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.Pei Wang et al. / IJAMML 8:1 (2018) 42
The paper establishes a theorem of data perturbation analysis for the support vector classifier dual problem, from which the data perturbation analysis of the corresponding primary problem may be performed through standard results. This theorem derives the partial derivatives of the optimal solution and its corresponding optimal decision function with respect to data parameters, and provides the basis of quantitative analysis of the influence of data errors on the optimal solution and its corresponding optimal decision function. The theorem provides the foundation for analyzing the stability and sensitivity of the support vector classifier.
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