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Pointwise manifold regularization for semi-supervised learning

Frontiers of Computer Science 2021年第1期15卷 91-98页

作者： Yunyun WANG Jiao HAN Yating SHEN Hui XUE Department of Computer Science and Engineering Nanjing University of Posts&TelecommunicationsNanjing 210046China School of Computer Science and Engineering Southeast UniversityNanjing 210096China

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“everywhere"to 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.

关键词： semi-supervised classification manifold regularization pairwise smoothness pointwise smoothness local density

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Semi-supervised learning via manifold regularization

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The Journal of China Universities of Posts and Telecommunications 2012年第6期19卷 79-88页

作者： MAO Yu ZHOU Yan-quan LI Rui-fan WANG Xiao-jie ZHONG Yi-xin School of Telecommunication Engineering Beijing University of Posts and Telecommunications

This paper proposes a novel graph-based transductive learning algorithm based on manifold regularization. First, the manifold regularization was introduced to probabilistic discriminant model for semi-supervised classification task. And then a variation of the expectation maximization （EM） algorithm was derived to solve the optimization problem, which leads to an iterative algorithm. Although our method is developed in probabilistic framework, there is no need to make assumption about the specific form of data distribution. Besides, the crucial updating formula has closed form. This method was evaluated for text categorization on two standard datasets, 20 news group and Reuters-21578. Experiments show that our approach outperforms the state-of-the-art graph-based transductive learning methods.

关键词： manifold regularization semi-supervised learning transductive learning expectation maximization algorithm classification text categorization

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Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

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Journal of the Operations Research Society of China 2022年第1期10卷 89-112页

作者： Jia-Bin Zhou Yan-Qin Bai Yan-Ru Guo Hai-Xiang Lin Department of Mathematics Shanghai UniversityShanghai 200444China Delft Institute of Applied Mathematics Delft University of TechnologyDelft 2600GAThe Netherlands

In general,data contain noises which come from faulty instruments,flawed measurements or faulty communication.Learning with data in the context of classification or regression is inevitably affected by noises in the data.In order to remove or greatly reduce the impact of noises,we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine(Lap-TSVM).A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine(IFLap-TSVM)is presented.Moreover,we extend the linear IFLap-TSVM to the nonlinear case by kernel function.The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classi-fier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization.Experiments with constructed artificial datasets,several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine(TSVM),intuitionistic fuzzy twin support vector machine(IFTSVM)and Lap-TSVM.

关键词： Twin support vector machine Semi-supervised classification Intuitionistic fuzzy manifold regularization Noisy data

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Semi-supervised Generative Adversarial Networks Based on Scalable Support Vector Machines and manifold regularization

Semi-supervised Generative Adversarial Networks Based on Sca...

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第32届中国控制与决策会议

作者： Xianlun Tang Xinxian Yu Jin Xu Yingjie Chen Runzhu Wang College of Automation Chongqing University of Posts and Telecommunications College of Computer Science and Technology Chongqing University of Posts and Telecommunications College of Union with University of Cincinnati University of Chongqing

Generative adversarial networks（GANs） are potential models in semi-supervised learning because of the excellent performance of GANs.However,most GAN-based semi-supervised models are sensitive to local perturbation,which means those models are not stable enough.Besides,Softmax classifier is the first choice of those models.In this paper,a novel method is proposed by introducing a discriminator using scalable SVM classifier with manifold regularization.Scalable SVM classifiers typically perform better in small sample data sets compared with other classifiers,which is consistent with the feature that semi-supervised learning consists of a few labeled data and a large number of unlabeled data.manifold regularization forces discriminator to keep invariable to local perturbations.By incorporating into feature-matching GAN architecture,the proposed GANs-based semi-supervised learning algorithm has advantages over other methods on the Cifar-10,SVHN and Cifar-100 datasets.The results show that the proposed model SSVM-GAN has good robustness and strong generalization ability.

关键词： Generative adversarial networks semi-supervised learning Scalable SVM manifold regularization

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manifold Regularized Low Rank Embedding for Hyperspectral Image Feature Extraction

Manifold Regularized Low Rank Embedding for Hyperspectral Im...

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第四届高分辨率对地观测学术年会

作者：李恒超 Yang-Jun Deng Wen Yang School of Information Science and Technology Southwest Jiaotong University School of Electronic Information Wuhan University

Recently,low rank embedding(LRE) method has achieved great success in robust image feature extraction,which aims to embed the data into a low dimensional space with the low rank reconstruction relationship preserved.Since the high dimensional data of hyperspectral image(HSI) often leads to information redundancy,LRE is considered to perform the feature extraction of HSI in this paper.Although LRE can seek the low rank representation(LRR) and optimal subspace simultaneously,the characteristic of LRR results in that the subspace obtained by LRE only considers the global Euclidean structure and ignores the local manifold structure.However,the local manifold structure generally plays a important role for HSI robust features extracting.In order to exploit the local manifold structure of the data,a Laplacian graph characterized manifold regularization has been incorporated into LRE,leading to our proposed Laplacian regularized LRE(Lap LRE).Classification by a existing classifier is implemented to verify the robustness of features extracted by Lap LRE.Experimental results on two HSI data sets demonstrate that the performance of LRE has been enhanced by using the manifold regularization.

关键词： low rank embedding hyperspectral image feature extraction manifold regularization classification

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manifold Regularized Robust Unsupervised Feature Selection for Image Clustering

Manifold Regularized Robust Unsupervised Feature Selection f...

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第36届中国控制会议

作者： Yuqing Shi Shiqiang Du School of Electrical Engineering Northwest Minzu University School of Mathematics and Computer Science Northwest Minzu University

ISBN: (纸本)9781538629185

Dimensionality reduction is a challenging task for high dimensional data processing in machine learning and data mining.As an effective dimension reduction technique,unsupervised feature selection aims at finding a subset of features to retain the most relevant information.In this paper,we propose a novel unsupervised feature selection method,called manifold Regularized Robust Unsupervised Feature Selection(MRUFS) for image clustering.MRUFS performs robust discriminative feature selection and robust clustering simultaneously under l

关键词： unsupervised feature selection manifold regularization matrix factorization dimensionality reduction

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Optimal regularization Parameters Selection for Laplacian Support Vector Machine

Optimal Regularization Parameters Selection for Laplacian Su...

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第二十七届中国控制会议

作者： Li Juntao1,Jia Yingmin1,Du Junping2,Li Wenlin3 1.The Seventh Research Division,Beihang University(BUAA) ,Beijing 100083,P.R.China 2.Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia,School of Computer Science and Technology,Beijing University of Posts and Telecommunications,Beijing 100876,P.R.China 3.College of Mathematics and Information Science,Henan Normal University,Xingxiang 453007,P.R.China

Laplacian support vector machine（LapSVM） is an attracting tool for semi-supervised classification with manifold regularization.In this paper,we devote to selecting the extrinsic and intrinsic regularization parameters.To this end,a fusion of training and validation levels is first proposed,based on which,the optimal regularization parameters selection problem can be cast as a standard semidefinite programming.Then,a hybrid manifold regularization algorithm is also developed,thus eliminating the difficulty of balancing between the ambient space and the intrinsic geometric of the data distribution.Finally,experiments are performed that verify the research results.

关键词： Laplacian support vector machine manifold regularization Semidefinite programming （SDP）

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