Open AccessRecognition of Generalized Patterns by a Differential Polynomial Neural Network
Author(s) -
Ladislav Zjavka
Publication year - 2012
Publication title -
engineering, technology and applied science research/engineering, technology and applied science research
Language(s) - English
Resource type - Journals
eISSN - 2241-4487
pISSN - 1792-8036
DOI - 10.48084/etasr.28
Subject(s) - mathematics , generalization , polynomial , artificial neural network , similarity (geometry) , identification (biology) , parametric statistics , differential equation , range (aeronautics) , differential (mechanical device) , pure mathematics , computer science , mathematical analysis , artificial intelligence , statistics , botany , materials science , composite material , engineering , image (mathematics) , biology , aerospace engineering
A lot of problems involve unknown data relations, identification of which can serve as a generalization of their qualities. Relative values of variables are applied in this case, and not the absolute values, which can better make use of data properties in a wide range of the validity. This resembles more to the functionality of the brain, which seems to generalize relations of variables too, than a common pattern classification. Differential polynomial neural network is a new type of neural network designed by the author, which constructs and approximates an unknown differential equation of dependent variables using special type of root multi-parametric polynomials. It creates fractional partial differential terms, describing mutual derivative changes of some variables, likewise the differential equation does. Particular polynomials catch relations of given combinations of input variables. This type of identification is not based on a whole-pattern similarity, but only to the learned hidden generalized relations of variables.