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Paper details
Number 3 - September 2002
Volume 12 - 2002
Improving the generalization ability of neuro-fuzzy systems by ε-insensitive learning
Jacek Łęski
Abstract
A new learning method tolerant of imprecision is introduced and used in neuro-fuzzy modelling. The proposed method makes it possible to dispose of an intrinsic inconsistency of neuro-fuzzy modelling, where zero-tolerance learning is used to obtain a fuzzy model tolerant of imprecision. This new method can be called ε-insensitive learning, where, in order to fit the fuzzy model to real data, the ε-insensitive loss function is used. ε-insensitive learning leads to a model with minimal Vapnik-Chervonenkis dimension, which results in an improved generalization ability of this system. Another advantage of the proposed method is its robustness against outliers. This paper introduces two approaches to solving ε-insensitive learning problem. The first approach leads to a quadratic programming problem with bound constraints and one linear equality constraint. The second approach leads to a problem of solving a system of linear inequalities. Two computationally efficient numerical methods for ε-insensitive learning are proposed. Finally, examples are given to demonstrate the validity of the introduced methods.
Keywords
fuzzy systems, neural networks, tolerant learning, generalization control, robust methods