Sample Complexity Bounds for Low-Separation-Rank Dictionary Learning

Mohsen Ghassemi, Zahra Shakeri, Waheed U. Bajwa, Anand D. Sarwate

Abstract: This work addresses the problem of structured dictionary learning for computing sparse representations of tensor-structured data. It introduces a low-separation-rank dictionary learning (LSR-DL) model that better captures the structure of tensor data by generalizing the separable dictionary learning model. A dictionary with p columns that is generated from the LSR-DL model is shown to be locally identifiable from noisy observations with recovery error at most ρ given that the number of training samples scales with (# of degrees of freedom in the dictionary)×p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ρ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> .