Research Of Semi-supervised Manifold Regularization With Adaptive Graph Learning

Semi-supervised classification learning is an important research field in classification learning.Large amounts of semi-supervised classification methods have been developed recently,however,there is no related guidance in literature or empiricial,and further,it is really hard to decide which one to use in real learning tasks.Moreover,Manifold regularization(MR)provides a powerful framework for semi-supervised classification(SSC)learning.However,there are still some issues whith MR: 1)The manifold graph is usually pre-constructed before classification,and fixed during the classification learning process.As a result,independent with the subsequent classification,the graph does not necessarily benefit the classification performance.2)There are parameters needing tuning in the graph construction,while parameter selection in semi-supervised learning is still an open problem currently,which sets up another barrier for constructing an appropriate manifold graph benefiting the performance.As a result,the main work is focused on the following two parts:Firstly,empirical comparisons over several typical methods are performed to provide some useful suggestions.In fact,semi-supervised classification methods can be categorized by data distribution assumptions.Therefore,typical methods with different data distribution assumptions are compared.Specifically,the methods include transductive support vector machine(TSVM)using the cluster assumption,laplacian regularized least squares classification(LapRLSC)using the manifold assumption,SemiBoost using cluster assumption and manifold assumption,and implicitly constrained least squares(ICLS)without any assumption,with the supervised least squares classification(LS)as the base line.Finally,several suggestions are provided: 1)When the data distribution is given,the semi-supervised classification method that adopts the corresponding assumption can lead to the best performance.2)Without any prior knowledge about the data distribution,TSVM will be a good choice when the given labeled samples are extremely limited.3)When the labeled samples are not so scarce,and at the same time,if the learning safety is emphasized,ICLS is suggested,otherwise,Lap RLSC will be a good choice.Secondly,this paper also develops a novel semi-supervised manifold regularization with adaptive graph(AGMR for short)by integrating the graph construction and classification learning into a unified framework.AGMR integrates the graph construction and classification learning into a unified framework,so that the manifold graph along with its parameters will be optimized in learning rather than pre-defined,consequently,it will be adaptive to the classification,and benefit the performance.Further,by adopting the entropy and sparse constraints respectively for the graph weights,we derive two specific methods called AGMR_entropy and AGMR_sparse,respectively.Experiments on different datasets indicate that the proposed AGMR strategy can enhance the classification performance of traditional MR.