摘要
为了降低乘性迭代算法在求解非负Tucker分解时的计算复杂度,该文在乘性迭代的基础上,提出了一种随机方差缩减乘性更新方法。该方法先将待分解的非负张量n-模式矩阵化,再运用随机方差缩减乘性更新算法对矩阵进行非负分解,得到模式矩阵,最后通过梯度下降思想来更新核心张量。对高维数据进行非负Tucker分解时,加快收敛速度且降低计算复杂度,提高了张量分解性能。在人工合成数据集及真实数据集上进行数值实验,结果验证了所提算法的可行性和有效性。
To reduce the computational complexity of the multiplicative iterative algorithm in solving the non-negative Tucker decomposition problem,this paper proposes a stochastic variance reduction multiplicative updating method based on the multiplicative iterative algorithm.The algorithm first matricizes the non-negative tensor alone the nth mode.Then the stochastic variance reduction multiplicative updating algorithm is employed to perform non-negative matrix factorization to obtain the mode matrix.Finally,the core tensor is updated by the idea of gradient descent.For the non-negative Tucker decomposition of high-dimensional data,the method can accelerate the convergence speed and reduce the computational complexity.Meanwhile,the tensor decomposition performance is improved.Numerical experiments are carried out on synthetic data sets and real data sets.The experiments results show that the proposed algorithm is feasible and effective.
作者
白姗姗
史加荣
Bai Shanshan;Shi Jiarong(School of Science,Xi’an University of Architecture and Technology,Xi’an 710055,China)
出处
《南京理工大学学报》
EI
CAS
CSCD
北大核心
2021年第2期197-204,共8页
Journal of Nanjing University of Science and Technology
基金
国家自然科学基金(61403298)
陕西省自然科学基金(2021JM-378)。
关键词
非负Tucker分解
随机方差缩减梯度算法
乘性更新
梯度下降
non-negative Tucker decomposition
stochastic variance reduction gradient algorithm
multiplicative update
gradient descent
作者简介
白姗姗(1995-),女,硕士生,主要研究方向:机器学习,E-mail:17802971126@163.com;通讯作者:史加荣(1979-),男,博士,教授,主要研究方向:机器学习,E-mail:shijiarong@xauat.edu.cn。
