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Auto-Associative models and generalized Principal Component Analysis

Stéphane Girard 1, 2 Serge Iovleff 3, 4
4 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : In this communication, 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. 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.
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Stéphane Girard, Serge Iovleff. Auto-Associative models and generalized Principal Component Analysis. Workshop on principal manifolds for data cartography and dimension reduction, Aug 2006, Leicester, United Kingdom. ⟨hal-00985337⟩

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