The Computation of Low Multilinear Rank Approximations of Tensors via Power Scheme and Random Projection
Maolin Che, Yimin Wei, Hong Yan
Abstract
This paper is devoted to the computation of low multilinear rank approximations of tensors. Combining the stretegy of power scheme, random projection, and singular value decomposition, we derive a three-stage randomized algorithm for the low multilinear rank approximation. Based on the singular values of sub-Gaussian matrices, we derive the error bound of the proposed algorithm with high probability. We illustrate the proposed algorithms via several numerical examples.
Topics & Concepts
Multilinear mapMathematicsSingular value decompositionRank (graph theory)ComputationSingular valueRandom projectionMultilinear algebraProjection (relational algebra)Applied mathematicsGaussianLow-rank approximationAlgorithmTensor (intrinsic definition)Algebra over a fieldPure mathematicsCombinatoricsEigenvalues and eigenvectorsFiltered algebraPhysicsQuantum mechanicsDivision algebraTensor decomposition and applicationsSparse and Compressive Sensing TechniquesMatrix Theory and Algorithms