面向大规模噪声数据的软性核凸包支持向量机

现有的面向大规模数据分类的支持向量机（support vector machine，SVM）对噪声样本敏感，针对这一问题，通过定义软性核凸包和引入pinball损失函数，提出了一种新的软性核凸包支持向量机（soft kernel convex hull support vector machine for large scale noisy datasets，SCH-SVM）.SCH-SVM首先定义了软性核凸包的概念，然后选择出能代表样本在核空间几何轮廓的软性核凸包向量，再将其对应的原始空间样本作为训练样本并基于pinball损失函数来寻找两类软性核凸包之间的最大分位数距离.相关理论和实验结果亦证明了所提分类器在训练时间，抗噪能力和支持向量数上的有效性.

Soft Kernel Convex Hull Support Vector Machine for Large Scale Noisy Datasets

Current support vector machines (SVMs) for large-scale datasets classification problems are almost sensitive to noises.To overcome this problem,a new soft kernel convex hull support vector machine called SCH-SVM is proposed based on the soft kernel convex hull and pinball loss function.SCH-SVM extracts the soft convex hull vectors in the kernel space,which can represent geometric profile of data in the kernel space.Then SCH-SVM represents the original samples which projected as the soft convex hull vectors for the training samples,and finds the maximum quantile distance between soft kernel convex hulls belonging to two classes by using pinball loss function.Theoretical analysis and numerical experiments show that SCH-SVM has distinctive ability of training time,noise resistibility,and the number of support vectors.