The mathematical foundation and a step by step description for 17 algorithms on artificial neural networks

Authors:
Nicolae Popoviciu;Floarea Baicu
Affiliations:
Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania;Hyperion University of Bucharest, Faculty of Mathematics-Informatics, Bucharest, Romania
Venue:
AIKED'10 Proceedings of the 9th WSEAS international conference on Artificial intelligence, knowledge engineering and data bases
Year:
2010

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Abstract

We present a description of a set of 17 algorithms on neural networks and indicate the area where the algorithms could be applied. All algorithms are a part of the monograph (2009) Neural Networks. Mathematical Foundation, Algorithms and Applications, authors Nicolae Popoviciu and Floarea Baicu. Each algorithm has its mathematical foundation and the algorithms treat many aspects related with neural networks. We enumerate several directions: separable sets, supervised and unsupervised learning, BKP, MLP geometric algorithm, SOM competitive learning, ISODATA, Kohonen competitive algorithm, ART1 competitive algorithm, stock-recall problem, sales traveling problem, c-means algorithm for prototype vectors, RBF algorithms in batch version and sequential version, Householder decomposition etc. All algorithms are described step by step and are illustrated by many numerical examples.