Research On Graph Regularized Non-negative Matrix Factorization Algorithm Under Multiple Constraints

With the popularization and development of electronic devices,massive amounts of data have been generated,which usually have the characteristics of high dimension,complex structure and redundancy,resulting in the problem of "dimension disaster".Therefore,in the face of a large amount of complex data,how to effectively mine useful information in the original high-dimensional data becomes important.In the analysis and processing of such real data,in order to emphasize the interpretability of the analysis results,the "non-negativity" constraint should be satisfied.Non-negative matrix factorization is a well-known "non-negative" low-rank learning method.Due to the existence of the "non-negativity" constraint in the decomposition process,this method only allows purely additive linear combinations,which also makes the decomposition results based on partial representations.In addition,this expression method is in line with the cognitive mode of "parts constitute a whole" in the human brain,and has the characteristics of interpretability.From the perspective of graph regularization,in view of the problems existing in the current graph regularization non-negative matrix factorization algorithm,by introducing different multi-constraints,the following research work is carried out:(1)To address the problem of inaccurate description of spatial association of sample points in the traditional graph regularization.Based on the dual graph structure,this paper proposes two semi supervised dual graph multi constrained non-negative matrix decomposition algorithms,namely,semi supervised dual graph regularized bi-orthogonal non-negative matrix decomposition(SDGNMF-BO)algorithm and Sinkhorn distance feature scaling multi-constrained non-negative matrix decomposition(S3GNMF)algorithm.The SDGNMF-BO algorithm constructs two similarity matrices through the local linear embedding algorithm,which are used to explore the sample correlation and feature correlation of the original data,and combines them into a regularization term to make full use of the manifold structure information of the original data;Then a global constraint matrix is constructed based on partial label information to improve the discriminant power of the algorithm;Finally,additional orthogonal constraints are imposed on the decomposition factors to improve the exclusivity of low dimensional features.The S3 GNMF algorithm considers the distribution characteristics of the original data in the manifold space,and proposes a preprocessing method based on the scaling of the Sinkhorn distance feature to smooth the curly manifold of the original data,which is conducive to weakening the interference of outliers on the graph regularization term and improving the robustness of the algorithm;In addition,S3 GNMF uses semi supervised learning,dual graph regularization and sparse constraints to improve the subspace learning ability of the algorithm.Through comparative experiments on standard image datasets and translation noise image datasets,the effectiveness of two semi supervised dual graph multi constrained non negative matrix decomposition algorithms in dealing with standard data feature extraction and noise data feature extraction is verified respectively.(2)To deal with the problem of too close distance between dissimilar samples in the traditional graph regularized non-negative matrix decomposition algorithm.Based on the adversarial graph structure,an adversarial graph regularization deep non-negative matrix factorization(AGDNMF)algorithm is proposed,which considers the unique hierarchical structure information of the original data,and constructing a bidirectional depth decomposition structure can effectively explore the deep structural information of this type of data;In addition,the algorithm considers the local similarity relationship between the sample inside and outside the class and constructs a pair of adversarial graph regularization terms to reward the same sample distance and penalize the heterogeneous sample distance,which can effectively strengthen the discriminative power of the low-dimensional representation matrix.(3)To address the problem of inconsistency between label information and graph structure in semi-supervised graph regularization.Based on the structure of adaptive neighborhood graph,a semi supervised adaptive neighborhood graph updating three factor non-negative matrix factorization(ABNMTF)algorithm is proposed.This algorithm solves the problem that the algorithm’s adaptability decreases due to too many adjustable parameters in the multi constrained non-negative matrix algorithm.In this algorithm,an adaptive neighborhood graph updating method is proposed,which can improve the accuracy of the internal association structure of graph regularization items while only adding an adjustable parameter;In addition,the semi-supervised information-based hard constraint method and flexible three-factor decomposition structure can significantly enhance the subspace learning ability of the algorithm and improve the flexibility of the algorithm.The proposed algorithm achieves the highest clustering performance in the clustering comparison experiments on multiple image datasets,and has the advantages of less time-consuming with weak parameter sensitivity.The above work mainly focuses on the non-negative feature extraction of data.In addition,this paper makes further research on the weak unmixing performance due to the complexity of hyperspectral data in hyperspectral unmixing applications,and proposes multi-regularized non-negative matrix factorization for hyperspectral unmixing(SMRNMF).The algorithm fully considers the complexity of hyperspectral data,that is,the uneven distribution of mixed end elements,the sparseness of abundance information and the spectral smoothness of pure end elements.Specifically,in order to fully consider the complex correlation information in hyperspectral data,an adaptive neighborhood dual graph regularization term based on local correlation,a subspace structure regularization term based on global correlation,a sparse constraint term of the abundance matrix satisfying the abundance sparsity and a flexible smoothing adjustment matrix are proposed.Through the comparative unmixing experiments on several hyperspectral data sets,the effectiveness of the adaptive neighborhood dual graph multi regularization non negative matrix decomposition algorithm on the unmixing of hyperspectral data is verified.