title: Nonsmooth nonnegative matrix factorization (nsNMF).
abstract: We propose a novel nonnegative matrix factorization model that aims at finding localized, part-based, representations of nonnegative multivariate data items. Unlike the classical nonnegative matrix factorization (NMF) technique, this new model, denoted "nonsmooth nonnegative matrix factorization" (nsNMF), corresponds to the optimization of an unambiguous cost function designed to explicitly represent sparseness, in the form of nonsmoothness, which is controlled by a single parameter. In general, this method produces a set of basis and encoding vectors that are not only capable of representing the original data, but they also extract highly localized patterns, which generally lend themselves to improved interpretability. The properties of this new method are illustrated with several data sets. Comparisons to previously published methods show that the new nsNMF method has some advantages in keeping faithfulness to the data in the achieving a high degree of sparseness for both the estimated basis and the encoding vectors and in better interpretability of the factors.
authors.affiliation: Computer Architecture and System Engineering Department, Facultad de Ciencias Físicas, Universidad Complutense, Madrid, Spain. pascual@fis.ucm.es
authors.forename: Alberto
authors.initials: A
authors.lastname: Pascual-Montano
authors.forename: J M
authors.initials: JM
authors.lastname: Carazo
authors.forename: Kieko
authors.initials: K
authors.lastname: Kochi
authors.forename: Dietrich
authors.initials: D
authors.lastname: Lehmann
authors.forename: Roberto D
authors.initials: RD
authors.lastname: Pascual-Marqui
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D004569:Electroencephalography / Q000379:methods*; D005145:Face / Q000033:anatomy & histology*; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D012680:Sensitivity and Specificity; D012984:Software