Design of semi-tensor product-based kernel function for SVM nonlinear classification
Shengli Xue1
Lijun Zhang2
Zeyu Zhu2
1.School of Mathematics and Statistics,Yulin University,Yulin 719000,Shaanxi,China2.School of Marine Science and Technology,Northwestern Polytechnical University,Xi'an 710000,Shaanxi,China
摘要：The kernel function method in support vector machine(SVM)is an excellent tool for nonlinear classification.How to design a kernel function is difficult for an SVM nonlinear classification problem,even for the polynomial kernel function.In this paper,we propose a new kind of polynomial kernel functions,called semi-tensor product kernel(STP-kernel),for an SVM nonlinear classification problem by semi-tensor product of matrix(STP)theory.We have shown the existence of the STP-kernel function and verified that it is just a polynomial kernel.In addition,we have shown the existence of the reproducing kernel Hilbert space(RKHS)associated with the STP-kernel function.Compared to the existing methods,it is much easier to construct the nonlinear feature mapping for an SVM nonlinear classification problem via an STP operator.
机标关键词：designfunctionkernelclassificationnonlinearproduct-basedsemi-tensor
论文发表日期：2022-11-05
在线出版日期：2025-08-15（本平台首次上网日期，不代表文献的发表时间）
页数：9( 456-464 )
英文信息