Auto-Associative models and generalized Principal Component Analysis

Stéphane Girard (1, 2) , Serge Iovleff (3, 4)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul
2 MISTIS [?-2006] - Modelling and Inference of Complex and Structured Stochastic Systems [?-2006]
3 LPP - Laboratoire Paul Painlevé - UMR 8524
4 MODAL - MOdel for Data Analysis and Learning

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.

Domaines: Machine Learning [stat.ML]

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⟩