A kernel-free fuzzy reduced quadratic surface [formula omitted]-support vector machine with applications

Abstract

The kernel-free support vector machine (SVM) models are recently developed and studied to overcome some drawbacks induced by the kernel-based SVM models. To further improve the classification accuracy and computational efficiency of existing kernel-free quadratic surface support vector machine (QSSVM) models, a novel kernel-free ν-fuzzy reduced QSSVM model is proposed. The proposed model utilizes a reduced quadratic surface for nonlinear binary classification as well as reducing the effect of outliers in the data set. Some theoretical properties are rigorously studied, especially, the effects of the parameter ν on the dual feasibility and the number of support vectors. Computational experiments are conducted on some public benchmark data sets to indicate the superior performance of the proposed model over some well-known binary classification models. The numerical results also favors the higher training efficiency of the proposed model over those of other kernel-free SVM models. Moreover, the proposed model is successfully applied to the prodromal detection of Alzheimer’s Disease with good performance, by using the data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database.