  Nonnegative matrix factorization (NMF) is widely used for clustering with
strong interpretability. Among general NMF problems, symmetric NMF is a special
one that plays an important role in graph clustering where each element
measures the similarity between data points. Most existing symmetric NMF
algorithms require factor matrices to be nonnegative, and only focus on
minimizing the gap between similarity matrix and its approximation for
clustering, without giving a consideration to other potential regularization
terms which can yield better clustering. In this paper, we explore factorizing
a symmetric matrix that does not have to be nonnegative, presenting an
efficient factorization algorithm with a regularization term to boost the
clustering performance. Moreover, a more general framework is proposed to solve
symmetric matrix factorization problems with different constraints on the
factor matrices.
