  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.
