Document Type : Original Paper


1 Department of Computer Science, Faculty of Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran

2 Department of Applied Mathematics, Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of Iran


Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high computational cost.   In this paper, based on the properties of norms and orthogonal transformations we propose a framework to project NMF’s convex sub-problems to smaller problems. This projection reduces the time of finding NMF factors. Also every method on ALS class can be used with our proposed framework.