Symmetric Nonnegative Matrix Factorization With Beta-Divergences

Nonnegative matrix factorization/approximation (NMF) is a recently developed technology for dimensionality reduction and parts based data representation. The symmetric NMF (SNMF) decomposition is a special case of NMF, in which both factors are identical. This paper discusses SNMF decomposition with beta divergences. A multiplicative update algorithm is developed. It is capable of iteratively finding a factorization for SNMF problem by minimizing beta divergences between an input nonnegative semidefinite matrix and its SNMF approximation. In addition, we prove that the beta divergence sequence is monotonically convergent under this algorithm. Furthermore, we validate it by experiments on both synthetic and real-world datasets.