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Fuzzy Linear Analysis of MLPs and Its Applications

Author: LiuHongBo
Tutor: FengTianZuo
School: Ocean University of China
Course: Signal and Information Processing
Keywords: Multilayer Perceptron Fuzzy linear discriminant function Initialize the weights hypersphere Medical diagnosis Optimal hyperplane
CLC: TP183
Type: Master's thesis
Year: 2005
Downloads: 138
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Abstract


Right neural network internal behavior of research has been yes neural networks field of study a big subject, in particular, yes right the application a wide range of multilayer perceptron the research value of is particularly prominent. Research The results pairs of-depth understanding of neural networks the internal behavior of, optimize network, improve network performance as well as knowledge extraction and so has a positive role. Linear discriminant function theory is the linear classifier analytical foundation, not suitable for nonlinear classifier makers. For simple to complete linear classification function's perceptron, there are already systematic theoretical guidance, but for much more complex multilayer perceptron, is currently no systematic theoretical guidance, still in the development stage. In pattern recognition classical discriminant function based on the theory, combined with the fuzzy set theory, right used for pattern recognition and classification multilayer perceptron's behavior analysis carried out, to borrow classical discriminant function theory the concept of, put nonlinear activation function deemed to be subjection degree function, put forward fuzzy linear discriminant function, fuzzy discriminant surface and the fuzzy linear classifier the concept of, get the the following conclusions F-LDF: 1) Fuzzy Linear discriminant function net (X) = W T X b Control via ultra-plane (discriminant boundary) net (X) = 0 the feature space partition (with Fuzzy Regional); 2) of the weights of the neurons weight vector W is Fuzzy Identification the surface normal vector of, identified by fuzzy discriminant surface the orientation of ; 3) origin to the discriminant surface of the distance of r =-b / ‖ W ‖, offset amount (b) determines significantly Fuzzy Identification surface location, changing the offset amount (b) value of the i.e., the mobile Fuzzy discriminant surface with respect to distance from the origin. Make use of the concept is, right used for pattern recognition and classification multilayer perceptron the classification of behavior of conducted a explain the, making the pairs of multilayer perceptron classification behavior of understanding of more clarity. On this basis, take advantage of the concept is pairs of multilayer perceptron with the weight value carry on analysis, the to obtain the following conclusion: 1) H months saphenous layer neural yuan generate H months blur ultra-plane will feature space segmentation (with fuzzy district). 2) due to implicit layer neural Yuan the weights the initial vector W 0 perpendicular to at the respective initial discriminant noodles, so the, H th weight-the initial vector uniformly distributed in the the weights space in the a ultra-spherical surface, means that in the feature space set up set the from the origin Distance r =-b / ‖ W ‖ of the H discriminant faces, they is a certain super-spherical surface of aspect (super plane), uniform distribution (as many as possible toward the) in the feature space. When the of a problem solving when, any needed direction from the local discriminant surface of, has a associated closer to the initial discriminant surface of exist, and this

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