Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor decomposition and related problems arising from statistics and machine learning. By exploiting the multilinearity as well as the sparsity structure of the problem, four approximation algorithms are proposed, which are easily implemented, of low computational complexity, and can serve as initial procedures for iterative algorithms. In addition, theoretically guaranteed worst-case approximation lower bounds are proved for all the algorithms. We provide numerical experiments on synthetic and real data to illustrate the effectiveness of the proposed algorithms.

翻译：粗散的抗拉- 最高级-1 近似值( BR1Approx) 是密度密度高的抗拉- BR1Approx 的宽度一般化, 是稀薄的矩阵 BR1Aprox 的更高级延伸, 是稀疏的抗拉分解和相关统计和机器学习问题的最重要问题之一。 通过利用多线性和问题宽度结构,提出了四种容易实施的、低计算复杂性的近似算法,可以作为迭代算法的初始程序。 此外,理论上保证最坏的近似值是所有算法的下限。 我们对合成和真实数据进行数字实验,以说明拟议算法的有效性。