Matrix factorization with neural networks
Francesco Camilli, Marc Mézard
Abstract
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.
Topics & Concepts
DecimationComputer scienceFactorizationArtificial neural networkMatrix decompositionContext (archaeology)Binary numberContent-addressable memoryMatrix (chemical analysis)Artificial intelligenceRank (graph theory)AlgorithmPattern recognition (psychology)Theoretical computer scienceArithmeticMathematicsPhysicsFilter (signal processing)Computer visionQuantum mechanicsBiologyCombinatoricsPaleontologyEigenvalues and eigenvectorsComposite materialMaterials scienceBlind Source Separation TechniquesSparse and Compressive Sensing TechniquesNeural Networks and Applications