论文标题
$ p $ - 订购张量产品，具有可逆线性变换
$p$-order Tensor Products with Invertible Linear Transforms
论文作者
论文摘要
本文研究了有关张量的问题。提到了三种典型的张量分解。在这些分解中，在这十年中提出了T-SVD。等级的不同定义来自张量分解。基于有关具有可逆变换的高阶张量T张产品和张量产品的研究，本文介绍了具有可逆变换的高阶张量产品的产品，这是迄今为止最概括的情况。此外，证明了一些属性。由于低排时恢复的优化模型通常使用核标准，因此该论文试图概括核标准，并证明其与多级张量的关系。定理为将来的高阶张量恢复铺平了道路。
This paper studies the issues about tensors. Three typical kinds of tensor decomposition are mentioned. Among these decompositions, the t-SVD is proposed in this decade. Different definitions of rank derive from tensor decompositions. Based on the research about higher order tensor t-product and tensor products with invertible transform, this paper introduces a product performing higher order tensor products with invertible transform, which is the most generalized case so far. Also, a few properties are proven. Because the optimization model of low-rank recovery often uses the nuclear norm, the paper tries to generalize the nuclear norm and proves its relation to multi-rank of tensors. The theorem paves the way for low-rank recovery of higher order tensors in the future.
