A non-convex optimization framework for large-scale low-rank matrix factorization

Low-rank matrix factorization problems such as non negative (NMF) can be categorized a clustering or dimension reduction technique. The latter denotes techniques designed to find representations of some high dimensional dataset in lower manifold without significant loss information. If representation exists, the features ought contain most relevant dataset. Many linear dimensionality formulated factorization. In this paper, we combine conjugate gradient (CG) method with Barzilai and Borwein (BB) method, propose BB scaling CG for NMF problems. new does not require compute store matrices associated Hessian objective functions. Moreover, adopting suitable step size along proper nonmonotone strategy which comes by convex parameter ηk, results algorithm that significantly improve CPU time, efficiency, number function evaluation. Convergence result is established numerical comparisons methods on both synthetic real-world datasets show proposed efficient comparison existing demonstrate superiority our algorithms.