基于流形正则化的分类与回归算法及应用

A Classification and Regression Algorithm Based on Manifold Regularization and Its Application

利用流形正则化的思想,围绕半监督学习,提出了一种针对流形正则化的模式分类和回归分析的新算法。该算法基于流形上的正则化项和传统的正则化项相结合的方法,利用支持向量机分类与回归已有的结果,解决半监督学习的分类与回归问题,提高了泛化能力。该算法实现简单,无需调用其他程序。通过数值试验,验证了该算法具有较好的泛化能力,对噪音具有较强的鲁棒性。且在分类问题上,该算法在输入极少数有标签样本时,也能保持较好的分类效果;在回归问题上,也具有较好的学习精度,尤其在输入带有噪音的流形数据上时,表现就更为突出。

Based on the theory of manifold regularization,a new algorithm of semi-supervised learning for the problem of classification and regression is proposed.The algorithm is deduced by the connection between the regularization term on the manifold and the classical regularization term.Using the result of support vector classification and regression,the algorithm not only solves the problem of semi-supervised learning but also improves generalization capability.The algorithm is simple and doesnt＇t need to call other optimization programs.Numerical experiment results show that the algorithm enhances generalization capability and is robust to noise.The algorithm to the classification problems is very promising on a small number of unlabeled examples.The experiment results are more accurate by using the algorithm than by support vector regression.