Negative Binomial Matrix Factorization
Olivier Gouvert, Thomas Oberlin, Cédric Févotte
Abstract
We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom for controlling the dispersion, making NBMF more robust to outliers. We describe a majorization-minimization (MM) algorithm for a maximum likelihood estimation of the parameters. We provide results on a recommendation task and demonstrate the ability of NBMF to efficiently exploit raw data.
Topics & Concepts
FactorizationMatrix decompositionMultiplicative functionComputer scienceAlgorithmTerm (time)OutlierMajorizationNon-negative matrix factorizationMatrix (chemical analysis)Sparse matrixPoisson distributionMathematicsStatisticsArtificial intelligenceCombinatoricsComposite materialPhysicsMathematical analysisMaterials scienceEigenvalues and eigenvectorsGaussianQuantum mechanicsBayesian Methods and Mixture ModelsAdvanced Adaptive Filtering TechniquesTensor decomposition and applications