Tensor decomposition
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.
Tensors are generalizations of matrices to higher dimensions and can consequently be treated as multidimensional fields.
The main tensor decompositions are:
- Tensor rank decomposition;
- Higher-order singular value decomposition;
- Tucker decomposition;
- matrix product states, and operators or tensor trains;
- Online Tensor Decompositions
- hierarchical Tucker decomposition;
- block term decomposition
Notation
This section introduces basic notations and operations that are widely used in the field.| Symbols | Definition |
| scalar, vector, row, matrix, tensor | |
| vectorizing either a matrix or a tensor | |
| matrixized tensor | |
| mode-m product |