Manifold ranking graph regularization non-negative matrix factorization with global and local structures

Non-negative matrix factorization (NMF) is a recently popularized technique for learning parts-based, linear representations of non-negative data. Although the decomposition rate of NMF is very fast, it still suffers from the following deficiency: It only revealed the local geometry structure; global geometric information of data set is ignored. This paper proposes a manifold ranking graph regularization non-negative matrix factorization with local and global geometric structure (MRLGNMF) to overcome the above deficiency. In particular, MRLGNMF induces manifold ranking to the non-negative matrix factorization with Sinkhorn distance. Numerical results show that the new algorithm is superior to the existing algorithm.