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为了处理半监督支持向量分类优化中的非凸非光滑问题,引入一族多项式光滑函数来逼近非凸的目标函数,给出的多项式函数在样本的高密度区逼近精度高,逼近精度低时出现在样本的低密度区,同时可以根据不同的精度要求选择不同的逼近函数。采用BFGS算法求解模型。在人工数据和UCI数据集上的实验结果显示,算法不仅能保证标号数据很少时的分类精度,而且不因标号数据的增多而明显提高分类性能,因此给出的分类器性能是稳定的。
In order to deal with the non-convex nonsmooth problem in semi-supervised SVM, a family of polynomial smoothing functions is introduced to approximate the non-convex objective function. The polynomial function is given when the approximation precision of the high-density region is high and when the approximation accuracy is low. Samples of the low-density area, at the same time according to different accuracy requirements to choose different approximation function. Using BFGS algorithm to solve the model. The experimental results on artificial data and UCI datasets show that the proposed algorithm can not only ensure the classification accuracy when label data is seldom, but also improve the classification performance obviously due to the increase of label data. Therefore, the performance of the given classifier is stable.