The low-rank approximation of fourth-order partial-symmetric and conjugate partial-symmetric tensors

In this talk, we present an orthogonal matrix outer product decomposition for the fourth-order conjugate partial-symmetric （CPS) tensor and show that the successive rank-one approximation(SROA) algorithm can recover this decomposition exactly. Based on this matrix decomposition, the CP rank of CPS tensor is bounded by the matrix rank, which can be applied to low-rank tensor completion. Additionally, we give the rank-one equivalence of a given CPS tensor and its unfolding matrix, and a kind of convex optimization relaxation of rank-one approximation of the CPS tensor. Finally we show the efficiency of models presented with some numerical experiments.