Linear Dilation-Erosion Perceptron for Binary Classification

TL;DR

This paper introduces the linear dilation-erosion perceptron (l-DEP), a novel binary classifier that applies linear transformations before morphological operators, trained via a regularized hinge-loss minimization with concave-convex constraints.

Contribution

The paper proposes the l-DEP model, extending previous dilation-erosion perceptrons with a linear transformation step and a new training method involving regularized hinge-loss optimization.

Findings

Introduces the linear dilation-erosion perceptron (l-DEP) model.

Provides a training method based on regularized hinge-loss minimization.

Includes an illustrative example demonstrating the approach.

Abstract

In this work, we briefly revise the reduced dilation-erosion perceptron (r-DEP) models for binary classification tasks. Then, we present the so-called linear dilation-erosion perceptron (l-DEP), in which a linear transformation is applied before the application of the morphological operators. Furthermore, we propose to train the l-DEP classifier by minimizing a regularized hinge-loss function subject to concave-convex restrictions. A simple example is given for illustrative purposes.