Training Single-Layer Morphological Perceptron Using Convex-Concave Programming
Iara Cunha, Marcos Eduardo Valle
TL;DR
This work addresses training a single-layer morphological perceptron (SLMP) with dendritic structure for binary classification. It introduces the $K$-DDCCP algorithm by formulating the non-convex training problem as a DC program and solving it via disciplined convex-concave programming, building on WDCCP and Ritter-Urcid's SLMP. Experimental results on synthetic and real datasets show competitive accuracy and improved generalization compared to greedy training, highlighting the value of dendritic computations and DC-based optimization in morphological neural networks. The study contributes a tractable training framework that extends morphological networks to more complex decision surfaces and lays groundwork for scaling and variant architectures.
Abstract
This paper concerns the training of a single-layer morphological perceptron using disciplined convex-concave programming (DCCP). We introduce an algorithm referred to as K-DDCCP, which combines the existing single-layer morphological perceptron (SLMP) model proposed by Ritter and Urcid with the weighted disciplined convex-concave programming (WDCCP) algorithm by Charisopoulos and Maragos. The proposed training algorithm leverages the disciplined convex-concave procedure (DCCP) and formulates a non-convex optimization problem for binary classification. To tackle this problem, the constraints are expressed as differences of convex functions, enabling the application of the DCCP package. The experimental results confirm the effectiveness of the K-DDCCP algorithm in solving binary classification problems. Overall, this work contributes to the field of morphological neural networks by proposing an algorithm that extends the capabilities of the SLMP model.