In dictionary learning, a matrix comprised of signals Y is factorized into the product of two matrices: a matrix of prototypical "atoms" D, and a sparse matrix containing coefficients for atoms in D, called X. Dictionary learning finds applications in signal processing, image recognition, and a number of other fields. Many algorithms for solving the dictionary learning problem follow the alternating minimization paradigm; that is, by alternating solving for D and X. In 2014, Agarwal et al. proposed a dictionary initialization procedure that is used before this alternating minimization process. We show that there is a modification to this initialization algorithm and a corresponding data generating process under which full recovery of D is possible without a subsequent alternating minimization procedure. Our findings indicate that the costly step of alternating minimization can be bypassed, and that other data models may enjoy the same features as the one we propose.
Zanotti, Greg and Au-Yeung, Enrico
"Exact Recovery of Prototypical Atoms through Dictionary Initialization,"
DePaul Discoveries: Volume 7, Article 12.
Available at: https://via.library.depaul.edu/depaul-disc/vol7/iss1/12