The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses perturbative corrections to the subproblems rather than recomputing the tensor contractions. This approximation is accurate when the factor matrices are changing little across iterations, which occurs when alternating least squares approaches convergence. We provide a theoretical analysis to bound the approximation error. Our numerical experiments demonstrate that the proposed pairwise perturbation algorithms are easy to control and converge to minima that are as good as alternating least squares. The experimental results show improvements of up to 3.1X with respect to state-of-the-art alternating least squares approaches for various model tensor problems and real datasets.

翻译：CP 和 Tucker 分解的交替最小方程式算法以成本为主,以建立二次优化子问题所需的抗拉收缩为主。 我们引入了一个新型的算法组合, 使用对子问题有扰动性的更正, 而不是对抗拉收缩进行再比较。 当要素矩阵在迭代之间变化不大时, 即当最小方位交替接近趋同时, 则这种近似值是准确的。 我们提供了理论分析, 以约束近似错误。 我们的数字实验表明, 提议的对称扰动算法很容易被控制, 并且与最不易交替的最小方形相趋近。 实验结果显示, 各种模型的多方形问题和真实数据集, 在最先进的交替最小方位方法方面, 最高可改进到 3.1X 。