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Title: Gaussian kernel based fuzzy rough sets : model, uncertainty measures and applications
Authors: Hu, Q
Zhang, L 
Chen, D
Pedrycz, W
Yu, D
Keywords: Feature selection
Fuzzy set
Gaussian kernel
Rough set
Uncertainty measure
Issue Date: 2010
Publisher: Elsevier
Source: International journal of approximate reasoning, 2010, v. 51, no. 4, p. 453-471 How to cite?
Journal: International journal of approximate reasoning 
Abstract: Kernel methods and rough sets are two general pursuits in the domain of machine learning and intelligent systems. Kernel methods map data into a higher dimensional feature space, where the resulting structure of the classification task is linearly separable; while rough sets granulate the universe with the use of relations and employ the induced knowledge granules to approximate arbitrary concepts existing in the problem at hand. Although it seems there is no connection between these two methodologies, both kernel methods and rough sets explicitly or implicitly dwell on relation matrices to represent the structure of sample information. Based on this observation, we combine these methodologies by incorporating Gaussian kernel with fuzzy rough sets and propose a Gaussian kernel approximation based fuzzy rough set model. Fuzzy T-equivalence relations constitute the fundamentals of most fuzzy rough set models. It is proven that fuzzy relations with Gaussian kernel are reflexive, symmetric and transitive. Gaussian kernels are introduced to acquire fuzzy relations between samples described by fuzzy or numeric attributes in order to carry out fuzzy rough data analysis. Moreover, we discuss information entropy to evaluate the kernel matrix and calculate the uncertainty of the approximation. Several functions are constructed for evaluating the significance of features based on kernel approximation and fuzzy entropy. Algorithms for feature ranking and reduction based on the proposed functions are designed. Results of experimental analysis are included to quantify the effectiveness of the proposed methods.
ISSN: 0888-613X
DOI: 10.1016/j.ijar.2010.01.004
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