By Udo Seiffert
The Self-Organizing Map (SOM) is without doubt one of the most often used architectures for unsupervised man made neural networks. brought via Teuvo Kohonen within the Eighties, SOMs were built as the most important approach for visualisation and unsupervised category projects through an lively and cutting edge group of interna tional researchers. a couple of extensions and variations were built over the last 20 years. the reason being absolutely now not that the unique set of rules used to be imperfect or inad equate. it is vitally the common applicability and straightforward dealing with of the SOM. Com pared to many different community paradigms, just a couple of parameters must be prepared and hence additionally for a newbie the community results in worthy and trustworthy effects. by no means theless there's scope for advancements and complicated new advancements as this ebook impressively demonstrates. The variety of released functions using the SOM seems to be never-ending. because the name of this ebook exhibits, the reader will make the most of a number of the most up-to-date the oretical advancements and may develop into conversant in a couple of demanding real-world purposes. Our goal in generating this booklet has been to supply an up to-date therapy of the sector of self-organizing neural networks, on the way to be ac cessible to researchers, practitioners and graduated scholars from assorted disciplines in teachers and undefined. we're very thankful to the daddy of the SOMs, Professor Teuvo Kohonen for sup porting this publication and contributing the 1st bankruptcy.
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The rule ordering algorithm first creates a list Ä that contains all extracted rules. Assume that the list Ä is divided into two lists, a head list (Ä ) and a tail list (ÄØ ), where Ä is the list of all ordered rules and ÄØ is the list of all remaining (unordered) rules2 . Initially, Ä is empty and ÄØ includes all the extracted rules. A performance criteria is used to select one rule from ÄØ to be moved to the end of Ä , and the process continues till ÄØ is null. The steps of the rule ordering algorithm are as follows: 1.
A fuzzy rule base, which represents the fuzzy relationships between input-output fuzzy variables. The output of the fuzzy rule base is determined based on the degree of membership specified by the fuzzifier. An inference engine, which controls the rule base. A defuzzifier, which converts the output of the fuzzy rule base into a crisp value. Such fuzzy logic systems often suffer from two main problems. First, designing the right membership function that represents each input and output variable may be nontrivial.
For each extracted set of rules with the same consequent, if the sum of the completeness measures of all rules in this set equals the total number of input patterns having the corresponding output then this set of extracted rules is 100% complete with respect to that consequent. An extracted rule with zero completeness measure but having a soundness measure ¼ means that there is a © 2000 by CRC Press LLC preceding rule(s), in the order of rule application, that covers the same input patterns that this rule covers.