Non-negative Matrix Factorization Based On Local Constraints

With the rapid development of science and technology,the dimension of data which we have obtained is becoming larger and larger,applying these high-dimension data directly to the data analysis problem will increase the redundancy between data and result in a large number of computational cost,thus the data analysis problem will become more and more difficult,feature extraction is an effective method to solve the above problems.Therefore,feature extraction method is widely used in the field of pattern recognition,computer vision and information retrieval.In a number of feature extraction methods,scholars have focused on the Non-negative Matrix Factorization(NMF)method and its improved methods.Although the methods which are based on NMF have achieved good performance,there are still many limitations to be further solved and improved.According to the summary and analysis of the existing NMF methods,we propose a novel feature extraction method called Local Constraint Graph Regularized Non-negative Matrix Factorization(LC_GNMF).In LC_GNMF,the local constraints and Graph Regularized Non-negative Matrix Factorization(GNMF)are integrated into a new unified framework.LC_GNMF algorithm not only takes the local information of the data into account,but also ensures the reconstruction coefficients of two data points which are close in the intrinsic geometry are also close to each other.In addition,the proposed LC_GNMF method can simultaneously complete graph optimization and data dimensionality reduction,and then get the graph structure which is more advantageous to data dimensionality reduction.In order to verify the validity of the proposed algorithm,we performed classification experiment on four face databases and clustering experiment on five UCI datasets,and we compared LC_GNMF with standard NMF method and some algorithms which are based on NMF.The extensive experimental results show that the LC_GNMF algorithm has better performance.