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Reduced Dilation-Erosion Perceptron for Binary Classification

Author

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  • Marcos Eduardo Valle

    (Department of Applied Mathematics, University of Campinas, Campinas 13083-859, Brazil)

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 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.

Suggested Citation

  • Marcos Eduardo Valle, 2020. "Reduced Dilation-Erosion Perceptron for Binary Classification," Mathematics, MDPI, vol. 8(4), pages 1-21, April.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:512-:d:340695
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    References listed on IDEAS

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    1. Ercan Oztemel & Samet Gursev, 2020. "Literature review of Industry 4.0 and related technologies," Journal of Intelligent Manufacturing, Springer, vol. 31(1), pages 127-182, January.
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    Cited by:

    1. Vassilis G. Kaburlasos, 2022. "Lattice Computing: A Mathematical Modelling Paradigm for Cyber-Physical System Applications," Mathematics, MDPI, vol. 10(2), pages 1-3, January.

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