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Multiway Data

Multiway data are observations arranged in an array indexed by several distinct kinds of variables, called modes (Kolda and Bader 2009). Higher-order data have three or more modes and are represented by a tensor. For example, measurements indexed by subject, measurement type, and time form a three-way array x_(ijk).

The CANDECOMP/PARAFAC decomposition and Tucker decomposition analyze such data while retaining their multiple-index structure. Each factor describes variation along one mode.

See also

Array, CANDECOMP/PARAFAC Decomposition, Tensor, Tensor Decomposition, Tucker Decomposition

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References

Kolda, T. G. and Bader, B. W. "Tensor Decompositions and Applications." SIAM Rev. 51, 455-500, 2009. https://doi.org/10.1137/07070111X.

Cite this as:

Weisstein, Eric W. "Multiway Data." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MultiwayData.html

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