International Journal of Applied Mathematics and Machine LearningAuthor's: Pei Wang, Chun Cai, Dalian Liu and Xinfeng Wang
Pages: [41] - [62]
Received Date: March 30, 2018
Submitted by: Jianqiang Gao
DOI: http://dx.doi.org/10.18642/ijamml_7100121954
The support vector regression based on the Statistical Learning Theory avoids the inadequacy of traditional function approximation methods and proves to be highly available for learning and generalization. Its mathematical model is a convex quadratic programming, of which the optimality condition (i.e., the KKT condition) is sufficient and necessary for an optimal solution. In this paper, the quadratic programming of the support vector regression is reduced to linear programming. Based on sensitivity analysis of the linear programming, analysis is conducted on data perturbation due to the decrease (missing) and increase of the initial data. This paper provides the sufficient conditions for remaining the support vectors unchanged under the above cases of perturbation and explains the change in the fitting function.
support vector regression, linear programming, sensitivity analysis, data perturbation, KKT condition.
