Tucker decomposition

Tucker decomposition

In mathematics, Tucker decomposition is decomposing a tensor into a set of matrices and one small core tensor.It is named after Ledyard R. Tucker [Cite journal
author = Ledyard R. Tucker
title = Some mathematical notes on three-mode factor analysis
journal = Psychometrika
volume = 31
issue = 3
month = September
year = 1966
doi = 10.1007/BF02289464
pages = 279–311
] though going back to Hitchcock in 1927. [Cite journal
author = F. L. Hitchcock
title = The expression of a tensor or a polyadic as a sum of products
journal = Journal of Mathematical Physics
volume = 6
pages = 164–189
year = 1927
] 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 as a more flexible PARAFAC model.In PARAFAC the core tensor is restricted to be "diagonal".

References


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