Probabilistic auto-associative models and semi-linear PCA

Auto-Associative models cover a large class of methods used in data analysis, among them are for example the famous PCA and the 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.