  In recent years, a class of dictionaries have been proposed for
multidimensional (tensor) data representation that exploit the structure of
tensor data by imposing a Kronecker structure on the dictionary underlying the
data. In this work, a novel algorithm called "STARK" is provided to learn
Kronecker structured dictionaries that can represent tensors of any order. By
establishing that the Kronecker product of any number of matrices can be
rearranged to form a rank-1 tensor, we show that Kronecker structure can be
enforced on the dictionary by solving a rank-1 tensor recovery problem. Because
rank-1 tensor recovery is a challenging nonconvex problem, we resort to solving
a convex relaxation of this problem. Empirical experiments on synthetic and
real data show promising results for our proposed algorithm.

Machine Learning;Machine Learning