Tensor completion and low-n-rank tensor recovery via convex optimization
Tensor completion and low-n-rank tensor recovery via convex optimization
复制标题
DOI：
10.1088/0266-5611/27/2/025010
复制
发表时间：
2011-02-01
期刊：
影响因子：
2.1
通讯作者：
Yamada, Isao
中科院分区：
文献类型：
--
作者：
Gandy, Silvia;Recht, Benjamin;Yamada, Isao
在本文中，我们考虑张量水平上的稀疏性，由张量的n秩给出。在一个重要的稀疏向量逼近问题（压缩感知）和低秩矩阵恢复问题中，采用凸松弛技术被证明是一种有价值的求解策略。在这里，我们将使这些技术适应张量设置。我们使用张量的n秩作为稀疏性度量，并考虑低n秩张量恢复问题，即找到满足某些线性约束的最低n秩张量的问题。我们引入了一个易于处理的凸松弛的n秩，并提出了有效的算法来解决低n秩张量恢复问题的数值。该算法是基于道格拉斯-Rachford分裂技术及其对偶变体，交替方向的乘法器的方法。
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas-Rachford splitting technique and its dual variant, the alternating direction method of multipliers.