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Auto-associative models and generalized principal component analysis

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  • Girard, Stéphane
  • Iovleff, Serge

Abstract

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.

Suggested Citation

  • Girard, Stéphane & Iovleff, Serge, 2005. "Auto-associative models and generalized principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 21-39, March.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:21-39
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    References listed on IDEAS

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    1. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
    2. Michael E. Tipping & Christopher M. Bishop, 1999. "Probabilistic Principal Component Analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 611-622.
    3. Durand, Jean-Francois, 1993. "Generalized principal component analysis with respect to instrumental variables via univariate spline transformations," Computational Statistics & Data Analysis, Elsevier, vol. 16(4), pages 423-440, October.
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    Cited by:

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    2. P Baraldi & E Zio & G Gola & D Roverso & M Hoffmann, 2008. "Genetic algorithms for signal grouping in sensor validation: A comparison of the filter and wrapper approaches," Journal of Risk and Reliability, , vol. 222(2), pages 189-206, June.

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