On the clustering aspect of nonnegative matrix factorization

This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still has clustering capability, thus giving a theoretical support for many works, e.g., Xu et al. and Kim et al., that show the superiority of the standard NMF as a clustering method.