Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems, and machine learning. We introduce a decimation scheme that maps it to neural network models of associative memory and provide a detailed theoretical analysis of its performance, showing that decimation is able to factorize extensive-rank matrices and to denoise them efficiently. In the case of binary prior on the signal components, we introduce a decimation algorithm based on a ground-state search of the neural network, which shows performances that match the theoretical prediction.

• Received 21 November 2022
• Revised 3 March 2023
• Accepted 23 May 2023

DOI:https://doi.org/10.1103/PhysRevE.107.064308