Application of nonlinear correlation functions and equivalence models in advanced neuronets

Abstract

Mathematical fundamentals of neurobiologic, equivalence algebra and equivalence models of neural networks are considered. Modified equivalence models of neural networks and associative memory for space-invariant 2D pattern recognition are proposed. They are based on the use of equivalence functions, including normalized ones, characterizing the similarity equivalence degree of two images, depending on their mutual space displacement. Relations between the equivalence functions and correlation functions are found out. Simulation results, demonstrating efficiency of the models on the example of 8.8 pixels patterns recognition with number of etalons, equaled to 4. Possible variants of the models implementations are considered. Neural networks architecture for invariant 2D pattern recognition consists of equivalentors, every of which replace two correlators.