Hybrid Gray-Scale and Fuzzy Morphological/Linear Perceptrons Trained By Extreme Learning Machine

Morphological perceptrons (MPs) belong to the class of morphological neural networks (MNNs) whose neuronal aggregation functions are drawn from mathematical morphology (MM). Most MNN models including MPs employ operators of gray-scale mathematical morphology as aggregation functions. Recently, a hybrid morphological/linear perceptron (HMLP) appeared in the literature. This neural network model combines the approximation capabilities of the two-layer perceptron having sigmoid activation functions with the capability of the MP to represent non-differentiable functions. For a number of reasons, that include the non-differentiability of morphological operators, it is advantageous to train HMLPs using extreme learning machine (ELM). The fact that gray-scale MM is closely related to fuzzy MM based on Lukasiewicz operators motivated us to introduce hybrid fuzzy morphological/linear perceptrons (FMLPs) and train them using ELM in this paper. We compare the performances of the HMLP and the FMLP with the ones of some related models in a number of well-known classification problems.