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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 614543, 9 pages
http://dx.doi.org/10.1155/2013/614543
Research Article

Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

1Department of Information Engineering, I-Shou University, Kaohsiung 84001, Taiwan
2Department of Electrical Engineering, I-Shou University, Kaohsiung 84001, Taiwan

Received 10 April 2013; Accepted 20 May 2013

Academic Editor: Ker-Wei Yu

Copyright © 2013 Yih-Lon Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.