A randomized algorithm for a tensor-based generalization of the singular value decomposition (Q861021)

The authors present and analyze an algorithm for the problem: Given as input a \(d\) mode tensor \(A\), compute an approximation to \(A\). The approximation is computed by performing the following for each of the \(d\) modes: first implicitly from a matrix by ``unfolding'' the tensor along that mode; then, choose columns from the matrices thus generated; and finally, project the tensor along that mode onto the span of those columns. They present two specific algorithms for handling the following problem: given an input matrix and a target rank, select columns that can a space close to the best rank subspace of the matrix.