一族三次样条光滑半监督支持向量机

摘要

For the problem of non-convex non-smooth in semi-supervised support vector classification optimisation, we built a smooth semi-supervised support vector machine ( SVM ) model, and proposed to construct a new cubic spline smooth function based on piecewise polynomial function and interpolation idea, so as to better approach the non-smooth symmetric hinge loss function part in semi-supervised SVM, and construct the semi-supervised SVM model which is based on this smooth function and has two-order smooth.Furthermore the smooth algorithm in optimisation can be used to solve the model.We also analyse the approaching accuracy of the constructed cubic spline function on symmetric hinge loss function.Through data experiment it is proved that the built new smooth semi-supervised SVM model has better classification effect and efficiency.%针对半监督支持向量分类优化中的非凸非光滑化问题，建立光滑半监督支持向量机模型，提出基于分段多项式函数和插值思想构造一个新的三次样条光滑函数，从而可以更好地逼近对半监督支持向量机中非光滑的对称铰链损失函数部分，构造出基于此光滑函数的具有二阶光滑的半监督支持向量机模型。进而可以用优化中的光滑算法来求解该模型，并分析所构造的三次样条函数对对称铰链损失函数的逼近精度。通过数据实验证明所构造的新的光滑半监督模型具有较好的分类效果和效率。