Least-Squares Linear Dilation-Erosion Regressor Trained using Stochastic Descent Gradient or the Difference of Convex Methods

This paper presents a hybrid morphological neural network for regression tasks called linear dilation-erosion regression ($\ell$-DER). In few words, an $\ell$-DER model is given by a convex combination of the composition of linear and elementary morphological operators. As a result, they yield continuous piecewise linear functions and, thus, are universal approximators. Apart from introducing the $\ell$-DER models, we present three approaches for training these models: one based on stochastic descent gradient and two based on the difference of convex programming problems. Finally, we evaluate the performance of the $\ell$-DER model using 14 regression tasks. Although the approach based on SDG revealed faster than the other two, the $\ell$-DER trained using a disciplined convex-concave programming problem outperformed the others in terms of the least mean absolute error score.