tensor decomposition

Successive Rank-One Approximations of Nearly Orthogonally Decomposable Symmetric Tensors

  • Donald Goldfarb
  • Daniel Hsu
  • Cun Mu
    • Categories Data-Mining, Global Optimization Applications, Statistics Tags , , ,

    Many idealized problems in signal processing, machine learning and statistics can be reduced to the problem of finding the symmetric canonical decomposition of an underlying symmetric and orthogonally decomposable (SOD) tensor. Drawing inspiration from the matrix case, the successive rank-one approximations (SROA) scheme has been proposed and shown to yield this tensor decomposition exactly, and … Read more

    New Ranks for Even-Order Tensors and Their Applications in Low-Rank Tensor Optimization

  • Bo Jiang
  • Shiqian Ma
  • Shuzhong Zhang
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper, we propose three new tensor decompositions for even-order tensors corresponding respectively to the rank-one decompositions of some unfolded matrices. Consequently such new decompositions lead to three new notions of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly symmetric M-rank in this paper. We discuss the bounds … Read more