论文标题
Tucker格式的张量
Hybrid CUR-type decomposition of tensors in the Tucker format
论文作者
论文摘要
该论文引入了一种混合方法，以塔克格式的张量分解cur型分解。混合算法的想法是编写张量$ \ Mathcal {x} $作为核心张量$ \ Mathcal {s} $的产物，该矩阵$ c $通过提取Mode-$ k $ fibers获得的矩阵$ c $ $ \ mathcal {x}} $ \ mathcal {x} $，和matrices $ u_j $ u_j $，u_j $，u_j $，u_j $，u_j $，u_j $，u_j $，u_j $，u_j $， $ j = 1，\ ldots，k-1，k+1，\ ldots，d $，用于最小化近似错误。可以轻松地修改近似值以在多个模式下保留纤维。以这种方式获得的近似误差小于标准张量cur型方法的近似误差。随着张量尺寸的增加，这种差异会增加。随着保留原始光纤降低的模式数量，它也会增加。
The paper introduces a hybrid approach to the CUR-type decomposition of tensors in the Tucker format. The idea of the hybrid algorithm is to write a tensor $\mathcal{X}$ as a product of a core tensor $\mathcal{S}$, a matrix $C$ obtained by extracting mode-$k$ fibers of $\mathcal{X}$, and matrices $U_j$, $j=1,\ldots,k-1,k+1,\ldots,d$, chosen to minimize the approximation error. The approximation can easily be modified to preserve the fibers in more than one mode. The approximation error obtained this way is smaller than the one from the standard tensor CUR-type method. This difference increases as the tensor dimension increases. It also increases as the number of modes in which the original fibers are preserved decreases.
