STARK: Structured Dictionary Learning Through Rank-one Tensor Recovery

TL;DR

STARK introduces a convex relaxation-based algorithm for learning Kronecker-structured dictionaries that effectively represent multidimensional tensor data, demonstrated through promising synthetic and real data experiments.

Contribution

The paper presents a novel algorithm, STARK, for learning Kronecker structured dictionaries by reformulating the problem as a rank-1 tensor recovery, applicable to tensors of any order.

Findings

Effective representation of tensor data using Kronecker-structured dictionaries.

Convex relaxation approach successfully approximates rank-1 tensor recovery.

Promising results demonstrated on synthetic and real datasets.

Abstract

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.