Affiliations: College of Mathematics and Systems Science, Xinjiang University, Urumqi, China
Correspondence:
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Corresponding author. Yuhong Sheng, College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China. E-mail: shengyh@xju.edu.cn.
Abstract: Support vector machine (SVM) is a supervised binary classifier with good generalization ability and excellent computational properties. It has been widely used in many fields such as image recognition, bioinformatics and so on. However, the traditional SVM requires the input data to be clear and knowable, while in the actual application process, there will be many cases that the input data is uncertain. In order to solve this problem, a new SVM model is proposed in this paper by combining the uncertainty theory with the SVM theory. The uncertainty theory was proposed by Liu in 2007, and it is often used to describe the uncertainty of things. The uncertain set in uncertainty theory is often used to model unsharp concepts. Therefore, this paper regards each uncertain data as an uncertain set and establishes a SVM model with uncertain chance constraints. However, the uncertain chance constraints are non-convex. Therefore, this paper gives the equivalent transformation process of constraint conditions when the input data are triangular uncertain sets. Finally, the non-convex constraint conditions are transformed into the linear constraint conditions, so that the model is transformed into a nonlinear programming model. In the numerical experiment, the Particle Swarm Optimization (PSO) algorithm is used to solve the problem, which proves the feasibility of the model.
Keywords: Support vector machine, uncertainty
theory, uncertain set, uncertain support vector machine
