Least-Squares Linear Dilation-Erosion Regressor Trained using a Convex-Concave Procedure

This paper presents a hybrid morphological neural network for regression tasks called linear dilation-erosion regressor ($\ell$-DER). An $\ell$-DER is given by a convex combination of the composition of linear and morphological operators. They yield continuous piecewise linear functions and, thus, are universal approximators. Besides introducing the $\ell$-DER model, we formulate their training as a difference of convex (DC) programming problem. Precisely, an $\ell$-DER is trained by minimizing the least-squares using the convex-concave procedure (CCP). Computational experiments using several regression tasks confirm the efficacy of the proposed regressor, outperforming other hybrid morphological models and state-of-the-art approaches such as the multilayer perceptron network and the radial-basis support vector regressor.