  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
