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Everything about Tensor decomposition
Process in algebra
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Tensor decompositionA 5-minute orientation
- Skim a recent paper: Channel Estimation for Movable-Antenna MIMO Systems via Tensor DecompositionInfluential work since 2022
- Pick up a classic book: Тензорная тригонометрияThe most-reprinted book on the subject
- Read the landmark paper: Tensor Decompositions and ApplicationsCited 8,735 times
- Go sideways: Multilinear principal component analysisA closely related topic
- Go sideways: Multilinear subspace learningA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Tensor Decompositions and Applications
Tensor-Train Decomposition
Smooth PARAFAC Decomposition for Tensor Completion
Robust tensor completion using transformed tensor singular value decomposition
Multilayer Sparsity-Based Tensor Decomposition for Low-Rank Tensor Completion
A Practical Randomized CP Tensor Decomposition
Symmetric tensor decomposition
Generalized Canonical Polyadic Tensor Decomposition
🆕 Influential since 2022
Channel Estimation for Movable-Antenna MIMO Systems via Tensor Decomposition
Tensor Completion via Fully-Connected Tensor Network Decomposition with Regularized Factors
Guaranteed Functional Tensor Singular Value Decomposition
Fully-connected tensor network decomposition for robust tensor completion problem
Efficient tensor decomposition-based filter pruning
📚 Books worth reading
Тензорная тригонометрияNinul Anatoly Sergeevich · 2004- 📕Krommingstensoren decompositietheorie en toepassingenDirk Janssens · 1981
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Tensor (machine learning) In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation…
- Higher-order singular value decomposition In multilinear algebra, the higher-order singular value decomposition (HOSVD) is a misnomer. There does not exist a single tensor decomposition that retains…
- HOSVD-based canonical form of TP functions and qLPV models Baranyi and Yam proposed the concept of M-mode SVD/HOSVD-based canonical form of TP functions and quasi-LPV system models. Szeidl et al. proved that the…
- Tensor rank decomposition In multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is…
- Non-negative matrix factorization Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra…
- Mode-k flattening In multilinear algebra, mode-m flattening, also known as matrixizing, matricizing is an operation that reshapes a multi-way array A {\displaystyle {\mathcal…