A class of hybrid morphological perceptrons with application in time series forecasting

In this work a class of hybrid morphological perceptrons, called dilation–erosion perceptron (DEP), is presented to overcome the random walk dilemma in the time series forecasting problem. It consists of a convex combination of fundamental operators from mathematical morphology (MM) on complete lattices theory (CLT). A gradient steepest descent method is presented to design the proposed DEP (learning process), using the back propagation (BP) algorithm and a systematic approach to overcome the problem of nondifferentiability of morphological operators. The learning process includes an automatic phase fix procedure that is geared at eliminating time phase distortions observed in some time series. Finally, an experimental analysis is conducted with the proposed DEP using five real world time series, where five well-known performance metrics and an evaluation function are used to assess the forecasting performance of the proposed model. The obtained results are compared with those generated by classical forecasting models presented in the literature.