A singular value decomposition of a \(k\)-way array for a principal component analysis of multiway data, \(\text{PTA-}k\)
A generalization of the singular value decomposition to multiindex arrays is studied. It finds a decomposition into a sum of rank one tensors, by first computing the best approximation of the given array by an outer product of vectors, and then recursively decomposing the lower-dimensional arrays obtained by contracting along the vectors of the best approximation. The first step is performed by an alternating Gauss Seidel type iteration. The primary use of this decomposition is to find low rank approximations in the spirit of the Eckart-Young theorem and perform a principal component analysis.
scientific article; zbMATH DE number 1100775