Algorithm Research Based On Discriminative Nonnegative Matrix Factorization

In the era of big data,it has become extremely important to discover the potential information of high-dimensional data,remove redundant features,and obtain effective low-dimensional data representation.Non-negative Matrix Factorization(NMF)decomposes the original data into basis matrix based on partial representation and effective low-dimensional representation.So,it is widely used in hyperspectral unmixing,clustering,face recognition and analysis because the advantages of nonnegativity and strong interpretability.Based on the existing NMF research,Discriminative Non-negative Matrix Factorization(DNMF)solve the problem of mapping the same label to a single point,which can obtain a more effective low-dimensional representation.Therefore,this paper proposes two improved algorithms based on DNMF to solve the problems of ignoring the inherent local geometry of data and including noise and outliers in data.First,we propose a semi-supervised NMF,called Feature Relationship Preservation Robust Discriminative Non-negative Matrix Factorization(FR-RDNMF).This method introduces feature relationship preservation constraints and l2,1 norm,which makes the centroid characteristics of the cluster proportional to the characteristics of the original data,ensures the orthogonality of the coefficient matrix,and obtains a more suitable and stable matrix factorization result for clustering.The corresponding multiplication update rules,convergence proof and complexity analysis are given through mathematical theory derivation.Finally,experiment results show the importance of feature relationship preservation constraints for clustering,and the experimental results on four data sets are more effective than other methods.Second,a supervised NMF was proposed,called Robust Dual-Graph Discriminative Non-negative Matrix Factorization(RDGDNMF).This model introduces dualgraph regularization to learn the inherent local geometry of data space and feature space at the same time,and uses l2,1/2 norm to improve the robustness.Similarly,the corresponding multiplication update rules,convergence proof and complexity analysis are given.According to the projection matrix learned by RDGDNMF,the original data are mapped to low-dimensional space and classified by k-nearest neighbor(KNN).The experimental results on four data sets show that using multiple classifiers to classify the effective low-dimensional representation of data is better than other methods,and KNN has the best classification effect.The algorithm converges quickly and is relatively stable,especially suitable for face data sets.