Label Learning Method With Spectral Graph Theory

In traditional data analysis and processing,supervised learning method uses the labeled data set to construct prediction model,and its performance generally increases with the number of labeled data.However,in many real life scenarios,the collected data are often unlabeled,and labels can only be obtained by manual labeling.It is extremely expensive to label the data manually.When facing of a small number of labeled,or even no labeled data,how to design an effective label learning method has become an important research topic in the cross-field of statistics and computer science.In this paper,based on the spectral graph theory,partial multi-view clustering and batch-mode active learning are studied respectively.The main tasks are as follows two aspects:(1)Partial multi-view label learning based on spectral graph learningTo solve the problem that some samples are completely missing in a particular view in unsupervised multi-view learning,we propose a spectral clustering framework.Under this framework,it constrains the label result of the shared part to be consistent across different views,while preserving different label information for specific part in different views.By designing reasonable non-negative and orthogonal constraints,the indicator matrix obtained by the proposed algorithm can contain direct clustering results,which can be regarded as label learning for unlabeled data.Finally,not only the convergence of the algorithm is proved theoretically,but also the effect of the method is illustrated by experiments.(2)Batch-mode label learning based on spectral graph learningAiming at the problem of redundant information in the samples which are selected by traditional representative-based active learning method,we propose a batch-mode active leaning method for unifying reconstructing original data by self-expression and Laplace regularization terms.This picking process can be combined with classification,regression,deep learning and so on.Besides,an optimization algorithm based on Alternating Direction Method of Multipliers(ADMM)is designed and its relative algorithm is convergence,and the validity of the method is verified by the experimental result.