Weighted Sparse Graph Non-negative Matrix Factorization based on L21 norm

Dimension reduction is widely concerned because of the rapid development of all walks of life, which leads to the exponential growth of data dimension. As a basic method of dimension reduction, non-negative matrix factorization is easily affected by noise, but its improved algorithm L
21
NMF is not sensitive to noise. Therefore, the paper proposes a weighted sparse graph non-negative matrix factorization based on L
21
norm(LSL
21
NMF). In this method, L
21
norm is used as the measure criterion, the non-negative matrix is decomposed into the summation of one error matrix and the product of two matrices non-negative, the weight sparse graph is applied to the regularization term to preserved geometrical structure of data. An efficient iterative approach is developed to solve the optimization problem of LSL
21
NMF. On the standard noisy public dataset,the experimental results show that the method is more effective and robust than other methods.