Tensor decomposition
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In multilinear algebra, a tensor decomposition is any scheme for expressing a tensor as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions.[1]
The main tensor decompositions are:
- tensor rank decomposition;
- higher-order singular value decomposition;
- Tucker decomposition;
- matrix product states, and operators or tensor trains;
- hierarchical Tucker decomposition; and
- block term decomposition.
References
- ^ Bernardi, A.; Brachat, J.; Comon, P.; Mourrain, B. (2013-05-01). "General tensor decomposition, moment matrices and applications". Journal of Symbolic Computation. 52: 51–71. arXiv:1105.1229. doi:10.1016/j.jsc.2012.05.012. ISSN 0747-7171. S2CID 14181289.
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