# Tucker decomposition

*34,190*pages on

this wiki

Assessment |
Biopsychology |
Comparative |
Cognitive |
Developmental |
Language |
Individual differences |
Personality |
Philosophy |
Social |

Methods |
Statistics |
Clinical |
Educational |
Industrial |
Professional items |
World psychology |

**Statistics:**
Scientific method ·
Research methods ·
Experimental design ·
Undergraduate statistics courses ·
Statistical tests ·
Game theory ·
Decision theory

In statistics, **Tucker decomposition** decomposes a tensor into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker^{[1]}
although it goes back to Hitchcock in 1927.^{[2]}
Initially described as a three-mode extension of factor analysis and principal component analysis it may actually be generalized to higher mode analysis.

It may be regarded as a more flexible PARAFAC (parallel factor analysis ) model. In PARAFAC the core tensor is restricted to be "diagonal".

## See alsoEdit

## References Edit

- ↑ Ledyard R. Tucker (September 1966). Some mathematical notes on three-mode factor analysis.
*Psychometrika***31**(3): 279–311. - ↑ F. L. Hitchcock (1927). The expression of a tensor or a polyadic as a sum of products.
*Journal of Mathematics and Physics***6**: 164–189.