论文标题
$ \ ell_1 $ regularized稀疏等级的实用近似算法 - $ 1 $ $ 1 $近似高阶张量
Practical Approximation Algorithms for $\ell_1$-Regularized Sparse Rank-$1$ Approximation to Higher-Order Tensors
论文作者
论文摘要
为$ \ ell_1 $调查的稀疏等级-1近似对高阶张量提出了两种近似算法。该算法基于多线性放松和稀疏性，这些松弛和稀疏易于实现且可扩展。特别是，第二个与输入张量的大小线性缩放。基于对$ \ ell_1 $调查的稀疏性的仔细估计，得出了理论近似的下限。我们的理论结果还提出了选择正则化参数的明确方法。提供数值示例以验证所提出的算法。
Two approximation algorithms are proposed for $\ell_1$-regularized sparse rank-1 approximation to higher-order tensors. The algorithms are based on multilinear relaxation and sparsification, which are easily implemented and well scalable. In particular, the second one scales linearly with the size of the input tensor. Based on a careful estimation of the $\ell_1$-regularized sparsification, theoretical approximation lower bounds are derived. Our theoretical results also suggest an explicit way of choosing the regularization parameters. Numerical examples are provided to verify the proposed algorithms.
