| Summary: | 博士 === 國立中山大學 === 電機工程學系研究所 === 95 === This thesis is divided into two parts. In the first part, a general problem of the robust template decomposition with restricted weights for cellular neural networks (CNNs) implementing an arbitrary Boolean function is investigated. In the second part, some primary study of the novel Wilcoxon learning machines is made.
In the first part of the thesis for the robust CNN template design, the geometric margin of a linear classifier with respect to a training data set, a notion borrowed from the machine learning theory, is used to define the robustness of an uncoupled CNN implementing a linearly separable Boolean function. Consequently, the so-called maximal margin classifiers can be devised via support vector machines (SVMs) to provide the most robust template design for uncoupled CNNs implementing linearly separable Boolean functions. Some general properties of robust CNNs with or without restricted weights are discussed. Moreover, all robust CNNs with restricted weights are characterized. For an arbitrarily given Boolean function, we propose an algorithm, which is the generalized version of the well known CFC algorithm, to find a sequence of robust uncoupled CNNs implementing the given Boolean function.
In the second part of the thesis, we investigate the novel Wilcoxon learning machines (WLMs). The invention of these learning machines was motivated by the Wilcoxon approach to linear regression problems in statistics. The resulting linear regressors are quits robust against outliers, as is well known in statistics. The Wilcoxon learning machines investigated in this thesis include Wilcoxon Neural Network (WNN), Wilcoxon Generalized Radial Basis Function Network (WGRBFN), Wilcoxon Fuzzy Neural Network (WFNN), and Kernel-based Wilcoxon Regressor (KWR).
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