%A Hui XUE, Haiming XU, Xiaohong CHEN, Yunyun WANG %T A primal perspective for indefinite kernel SVM problem %0 Journal Article %D 2020 %J Front. Comput. Sci. %J Frontiers of Computer Science %@ 2095-2228 %R 10.1007/s11704-018-8148-z %P 349-363 %V 14 %N 2 %U {https://journal.hep.com.cn/fcs/EN/10.1007/s11704-018-8148-z %8 2020-04-15 %X

Indefinite kernel support vector machine (IKSVM) has recently attracted increasing attentions in machine learning. Since IKSVM essentially is a non-convex problem, existing algorithms either change the spectrum of indefinite kernel directly but risking losing some valuable information or solve the dual form of IKSVM whereas suffering from a dual gap problem. In this paper, we propose a primal perspective for solving the problem. That is, we directly focus on the primal form of IKSVM and present a novel algorithm termed as IKSVM-DC for binary and multi-class classification. Concretely, according to the characteristics of the spectrum for the indefinite kernel matrix, IKSVM-DC decomposes the primal function into the subtraction of two convex functions as a difference of convex functions (DC) programming. To accelerate convergence rate, IKSVM-DC combines the classical DC algorithm with a line search step along the descent direction at each iteration. Furthermore, we construct a multi-class IKSVM model which can classify multiple classes in a unified form. A theoretical analysis is then presented to validate that IKSVM-DC can converge to a local minimum. Finally, we conduct experiments on both binary and multi-class datasets and the experimental results show that IKSVM-DC is superior to other state-of-the-art IKSVM algorithms.