STARK: Structured Dictionary Learning Through Rank-one Tensor Recovery
This work addresses the challenge of structured dictionary learning for multidimensional data, which is incremental as it builds on existing Kronecker-structured approaches.
The authors tackled the problem of learning Kronecker-structured dictionaries for tensor data representation by proposing the STARK algorithm, which enforces this structure through a convex relaxation of rank-1 tensor recovery, with empirical experiments on synthetic and real data showing promising results.
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.