# Tucker decomposition

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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.