论文标题
张量数据的代数方法
Algebraic Methods for Tensor Data
论文作者
论文摘要
我们开发了使用张量数据计算的代数方法。我们提供3个应用程序：在每种模式的正交对称性，张量光谱规范的近似以及低等级张量结构的扩增的近似值下提取不变的特征。我们介绍了彩色的Brauer图，这些图用于代数计算并分析其计算复杂性。我们提出了数值实验，其结果表明，可以使用张量放大来改善张量低级别的交替平方算法的性能。
We develop algebraic methods for computations with tensor data. We give 3 applications: extracting features that are invariant under the orthogonal symmetries in each of the modes, approximation of the tensor spectral norm, and amplification of low rank tensor structure. We introduce colored Brauer diagrams, which are used for algebraic computations and in analyzing their computational complexity. We present numerical experiments whose results show that the performance of the alternating least square algorithm for the low rank approximation of tensors can be improved using tensor amplification.
