使用交叉距离最小化算法设计支持向量机

Design of Support Vector Machines Using Cross Distance Minimization Algorithm

摘要: 针对核方法在处理非线性可分数据问题上的优势,将一种硬间隔无核支持向量机——交叉距离最小化算法(cross distance minimization algorithm,CDMA)推广到带核的版本,称为带核的交叉距离最小化算法(kernel cross distance minimization algorithm,KCDMA).利用乘子将交叉距离最小化算法表示为内积的形式,然后使用核函数代替内积运算,并且引入二次惩罚,这样扩展后的模型能处理非线性可分数据集,并且允许一定的分类偏差.实验结果表明,与一些经典的支持向量机方法相比,该方法具有明显的竞争力.

Abstract: According to the advantages of kernel method in dealing with non-linear separable data,a hard margin non-kernel support vector machine,i.e.Cross Distance Minimization Algorithm(CDMA) to its kernel version,called KCDMA,was extended.Firstly,CDMA was expressed as the form of inner product,and kernel function was introduced to replace inner product.After that,by using quadratic cost,CDMA was generalized to its extension,namely,KCDMA.KCDMA was applicable in the nonlinear case and allowed violations to classify non-separable data sets.Resultsshow that this method is totally very competitive with some well-known and powerful support vector machines.