# Least-Squares Linear Dilation-Erosion Regressor Trained using Stochastic Descent Gradient or the Difference of Convex Methods. (arXiv:2107.05682v1 [cs.LG])

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.