  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 can give clustering results, thus providing a theoretical support for
many works, e.g., Xu et al. [1] and Kim et al. [2], that show the superiority
of the standard NMF as a clustering method.
