Affiliations: School of Statistics and Data Science, Beijing WUZI University, Beijing, China
Correspondence:
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Corresponding author. Huan Yi, School of Information, Beijing WUZI University, Beijing, China. E-mail: 2352759878@qq.com.
Abstract: The classification problem is a key area of research in machine learning. The Least Squares Support Vector Machine (LSSVM) is an important classifier that is commonly used to solve classification problems. Its widespread use stems from its replacement of the inequality constraint in the Support Vector Machine (SVM) with the equality constraint, which transforms the convex quadratic programming (QP) problem of SVM into the solution of linear equations. However, when dealing with multi-class classification problems, LSSVM faces the challenges of lack of sparsity and sample noises, which can negatively impact its performance. Based on the modeling characteristics and data distribution of the multi-class LSSVM model, this paper proposes two improvements and establishes an improved fuzzy sparse multi-class least squares support vector machine (IF-S-M-LSSVM). The first improvement adopts a non-iterative sparse algorithm, which can delete training sample points to different degrees by adjusting the sparse ratio. The second improvement addresses the impact of sample noise on determining the optimal hyperplane by adding a fuzzy membership degree based on sample density. The advantages of the new model, in terms of training speed and classification accuracy, are verified through UCI machine learning standard data set experiments. Finally, the statistical significance of the IF-S-M-LSSVM model is tested using the Friedman and Bonferroni-Dunn tests.
Keywords: Least squares support vector machine, multi-class classification problem, fuzzy membership, sparse
