分段光滑的半监督支持向量分类机

Piecewise Smooth Semi-supervised Support Vector Machine for Classification

为了解决半监督支持向量分类优化模型中的非凸非光滑问题,基于分段逼近的思想提出了一个分段函数,并以此逼近非凸非光滑的目标函数。给出的分段函数可以根据不同的精度要求选择不同的逼近参数,同时构造出基于上述分段函数的光滑半监督支持向量机模型。采用了LDS(Low Density Separation)算法求解模型,分析了其对对称铰链损失函数的逼进精度。理论分析和数值实验结果都证明分段光滑的半监督支持向量机的分类性能和效率优于以往提出的光滑模型。

In order to focus on the non-smooth and non-convex problems of the semi-supervised support vector ma- chine, a piecewise function based on piecewise ideas was proposed to approach the non-convex and non-smooth objective function. The approach degree of the piecewise function to objective function can be chosen according to the accuracy demand. A new piecewise smooth semi-supervised support vector machine （PWSS3VM） model based on piecewise function was constructed. LDS algorithm was applied to solve the model and its approximation performance to the symmetric hinge loss function was analyzed. Theoretical analysis and numerical experiments confirm that PWSS3 VM model has better classification performance and higher classification efficiency than previous smooth models.