Reduced Dilation-Erosion Perceptron for Binary Classification

Abstract

Dilation and erosion are two elementary operations from mathematical morphology, a non-linear lattice computing methodology widely used for image processing and analysis. The dilation-erosion perceptron (DEP) is a morphological neural network obtained by a convex combination of a dilation and an erosion followed by the application of a hard-limiter function for binary classification tasks. A DEP classifier can be trained using a convex-concave procedure along with the minimization of the hinge loss function. As a lattice computing model, the DEP classifier assumes the feature and class spaces are partially ordered sets. In many practical situations, however, there is no natural ordering for the feature patterns. Using concepts from multi-valued mathematical morphology, this paper introduces the reduced dilation-erosion (r-DEP) classifier. An r-DEP classifier is obtained by endowing the feature space with an appropriate reduced ordering. Such reduced ordering can be determined using two approaches: One based on an ensemble of support vector classifiers (SVCs) with different kernels and the other based on a bagging of similar SVCs trained using different samples of the training set. Using several binary classification datasets from the OpenML repository, the ensemble and bagging r-DEP classifiers yielded in mean higher balanced accuracy scores than the linear, polynomial, and radial basis function (RBF) SVCs as well as their ensemble and a bagging of RBF SVCs.

Advances in Morphological Neural Networks: Training, Pruning and Enforcing Shape Constraints

“…Valle proposes a greedy algorithm where the dilation and the erosion perceptrons are trained separately and combined later by minimizing the average hinge loss [31]. This method allows the inclusion of a regularization term C u − r 1 in the objective function, where u = w or u = m and r is a reference term.…”

“…The Dilation-Erosion Perceptron suffers from a major flaw as a lattice-based model, it presupposes a partial ordering both on the features and the classes. By simply inverting the classes N P, the performance of the classifier might severely drop [31]. A way to counteract this behavior lies on the use of reduced morphological operators based on a reduced ordering: Definition 2.…”

Motion Recognition Based on Sum of the Squared Errors Distribution

“…Neural networks can be divided into feedforward neural networks (perceptron, back propagation neural network (BPNN), and convolutional neural network (CNN)), feedback neural networks (Elman and Hopfield neural networks), and self-organizing map (SOM) neural networks according to the interconnection of neurons in the network. The perceptron neural network can only handle linear problems [54]. BP neural network adds the number of layers and BP algorithm on the basis of the perceptron, and has strong nonlinear mapping and optimization computing ability [55].…”

Approximating morphological operators with part-based representations learned by asymmetric auto-encoders

“…Hence, we take advantage of the recent advances in deep, sparse and non-negative auto-encoders to design a new framework able to learn part-based representations of an image database, compatible with morphological processing. To that extent, this work is part of the resurgent research line investigating interactions between deep learning and mathematical morphology [9,22,23,27,32]. However with respect to these studies, focusing mainly on introducing morphological operators in neural networks, the present paper addresses a different question.…”