Off-diagonal symmetric nonnegative matrix factorization

Symmetric nonnegative matrix factorization (symNMF) is a variant of (NMF) that allows handling symmetric input matrices and has been shown to be particularly well suited for clustering tasks. In this paper, we present new model, dubbed off-diagonal symNMF (ODsymNMF), does not take into account the diagonal entries in objective function. ODsymNMF three key advantages compared symNMF. First, theoretically much more sound as there always exists an exact size at most n(n − 1)/2 where n dimension matrix. Second, it makes sense practice typically correspond similarity between item itself, bringing information. Third, optimization problem easier solve. particular, will allow us design algorithm based on coordinate descent minimizes component-wise ℓ1 norm its approximation. We prove better binary often encountered practice. also derive method ℓ2 norm, compare two approaches with synthetic document datasets.