A novel classification algorithm based on kernelized fuzzy rough sets
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ORIGINAL ARTICLE
A novel classification algorithm based on kernelized fuzzy rough sets Linlin Chen1 · Qingjiu Chen2 Received: 22 April 2020 / Accepted: 8 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Fuzzy kernels are a special kind of kernels which are usually employed to calculate the upper and lower approximations, as well as the positive region in kernelized fuzzy rough sets, and the positive region characterizes the degree of consistency between conditional attributes and decision attributes. When the classification hyperplane exists between two classes of samples, the positive region is transformed into the sum of the distances from the samples to classification hyperplane. The larger the positive region, the higher the degree of consistency. In this paper, we construct a novel model to solve the classification hyperplane from the geometric meaning of the positive region in kernelized fuzzy rough sets. Then, a classification model is developed through maximizing the sum of the distances from the samples to classification hyperplane, and this optimization problem that addresses this objective function is transformed to its dual problem. Experimental results show that the proposed classification algorithm is effective. Keywords Fuzzy kernel · Fuzzy rough set · Positive region · Classification hyperplane
1 Introduction As an extension of classical rough set [1], which is an important theoretical model of granular computing [2–5], fuzzy rough set [6–15] is mainly used in classification problems to address the inconsistency between attributes and decision labels, i.e., some samples have the similar attribute values but different decision labels. The inconsistency can be measured by assigning a membership to every sample with respect to decision labels with the lower approximation in fuzzy rough sets. In fuzzy rough sets, fuzzy similarity relations play a key role to measure similarity between two objects in the universe of discourses. It has been reported in [16, 17] that any kernel that maps Cartesian product of the universe of discourses to the unit interval with 1 in the diagonal of the kernel matrix is a special fuzzy similarity relation. This kind of kernels is named fuzzy kernels and has * Qingjiu Chen [email protected] Linlin Chen [email protected] 1
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
Hermes Microvision, Inc. An ASML Company, Beijing, China
2
been employed to develop kernelized fuzzy rough sets [18]. Kernelized fuzzy rough sets are applied to perform attribute reduction and improve performance of classifiers [19–27]. It is well known that kernels map input data into a higher dimensional feature space, and nonlinear learning tasks can be simplified as linear ones in this feature space [28–31]. Support vector machine [32, 33] is one of the most popular classification algorithms within the framework of kernel tricks. This algorithm aims at obtaining the classification hyperplane thro
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