Application And Initialization Of Non-negative Matrix Factorization

This paper describes the background and development status of non-negative matrix factorization, gives NMF main problem nowadays, introduce common NMF decomposition algorithm and initialization method, and then introduce the corresponding non-negative matrix factorization geometric interpretation, and combined with non-negative matrix factorization geometric interpretation, propose a method of optimizing various initialization method for non-negative matrix factorization algorithm.This strategy is based on the geometric interpretation of NMF, in the convex hull, the intersection point between the connect of two points and the corresponding boundary of probability simplex, is used to update the initial basis vectors corresponding point in the matrix, so that the base vector matrix extended, and it can better contain the original matrix. For the specific matrix and random matrices, different non-negative matrix factorization algorithm and various initial value and its optimization do the comparison experiment, the corresponding experiments demonstrate the effectiveness of this optimization method, and show that compared with other original initialization method, the optimization method gets better results. Finally, with non-negative matrix factorization research, introduces several practical applications of non-negative matrix factorization.