Nonnegative tensor factorizations using an alternating direction method  

作　　者：Xingju CAI Yannan CHEN Deren HAN 

机构地区：[1]School of Mathematical Sciences, Key Laboratory for NSLSCS of Jiangsu Province,Nanjing Normal University, Nanjing 210023, China [2]College of Science, Nanjing Forestry University, Nanjing 210037, China

出　　处：《Frontiers of Mathematics in China》2013年第1期3-18,共16页中国高等学校学术文摘·数学（英文）

摘　　要：The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method.The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method.

关 键 词：Nonnegative matrix factorization nonnegative tensor factorization nonnegative least squares alternating direction method 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] X523[自动化与计算机技术—计算机科学与技术]