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.

中文翻译：

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无限内核SVM问题的基本观点

不确定内核支持向量机（IKSVM）最近在机器学习中引起了越来越多的关注。由于IKSVM本质上是一个非凸问题，因此现有算法要么直接更改不确定内核的频谱，但有可能丢失一些有价值的信息，或者解决IKSVM的双重形式而遭受双重间隙问题。在本文中，我们提出了解决该问题的原始视角。也就是说，我们直接关注IKSVM的原始形式，并提出了一种用于二进制和多类分类的称为IKSVM-DC的新颖算法。具体而言，根据不确定核矩阵的频谱特征，IKSVM-DC将原始函数分解为两个凸函数的减法，这是凸函数（DC）编程的区别。为了加快收敛速度​​，IKSVM-DC在每次迭代中将经典DC算法与沿下降方向的线搜索步骤结合在一起。此外，我们构建了一个多类IKSVM模型，该模型可以统一形式对多个类进行分类。然后进行理论分析，以验证IKSVM-DC可以收敛到局部最小值。最后，我们对二进制和多类数据集进行了实验，实验结果表明，IKSVM-DC优于其他最新的IKSVM算法。