Nonnegative Matrix Factorization based on the Geometry of Positive Numbers

We consider the problem of nonnegative matrix factorization where the typical objective function is altered based on geometrical arguments. A noneuclidean geometry on positive real numbers is used to describe the nonnegative entries of a nonnegative matrix, influencing the factorization model. We design an optimization procedure from a differential geometric point of view for the newly proposed model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)