加权光滑CHKS孪生支持向量机

针对光滑孪生支持向量机(smooth twin support vector machines,简称STWSVM)采用的Sigmoid 光滑函数逼近精度低和STWSVM 对异常点敏感的问题,引入一种性能更好的光滑函数——CHKS 函数,提出了光滑CHKS孪生支持向量机模型(smooth CHKS twin support vector machines,简称SCTWSVM).在此基础上,根据样本点的位置为每个训练样本赋予不同的重要性,以降低异常点对非平行超平面的影响,提出了加权光滑CHKS 孪生支持向量机(weighted smooth CHKS twin support vector machines,简称WSCTWSVM).不仅从理论上证明了SCTWSVM 具有严凸性和任意阶光滑的性能,而且在数据集上的实验结果表明,相对于STWSVM,SCTWSVM 可以在更短的时间内获得更高的分类精度,同时验证了WSCTWSVM 的有效性和可行性.

Weighted Smooth CHKS Twin Support Vector Machines

Smooth twin support vector machines (STWSVM) uses Sigmoid function to transform the unsmooth twin support vector machines (TWSVM) into smooth ones. However, because of the low approximation ability of Sigmoid function, the classification accuracy of STWSVM is unsatisfactory. Furthermore, similar to TWSVM, STWSVM is sensitive to the abnormal samples. In order to address the above problems, this paper introduces CHKS function, and proposes a smooth twin support vector machines, smooth CHKS twin support vector machines (SCTWSVM). In order to reduce the influence of abnormal samples on SCTWSVM, different importance are given for each training sample according to the sample point positions for SCTWSVM, resulting in weighted smooth CHKS twin support vector machines (WSCTWSVM). The study proves that SCTWSVM is not only strictly convex, but also can meet the arbitrary order smooth performance. Meanwhile, the experimental results show that SCTWSVM has better performance than STWSVM. Furthermore, the experimental results also show that WSCTWSVM is effective and feasible relative to SCTWSVM.