University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 26 3 2015 09 01 A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization 273 279 55315 EN M. Rezghi Department of Computer Science, Faculty of Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran M. Yousefi Department of Applied Mathematics, Faculty of Sciences, Sahand University of Technology, Tabriz, Islamic Republic of Iran Journal Article 2014 07 23 <span>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.</span> https://jsciences.ut.ac.ir/article_55315_2115c7b81a5e4728a3ff207a0a9574b6.pdf