose the auto-associative (AA) model to generalize the 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 scatterplot by a differentiable manifold. We propose here to interpret them as Projection Pursuit models adapted to the auto-associative case. We establish their theoretical properties and show how they 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.
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https://hal.inria.fr/inria-00072224
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Submitted on : Tuesday, May 23, 2006 - 8:09:17 PM
Last modification on : Friday, April 29, 2022 - 10:12:48 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:59:18 PM

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  • HAL Id : inria-00072224, version 1

Citation

Stéphane Girard, Serge Iovleff. Auto-Associative Models and Generalized Principal Component Analysis. [Research Report] RR-4364, INRIA. 2002. ⟨inria-00072224⟩

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