BG-NMF: a variational Bayesian NMF model for bounded support data
2011 (English)Article in journal (Other academic) Submitted
In this paper, we present a new Bayesian nonnegative matrix factor-ization (NMF) method for bounded support data. The distribution of thebounded support data is modelled with the beta distribution. The parametersof the beta density function are considered as latent variables and factorizedinto two matrices (the basis matrix and the excitation matrix). Further-more, each entry in the factorized matrices is assigned with a gamma prior.Thus, we name this method as beta-gamma NMF (BG-NMF). Usually, theestimation of the posterior distribution does not have a closed-form solu-tion. With the variational inference framework and by taking the relativeconvexity property of the log-inverse-beta function, we derive a closed-formsolution to approximate the posterior distribution of the entries in the basisand the excitation matrices. Also, a sparse BG-NMF can be carried outby adding the sparseness constraint to the gamma prior. Evaluations withsynthetic data and real life data demonstrate that the proposed method isefficient for source separation, missing data prediction, and collaborativefiltering problems.
Place, publisher, year, edition, pages
Electrical Engineering, Electronic Engineering, Information Engineering Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-47407OAI: oai:DiVA.org:kth-47407DiVA: diva2:455011
QS 2011 QS 201203162011-11-082011-11-082012-03-16Bibliographically approved