Probabilistic Auto-Associative Models and Semi-Linear PCA

Serge Iovleff (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 MODAL - MOdel for Data Analysis and Learning

Auto-Associative models cover a large class of methods used in data analysis. In this paper, we describe the generals 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 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

Mots clés: Auto-Associative Models; Data Analysis; Non-Linear PCA

Domaines: Applications [stat.AP]; Machine Learning [stat.ML]

Serge Iovleff. Probabilistic Auto-Associative Models and Semi-Linear PCA. Advances in Data Analysis and Classification, 2015, 9 (3), pp.20. ⟨10.1007/s11634-014-0185-3⟩. ⟨hal-00734070v2⟩