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

arXiv: https://arxiv.org/abs/2107.05682 · HTML: https://mlsanity.com/paper/2107.05682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Disciplined Convex-Concave Programming](https://mlsanity.com/paper/1604.02639/) (2016)
- [Morphological Network: How Far Can We Go with Morphological Neurons?](https://mlsanity.com/paper/1901.00109/) (2019)
- [Reduced Dilation-Erosion Perceptron for Binary Classification](https://mlsanity.com/paper/2003.02306/) (2020)
- [Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure](https://mlsanity.com/paper/2011.06512/) (2020)

## Abstract (arXiv)

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.