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Probabilistic auto-associative models and semi-linear PCA

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  • Serge Iovleff

Abstract

Auto-associative models cover a large class of methods used in data analysis, including for example principal component analysis (PCA) and auto-associative neural networks. In this paper, we describe the general properties of these models when the projection component is linear and we propose and test an easy-to-implement probabilistic semi-linear auto-associative model in a Gaussian setting. We show that it is a generalization of the PCA model to the semi-linear case. Numerical experiments on simulated datasets and a real astronomical application highlight the interest of this approach. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Serge Iovleff, 2015. "Probabilistic auto-associative models and semi-linear PCA," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(3), pages 267-286, September.
    • Handle: RePEc:spr:advdac:v:9:y:2015:i:3:p:267-286
    DOI: 10.1007/s11634-014-0185-3
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    References listed on IDEAS

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    1. 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.
    2. Delicado, Pedro, 2001. "Another Look at Principal Curves and Surfaces," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 84-116, April.
    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.
    4. 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.
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