The sparse factorization of nonnegative matrix in distributed network

This paper proposes some distributed algorithms to solve the sparse factorization of a large-scale nonnegative matrix (SFNM). These distributed algorithms combine some merits of classical nonnegative matrix factorization (NMF) algorithms and distributed learning network. Our proposed algorithms utilize the whole nodes of network to solve a factorization problem of a nonnegative matrix; the fact is that per node copes with a part of the matrix, then uses the distributed average consensus (DAC) algorithm or regional nodes to communicate the parameters gained by each node to ensure them to be convergent or easy to calculation. Different from other existing distributed learning algorithms of NMF, which always need high-qualified hardware or complicated computing methods, our algorithms make a full use of the simplicity of traditional NMF algorithms and distributed thoughts. Some artificial datasets are used for testing these algorithms, and the experimental results with comparisons show that the proposed algorithms perform favorably in terms of accuracy and efficiency.