Abstract:

Tensors or multidimensional arrays are higher order generalizations of matrices. They are natural structures for expressing data that have inherent higher order structures. Tensor decompositions play an important role in learning those hidden structures. There exist both optimization-based methods and algebraic methods for the tensor decomposition problem, optimization-based methods regard the tensor decomposition problem as a nonconvex optimization problem and apply optimization methods to solve it. Hence, they usually suffer from local minimum and may not be able to find a satisfactory tensor decomposition. Algebraic methods usually require the tensor rank to be not too large and the running time is not so satisfying for large tensors.

In this talk, we present a novel algorithm to find the tensor decompositions utilizing generating polynomials. Under some conditions on the tensor's rank, we prove that the exact tensor decomposition can be found by our algorithm. Numerical examples successfully demonstrate the robustness and efficiency of our algorithm.