This paper provides a theoretical explanation on the clustering aspect of
nonnegative matrix factorization (NMF). We prove that even without imposing
orthogonality or sparsity constraint on the basis and/or coefficient matrix,
NMF still can give clustering results, thus providing a theoretical support for
the works of Xu et al. [1] and Kim et al. [2], where the authors showed the
superiority of the standard NMF as a clustering method.

This paper describes a clustering method to group the most similar and
important weblogs with their descriptive shared words by using a technique from
multilinear algebra known as PARAFAC tensor decomposition. The proposed method
first creates labeled-link network representation of the weblog datasets, where
the nodes are the blogs and the labels are the shared words.