Gaussian kernel fuzzy rough based attribute reduction: An acceleration approach

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Abstract
Presently, the Gaussian kernel approach has been widely accepted for measuring the similarities among samples and then constructing various fuzzy rough sets. Notably, the considered parameter plays a crucial role in deriving Gaussian kernel based similarities. This is mainly because different parameters will generate different scales of the similarities. From this point of view, different parameters may result in different fuzzy rough approximations and the corresponding reducts. Generally speaking, to search a parameterized reduct with better generalization performance, a naive approach can be designed by repeating the process of computing reduct through using different parameters. Obviously, it is very time-consuming. To fill such a gap, an acceleration approach is proposed which aims to reduce the elapsed time of searching reducts based on different parameters. The main mechanism of our proposed approach is to take the variation of the used parameters into account, and then the process of finding reduct under current parameter can be realized based on the previous parameter related reduct. The experimental results over 16 UCI data sets, which are obtained by testing different Gaussian kernel based fuzzy rough sets, demonstrate that our proposed acceleration strategy not only can significantly reduce the time consumption of finding reducts in terms of different parameters, but also will not lead to poorer classification performance and significant variation of length of the obtained reducts by comparing with the results obtained by the naive process. This study suggests technical support for quickly finding reducts of parameterized fuzzy rough sets.

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