Efficient MATLAB computations with sparse and factored tensors [electronic resource].
- Washington, D.C. : United States. Dept. of Energy, 2006.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
- Physical Description:
- 50 pages : digital, PDF file
- Additional Creators:
- Sandia National Laboratories, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- 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.
- Report Numbers:
- E 1.99:sand2006-7592
- Other Subject(s):
- Published through SciTech Connect.
Kolda, Tamara Gibson; Bader, Brett William.
- Funding Information:
View MARC record | catkey: 14344797