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 (ℓ-DER). An ℓ-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 ℓ-DER model, we formulate their training as a difference of convex (DC) programming problem. Precisely, an ℓ-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.