Morphological Perceptron with Competitive Layer: Training Using Convex-Concave Procedure
This work addresses a specific challenge in training non-differentiable neural networks for researchers in mathematical morphology and machine learning, but it is incremental as it applies an existing optimization technique to a niche architecture.
The paper tackles the problem of training morphological perceptrons with competitive layers (MPCLs) for multiclass classification, which are non-differentiable and thus incompatible with gradient-based methods, by proposing the convex-concave procedure (CCP) to formulate and solve the training as a difference of convex functions, resulting in effective classification performance as demonstrated in computational experiments.
A morphological perceptron is a multilayer feedforward neural network in which neurons perform elementary operations from mathematical morphology. For multiclass classification tasks, a morphological perceptron with a competitive layer (MPCL) is obtained by integrating a winner-take-all output layer into the standard morphological architecture. The non-differentiability of morphological operators renders gradient-based optimization methods unsuitable for training such networks. Consequently, alternative strategies that do not depend on gradient information are commonly adopted. This paper proposes the use of the convex-concave procedure (CCP) for training MPCL networks. The training problem is formulated as a difference of convex (DC) functions and solved iteratively using CCP, resulting in a sequence of linear programming subproblems. Computational experiments demonstrate the effectiveness of the proposed training method in addressing classification tasks with MPCL networks.