Nonnegative Matrix Factorization (NMF) is an efficient technique to approximate a large matrix containing only nonnegative elements as a product of two nonnegative matrices of significantly smaller size. The guaranteed nonnegativity of the factors is a distinctive property that other widely used matrix factorization methods do not have. Matrices can also be seen as second-order tensors. For som...

Uncovering community structures is important for understanding networks. Currently, several nonnegative matrix factorization algorithms have been proposed for discovering community structure in complex networks. However, these algorithms exhibit some drawbacks, such as unstable results and inefficient running times. In view of the problems, a novel approach that utilizes an initialized Bayesian...

Existing nonnegative matrix factorization methods usually focus on learning global structure of the data to construct basis and coefficient matrices, which ignores local that commonly exists among data. To overcome this drawback, in paper, we propose a new type method, learns similarity clustering mutually enhanced way. The learned representation is more representative it better reveals inheren...

This paper introduces a novel algorithm for the nonnegative matrix factorization and completion problem, which aims to find nonnegative matrices X and Y from a subset of entries of a nonnegative matrix M so that XY approximates M . This problem is closely related to the two existing problems: nonnegative matrix factorization and low-rank matrix completion, in the sense that it kills two birds w...

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an m-by-n nonnegative matrix X and a factorization rank r, find, if possible, an m-by-r nonnegative matrix W and an r-by-n nonnegative matrix H such that X = WH . In this paper, we propose two heuristics for exact NMF, one inspired from simulated annealing and the other from the greedy randomized adaptive sea...