TENSOR-TRAIN DECOMPOSITION
TENSOR-TRAIN DECOMPOSITION
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DOI：
10.1137/090752286
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发表时间：
2011-01-01
影响因子：
3.1
通讯作者：
Oseledets, I. V.
中科院分区：
文献类型：
--
作者：
Oseledets, I. V.
给出了d维张量分解的一种简单的非递归形式。它不固有地遭受维数灾难，它具有与典型分解渐近相同的参数数量，但它是稳定的，并且其计算基于辅助展开矩阵的低秩近似。新的表单提供了一种清晰方便的方式来有效地实现所有基本操作。提出了一种快速舍入方法，以及基本的线性代数运算。给出的例子显示的分解的好处，并证明了效率的最小特征值的19维算子的计算。
A simple nonrecursive form of the tensor decomposition in d dimensions is presented. It does not inherently suffer from the curse of dimensionality, it has asymptotically the same number of parameters as the canonical decomposition, but it is stable and its computation is based on low-rank approximation of auxiliary unfolding matrices. The new form gives a clear and convenient way to implement all basic operations efficiently. A fast rounding procedure is presented, as well as basic linear algebra operations. Examples showing the benefits of the decomposition are given, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.