A nonlinear PCA based on manifold approximation

Abstract : We address the problem of generalizing Principal Component Analysis (PCA) from the approximation point of view. Given a data set in a high dimensional space, PCA proposes approximations by linear subspaces. These linear models can show some limits when the data distribution is not Gaussian.To overcome these limits, we present Auto-Associative Composite (AAC) models based on manifold approximation. AAC models benefit from interesting theoretical properties, generalizing PCA ones. We take profit of these properties to propose an iterative algorithm to compute the manifold, and prove its convergence in a finite number of steps. PCA models and AAC models are first compared on a theoretical point of view. As a result, we show that PCA is the unique additive AAC model. Then a practical comparison of AAC and PCA models is presented on a data set made of curves.
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Article dans une revue
Computational Statistics, Springer Verlag, 2000, 15 (2), pp.145-167
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Soumis le : mercredi 22 août 2012 - 15:28:58
Dernière modification le : samedi 18 novembre 2017 - 01:09:33
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Stephane Girard. A nonlinear PCA based on manifold approximation. Computational Statistics, Springer Verlag, 2000, 15 (2), pp.145-167. 〈hal-00724764〉



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