Efficient MATLAB computations with sparse and factored tensors
Efficient MATLAB computations with sparse and factored tensors
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DOI：
10.1137/060676489
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发表时间：
2007-01-01
影响因子：
3.1
通讯作者：
Kolda, Tamara G.
中科院分区：
文献类型：
--
作者：
Bader, Brett W.;Kolda, Tamara G.
在本文中，术语张量简单地指多维或N路数组，我们考虑特殊结构的张量如何允许有效的存储和计算首先，我们研究稀疏张量，它具有绝大多数元素为零的属性。我们建议使用坐标格式存储稀疏张量，并描述了该方案的计算效率为各种数学运算，包括那些典型的张量分解算法。其次，我们研究因子张量，它具有的属性，他们可以从更基本的组件组装。我们考虑两种特定类型：塔克张量可以表示为核心张量（其本身可以是稠密的，稀疏的或因子化的）和沿每个模式的矩阵沿着的乘积，Kruskal张量可以表示为秩1张量的和。我们感兴趣的情况下，存储的组件是小于存储的全张量，我们证明了许多基本操作可以计算仅使用组件。本文中描述的所有效率都在MATLAB的张量函数中实现。
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation first, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: A Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.