Reduced Dilation-Erosion Perceptron for Binary Classification
This work addresses a specific limitation in morphological neural networks for binary classification, offering an incremental improvement over existing methods.
The paper tackled the problem of applying morphological neural networks to binary classification when feature spaces lack a natural ordering, by introducing a reduced dilation-erosion (r-DEP) classifier that uses reduced ordering determined via ensemble or bagging of support vector classifiers. The result showed that the r-DEP classifiers achieved higher mean balanced accuracy scores than various SVCs and their ensembles on multiple datasets from the OpenML repository.
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.