A convergent algorithm for bi-orthogonal nonnegative matrix tri-factorization

A convergent algorithm for nonnegative matrix factorization (NMF) with orthogonality constraints imposed on both basis and coefficient matrices is proposed in this paper. This concept was first introduced by Ding et al. (Proceedings of 12th ACM SIGKDD international conference knowledge discovery data mining, pp 126–135, 2006) intent to further improve clustering capability NMF. However, as the original developed based multiplicative update rules, convergence cannot be guaranteed. In paper, we utilize technique presented our previous work Mirzal (J Comput Appl Math 260:149–166, 2014a; Proceedings advanced information engineering (DaEng-2013). Springer, 177–184, 2014b; IEEE/ACM Trans Biol Bioinform 11(6):1208–1217, 2014c) develop a problem prove that it converges stationary point inside solution space. As very hard numerically show an NMF due slow numerical precision issues, experiments are instead performed evaluate whether has nonincreasing property (a necessary condition convergence) where shown property. Further, also inspected using Reuters-21578 corpus.