基于谱共轭梯度法的张量CP分解  

A spectral conjugate gradient algorithm for tensor CP decomposition

作　　者：王玉虎 王洁 WANG Yuhu;WANG Jie(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China;School of Sciences,China Jiliang University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018 [2]中国计量大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第4期90-96,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11901549)。

摘　　要：针对张量CANDECOMP/PARAFAC(CP)分解问题,提出一种高效的求解算法。首先,将张量CP分解问题转化为无约束优化问题;其次,结合谱梯度法和非线性共轭梯度法的思想,设计了一种基于谱共轭梯度法的优化算法。数值实验结果表明,在保持相同精度的情况下,与已有的基于梯度的优化算法相比,所提算法的计算时间和计算量更少。For the tensor CANDECOMP/PARAFAC(CP)decomposition problem,an efficient solution algorithm is proposed.Firstly,the tensor CP decomposition problem is transformed into an unconstrained optimization problem.Secondly,an optimization algorithm based on the spectral conjugate gradient method is designed by combining the ideas of the spectral gradient method and the nonlinear conjugate gradient method.Numerical experimental results show that,while maintaining the same accuracy,the proposed algorithm requires less computation time and computational effort than existing gradient-based optimization algorithms.

关 键 词：张量分解 CANDECOMP/PARAFAC分解 无约束优化 谱共轭梯度法 

分 类 号：O221.2[理学—运筹学与控制论]