Low-rank tensor approximation error bounds are proposed for the case of noisy input data that depend on low-rank representation type, rank and the dimensionality of the tensor. The bounds show that high-dimensional low-rank structured approximations provide superior noise-filtering properties compared to matrices with the same rank and total element count.

翻译：针对含有噪声的输入数据，本文提出了基于低秩表示类型、秩以及张量维度的低秩张量近似误差界限。理论界限表明，与具有相同秩和总元素数的矩阵相比，高维低秩结构化近似具有更优的噪声滤波特性。