Low multilinear rank tensor approximation via semidefinite programming

We present a novel method for tensor dimensionality reduction. The tensor rank reduction has many applications in signal and image processing including various blind techniques. In this paper, we generalize the trace class norm to higher-order tensors. Recently, the matrix trace class has received much attention in the compressed sensing applications. It is known to provide bounds for the minimum rank of a matrix. In this paper, a new tensor trace class norm is used to formulate an optimization problem for finding the best low multilinear rank tensor approximation. Our new formulation leads to a set of semidefinite programming subproblems where the nth subproblem approximates a low multilinear rank factor in the nth modal direction. Our method is illustrated on a real-life data set.