Tensor Rank Decomposition Task
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A Tensor Rank Decomposition Task is a tensor decomposition task that ...
- AKA: Canonical Polyadic Decomposition, CP Decomposition.
- Context:
- It can be a generalization to Singular Value Decomposition.
- It can be solved by a Tensor Rank Decomposition System (that implements a tensor rank decomposition algorithm).
- See: Multilinear Algebra, Tensor (Intrinsic Definition), Non-Negative Tensor Factorization.
References
2018
- (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Tensor_rank_decomposition Retrieved:2018-3-18.
- In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics. It was introduced by Hitchcock in 1927 and later rediscovered several times, notably in psychometrics.
For this reason, the tensor rank decomposition is sometimes historically referred to as PARAFAC or CANDECOMP.
The tensor rank decomposition expresses a tensor as a minimum-length linear combination of rank-1 tensors. Such rank-1 tensors are also called simple or pure. A pure tensor is the tensor product of a collection of vectors.
- In multilinear algebra, the tensor rank decomposition or canonical polyadic decomposition (CPD) may be regarded as a generalization of the matrix singular value decomposition (SVD) to tensors, which has found application in statistics, signal processing, psychometrics, linguistics and chemometrics. It was introduced by Hitchcock in 1927 and later rediscovered several times, notably in psychometrics.