In this paper, we propose the auto-associative (AA) model to generalize the Principal component analysis (PCA). AA models have been introduced in data analysis from a geometrical point of view. They are based on the approximation of the observations scatterplot by a differentiable manifold. We propose here to interpret them as Projection Pursuit models adapted to the auto-associative case. We establish their theoretical properties and show how they extend the PCA ones. An iterative algorithm of construction is proposed and its principle is illustrated both on simulated and real data from image analysis.