In mathematics, Tucker decomposition decomposes a tensor

Tensor

Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of...

 into a set of matrices and one small core tensor. It is named after Ledyard R. Tucker
although it goes back to Hitchcock in 1927.
Initially described as a three-mode extension of factor analysis

Factor analysis

Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved, uncorrelated variables called factors. In other words, it is possible, for example, that variations in three or four observed variables...

 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".