Probabilistic auto-associative models and semi-linear PCA

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.