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<p>A multi-layer morphological perceptron is a feedforward neural architecture composed of multiple layers whose neurons apply basic operations from mathematical morphology. In multi-class classification settings, the inclusion of a winner-take-all mechanism leads to the morphological perceptron with a competitive layer (MPCL). Due to the inherent nondifferentiability of morphological operations, conventional gradient-based learning algorithms may be unsuitable for training such models, motivating the adoption of optimization techniques that do not rely on derivatives. In this work, we present a training framework for MPCL networks based on the convex–concave procedure (CCP). The learning task is formulated as an optimization problem involving the difference-of-convex functions and is addressed through an iterative CCP scheme that yields a sequence of linear programming problems. Numerical results on classification benchmarks indicate that the proposed approach provides an effective and viable alternative for training MPCL networks. The source-code and Jupyter Notebooks are available at <a href="https://github.com/mevalle/MPCL-CCP">github.com/mevalle/MPCL-CCP</a>.</p>

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Training Morphological Perceptron with Competitive Layer using Convex-Concave Procedure

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月22日

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  • Marcos Eduardo Valle,
  • Iara Cunha

摘要

A multi-layer morphological perceptron is a feedforward neural architecture composed of multiple layers whose neurons apply basic operations from mathematical morphology. In multi-class classification settings, the inclusion of a winner-take-all mechanism leads to the morphological perceptron with a competitive layer (MPCL). Due to the inherent nondifferentiability of morphological operations, conventional gradient-based learning algorithms may be unsuitable for training such models, motivating the adoption of optimization techniques that do not rely on derivatives. In this work, we present a training framework for MPCL networks based on the convex–concave procedure (CCP). The learning task is formulated as an optimization problem involving the difference-of-convex functions and is addressed through an iterative CCP scheme that yields a sequence of linear programming problems. Numerical results on classification benchmarks indicate that the proposed approach provides an effective and viable alternative for training MPCL networks. The source-code and Jupyter Notebooks are available at github.com/mevalle/MPCL-CCP.