Clustering by Orthogonal NMF Model and Non-Convex Penalty Optimization

The non-negative matrix factorization (NMF) model with an additional orthogonality constraint on one of the factor matrices, called orthogonal NMF (ONMF), has been found a promising clustering and can outperform classical K-means. However, solving ONMF is challenging optimization problem because coupling non-negativity constraints introduces mixed combinatorial aspect into due to determination correct status variables (positive or zero). Most existing methods directly deal in its original form via various techniques, but are not scalable for large-scale problems. In this paper, we propose new based formulation that equivalently transforms set norm-based non-convex equality constraints. We then apply penalty (NCP) approach add them objective as terms, leading efficiently solvable. One smooth non-smooth respectively studied. build theoretical conditions penalized problems provide feasible stationary solutions problem, well proposing efficient algorithms two NCP methods. Experimental results both synthetic real datasets presented show proposed computationally time efficient, either match K-means terms performance.