THE NONNEGATIVE MATRIX FACTORIZATION: REGULARIZATION AND COMPLEXITY

Data continues to grow, and it has become ever important to find effective big data analysis techniques. Computational tools, such as singular value decomposition, have been employed in the interpretation of big data. Another tool has recently gained popularity and comparative success: the nonnegative matrix factorization (NMF). The NMF method is a feature selection, dimension reduction algorithm which takes a data matrix and finds a simpler representation. In this paper, we discuss the choice of regularization parameters for a regularized NMF problem, and we develop a primal-dual active set method which enhances the representation. In addition, we examine rank determination for the case of the NMF problem. We develop a method to choose the proper complexity based on the concept of NMF-singular values.