Nonnegative Matrix Factorization: Algorithms and Parallelization

An alternative to singular value decomposition (SVD) in the information retrieval is the low-rank approximation of an original non-negative matrix A by its non-negative factors U and V . The columns of U are the feature vectors with no non-negative components, and the columns of V store the non-negative weights that serve for the combination of feature vectors. First experiments show that restricting the decomposition of a non-negative matrix A to nonnegative factors leads to the better efficiency than the low-rank approximation using the SVD of A. Also, the non-negative feature vectors can be more easily interpreted in terms of a coded information than the left (right) singular vectors (which usually contain also negative components). We describe basic serial iterative algorithms for minimizing the difference A − UV in the Frobenius norm together with possible additional constraints. Next, the analysis of a possible parallelization of serial algorithms for distributed parallel architecture is provided.