Tensor Factorization System
A Tensor Factorization System is a Matrix Factorization System that implements a Tensor Factorization Algorithm to solve a Tensor Factorization Task.
- AKA: Tensor Decomposition System.
- Example(s):
- Counter-Example(s):
- See: Tensor Field, High-Order SVD, Tensors, Multilinear Algebra, Tensor, Matrix Decomposition, Tensor Rank Decomposition, Higher-Order Singular Value Decomposition, Tucker Decomposition, Matrix Product State, Hierarchical Tucker Decomposition, Block Term Decomposition.
References
2020
- (Wikipedia, 2020) ⇒ https://en.wikipedia.org/wiki/Tensor_decomposition Retrieved:2020-3-15.
- 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.
The main tensor decompositions are:
- 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.
2017
- (Panisson, 2017) ⇒ André Panisson (2017). "Tensor Decomposition With Python" (Slide Show). Published: Apr 9, 2017.
2009
- (Rendle et al., 2009) ⇒ Steffen Rendle, Leandro Balby Marinho, Alexandros Nanopoulos, and Lars Schmidt-Thieme. (2009). “Learning Optimal Ranking with Tensor Factorization for Tag Recommendation.” In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2009). doi:10.1145/1557019.1557100
2009
- (Kolda & Bader, 2009) ⇒ Tamara G. Kolda, and Brett W. Bader. (2009). “Tensor Decompositions and Applications.” In: SIAM review, 51(3). doi:10.1137/07070111X
- ABSTRACT: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with [math]\displaystyle{ N \geq 3 }[/math]) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.