Abstract: Semi-Nonnegative Matrix Factorization (Semi-NMF), as a variant of NMF, inherits the merit of parts-based representation of NMF and possesses the ability to process mixed sign data, which has attracted extensive attention. However, standard Semi-NMF still suffers from the following limitations. First of all, Semi-NMF fits data in a Euclidean space, which ignores the geometrical structu...

Given a matrix M (not necessarily nonnegative) and a factorization rank r, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix U with r columns and a nonnegative matrix V with r rows such that UV is the best possible approximation of M according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contributi...

In this paper, we propose a maximum-margin framework for classification using Nonnegative Matrix Factorization. In contrast to previous approaches where the classification and matrix factorization stages are separated, we incorporate the maximum margin constraints within the NMF formulation, i.e we solve for a base matrix that maximizes the margin of the classifier in the low dimensional featur...

SUMMARY Non-negative matrix factorization (NMF) is an increasingly used algorithm for the analysis of complex high-dimensional data. BRB-ArrayTools is a widely used software system for the analysis of gene expression data with almost 9000 registered users in over 65 countries. We have developed a NMF analysis plug-in in BRB-ArrayTools for unsupervised sample clustering of microarray gene expres...

Non-negative Matrix Factorisation (NMF) has become a standard method for source identification when data, sources and mixing coefficients are constrained to be positive-valued. The method has recently been extended to allow for negative-valued data and sources in the form of Semiand Convex-NMF. In this paper, we re-elaborate Semi-NMF within a full Bayesian framework. This provides solid foundat...

Semi-NMF is a matrix factorization technique that learns a low-dimensional representation of a dataset that lends itself to a clustering interpretation. It is possible that the mapping between this new representation and our original features contains rather complex hierarchical information with implicit lower-level hidden attributes, that classical one level clustering methodologies can not in...

This paper proposes an acoustic event detection (AED) method using semi-supervised non-negative matrix factorization (NMF) with a mixture of local dictionaries (MLD). The proposed method based on semi-supervised NMF newly introduces a noise dictionary and a noise activation matrix both dedicated to unknown acoustic atoms which are not included in the MLD. Because unknown acoustic atoms are bett...

Multiple graph and semi-supervision techniques have been successfully introduced into the nonnegative matrix factorization (NMF) model for taking full advantage of manifold structure priori information data to capture excellent low-dimensional representation. However, existing methods do not consider sparse constraint, which can enhance local learning ability improve performance in practical ap...

The dual formulation of the support vector machine (SVM) objective function is an instance of a nonnegative quadratic programming problem. We reformulate the SVM objective function as a matrix factorization problem which establishes a connection with the regularized nonnegative matrix factorization (NMF) problem. This allows us to derive a novel multiplicative algorithm for solving hard and sof...