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

TL;DR

This paper introduces a novel linear dilation-erosion regressor ($ ext{ extlbrackdbl}$-DER) that uses convex combinations of linear and morphological operators, trained via a convex-concave procedure, and demonstrates superior performance in regression tasks.

Contribution

The paper proposes the $ ext{ extlbrackdbl}$-DER model and formulates its training as a difference of convex programming problem solved by CCP, advancing morphological neural network methods.

Findings

Outperforms existing hybrid morphological models.

Achieves better results than multilayer perceptrons and support vector regressors.

Validated through multiple regression experiments.

Abstract

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.