Pointwise manifold regularization for semi-supervised learning

作     者：Yunyun WANG Jiao HAN Yating SHEN Hui XUE Yunyun WANG;Jiao HAN;Yating SHEN;Hui XUE

作者机构：Department of Computer Science and EngineeringNanjing University of Posts&TelecommunicationsNanjing 210046China School of Computer Science and EngineeringSoutheast UniversityNanjing 210096China 

出 版 物：《Frontiers of Computer Science》 (中国计算机科学前沿（英文版）)

年 卷 期：2021年第15卷第1期

页      面：91-98页

核心收录：

学科分类：0810[工学-信息与通信工程] 0808[工学-电气工程] 08[工学] 081104[工学-模式识别与智能系统] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.61876091) China Postdoctoral Science Foundation(2019M651918). 

主　　题：semi-supervised classification manifold regularization pairwise smoothness pointwise smoothness local density 

摘      要：Manifold regularization(MR)provides a powerful framework for semi-supervised classification using both the labeled and unlabeled data.It constrains that similar instances over the manifold graph should share similar classification out-puts according to the manifold assumption.It is easily noted that MR is built on the pairwise smoothness over the manifold graph,i.e.,the smoothness constraint is implemented over all instance pairs and actually considers each instance pair as a single operand.However,the smoothness can be pointwise in nature,that is,the smoothness shall inherently occur“everywhereto relate the behavior of each point or instance to that of its close neighbors.Thus in this paper,we attempt to de-velop a pointwise MR(PW_MR for short)for semi-supervised learning through constraining on individual local instances.In this way,the pointwise nature of smoothness is preserved,and moreover,by considering individual instances rather than instance pairs,the importance or contribution of individual instances can be introduced.Such importance can be described by the confidence for correct prediction,or the local density,for example.PW.MR provides a different way for implementing manifold smoothness Finally,empirical results show the competitiveness of PW_MR compared to pairwise MR.