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arXiv · 2107.05682

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

Angelica Lourenço Oliveira·Marcos Eduardo Valle
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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.

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BibTeXRIS

Angelica Lourenço Oliveira, Marcos Eduardo Valle. 2021-07-12. Least-Squares Linear Dilation-Erosion Regressor Trained using a Convex-Concave Procedure. https://arxiv.org/abs/2107.05682

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