Research On Multi-graph Regularized Non-negative Matrix Factorization Algorithm Based On L21 Norm

In today's era,with the popularization of highly informatization and network globalization,massive amounts of information and high-dimensional data have caused huge computational overhead,huge processing difficulties,and vague information transmission.How to effectively reduce the dimensionality of data is very important.As a dimension reduction method without losing inherent feature information,feature extraction is widely used in data mining,pattern recognition,machine learning,artificial intelligence and many other fields.Among many feature extraction methods,Non-negative Matrix Factorization(NMF)has become one of the research hotspots because of its non-negative constraints,sparse local expression,and good interpretability.In this paper,we research and analysis of non-negative matrix factorization related algorithms and propose new and improved algorithms,the main research work is as follows:1.Introduction of related theoretical knowledgeWe introduce the concepts,algorithm models,and practical applications of non-negative matrix factorization;research the theory of manifold learning and graph regularized non-negative matrix factorization algorithm;and analyze the common problems existing in related algorithms.2.Propose a multi-graph regularized non-negative matrix factorization algorithmFor the problem that graph regularized non-negative matrix factorization is limited to a single relational structure,based on manifold learning and graph knowledge,this paper constructs a neighbor graph,weight graph and sparse graph,and proposes an improved multi-graph regularized non-negative matrix factorization algorithm.The algorithm has a better representation of the data geometry,and maintains the neighbor information,spatial distance relationship,and sparse expression in the process of high-dimensional data being decomposed intolow-dimensional representation.Experiments on multiple data sets demonstrate the effectiveness of the constructed multi-graph structure and the feasibility of the proposed algorithm.3.Propose a Multi-graph regularized non-negative matrix factorization Algorithm based on L21 normFor the problem that the error function of L2 norm conforms to the Gaussian noise model and it is easy to be interfered by noise or singular values when constructing the algorithm function model.This paper is based on the L21 norm,which is insensitive to noise and more sparse in data requirements,and proposes a multi-graph regularized non-negative matrix factorization Algorithm based on L21 norm.This algorithm improves the robustness of the algorithm and the sparsity of the decomposition results.This paper builds the objective function of the algorithm,and gives the update rules and Proof of convergence.The comparative experiments with other algorithms on multiple classic data sets prove the advantages of the proposed algorithm in terms of the accuracy and the sparsity of the decomposition results.