In this paper, we introduce and provide a short overview of nonnegative matrix factorization (NMF). Several aspects of NMF are discussed, namely, the application in hyperspectral imaging, geometry and uniqueness of NMF solutions, complexity, algorithms, and its link with extended formulations of polyhedra. In order to put NMF into perspective, the more general problem class of constrained low-r...

We apply the vectorized Non-negative Matrix Factorization (NMF) method to post-processing of direct imaging data for exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a non-orthogonal and non-negative basis of components using given reference images, then models a target with the components. The constructed model is then rescaled with a factor t...

Blind source separation is a common processing tool to analyse the constitution of pixels of hyperspectral images. Such methods usually suppose that pure pixel spectra (endmembers) are the same in all the image for each class of materials. In the framework of remote sensing, such an assumption is no more valid in the presence of intra-class variabilities due to illumination conditions, weatheri...

Nonnegative Matrix Factorization (NMF) models are widely used to recover linearly mixed nonnegative data. When the data is made of samplings continuous signals, factors in NMF can be constrained samples rational functions, which allow fairly general models; this referred as using functions (R-NMF). We first show that, under mild assumptions, R-NMF has an essentially unique factorization unlike ...

Recently, lots of algorithms using machine learning approaches have been proposed in the speech enhancement area. One of the most well-known approaches is the non-negative matrix factorization (NMF) -based one which analyzes noisy speech with speech and noise bases. However, NMF-based algorithms have difficulties in estimating speech and noise encoding vectors when their subspaces overlap. In t...

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

Nonnegative matrix factorization (NMF) is a standard linear dimensionality reduction technique for nonnegative data sets. In order to measure the discrepancy between input and low-rank approximation, Kullback-Leibler (KL) divergence one of most widely used objective function NMF. It corresponds maximum likehood estimator when underlying statistics observed sample follows Poisson distribution, K...

Exposure of certain cell lines to the differentiation-inducing agent N-methylformamide (NMF) enhances their radiosensitivity. As part of an attempt to elucidate the mechanism of NMF-induced radiosensitization, we examined the effects of NMF on chromatin structure, as reflected by changes in DNA-protein cross-links (DPCs) and the chromatin protein/DNA ratio, in two cell lines, clone A and HCA-1....

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is to decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering), but in some cases NMF produces the results inappropria...