With the rapid development of multimedia technology and Internet technology,high-dimensional data have been produced gradually.These high-dimensional data make image features full,but at the same time,the computer processing will become complicated.Although these high-dimensional data are conducive to the expression of images,they also cause "dimensional disasters" of the data because of the large amount of information.Therefore,it is important to reduce the dimensionality of the data.The non-negative matrix factorization method is an effective dimensionality reduction algorithm.It emphasizes that the matrices before and after factorization must be non-negative,and can naturally express the idea of "partially forming the whole".However,the traditional non-negative matrix factorization method does not use the label information of the sample data and it is limited by the dimensional matching constraints.Aiming at the above two key issues,this paper carries out in-depth research and analysis around a new non-negative matrix factorization algorithm,which is based on semi-supervised learning theory and semi-tensor product theory.The main innovations and research results are presented as follows:(1)We propose a semi-supervised sparsely constrained non-negative matrix factorization algorithm.The semi-supervised theory is incorporated into the non-negative matrix factorization algorithm,and the non-negative matrix factorization algorithm is constrained with the label information of the samples,so that the samples with the same category of information are projected as a point in low-dimensional space.Specifically,the multiplicative iterative formula and algorithm flow are given in theory,and the convergence and efficiency of the model are verified by the experiments.(2)We propose a general non-negative matrix factorization method based on semi-tensor product.The semi-tensor product theory that breaks through the limitation of traditional matrix multiplication dimension matching is incorporated into the non-negative matrix factorization algorithm,saving storage space and improving the efficiency of the algorithm.Specifically,the convergence and the time validity of the algorithm are verified and analyzed from both experimental and theoretical aspects.(3)We propose a general non-negative matrix factorization algorithm based on semi-supervised learning,which combines semi-supervised and semi-tensor product.This algorithm not only makes full use of the known label information,but also breaks through the limitation of the dimension matching constraints of the traditional non-negative matrix factorization,saving storage space and improving the efficiency of the algorithm.Specifically,we give iterative update rules and algorithm flow,and analyze the effectiveness,complexity,convergence and classification performance of the proposed algorithm through the experiments. |