SK算法的核化及其在医学诊断中的应用

Kernelization of SK algorithm and its application in medical diagnosis

Schlesinger-Kozinec(SK)算法是一种典型的几何类支持向量机求解方法,具有理论基础坚实、分类过程直观等优点.对于线性可分的两类样本,SK算法可通过它们凸包间的最近点来求解分类超平面.对于非线性可分问题,核函数首先被引入,它能够实现原空间到高维特征空间的映射变换,即将特征空间中的内积运算转换为原空间的函数形式.然后,SK算法在特征空间中完成分类任务.文中首先介绍SK算法的步骤和几何意义.然后详细分析非线性可分条件下,SK算法的核化问题,并重点强调了一些运算过程的内积表达.最后,在医学诊断这一特定分类问题上对核化的SK算法进行实验测评.结果表明,相比于其他的经典支持向量机实现,核化的SK算法能够获得更高的诊断准确率.

Schlesinger-Kozinec( SK) algorithm is a typical method for solving the geometry-class support vector machine. It has the advantages of solid theoretical foundation and intuitive classification procedures. For two classes of linearly separable samples,The SK algorithm can solve the classification hyperplane by the nearest point between their convex hulls. For the nonlinear separable problem,the kernel function is first introduced,which can realize the mapping transformation from the original space to the high-dimensional feature space,i.e.,transforming the inner product operation in the feature space into the functional form of the original space.Then,the SK algorithm performs the classification task in the feature space. This paper first introduces the process and geometric meaning of SK algorithm. Then,kernelization of SK algorithm( named KSK) is analyzed under the nonlinearly separable condition. Furthermore,the inner product expression of some computational processes is emphasized. Finally,the experimental evaluation to KSK algorithm is conducted on several specific classification problems concerning medical diagnosis. The results show that compared with other classical support vector machines,the KSK algorithm can achieve higher prediction accuracy.