Despite its relative novelty, non-negative matrix factorization (NMF) method knew a huge interest from the scientific community, due to its simplicity and intuitive decomposition. Plenty of applications benefited from it, including image processing (face, medical, etc.), audio data processing or text mining and decomposition. This paper briefly describes the underlaying mathematical NMF theory ...

Endmember extraction and spectral unmixing is a very challenging task in multispectral/hyperspectral image processing due to the incompleteness of information. In this paper, a new method for endmember extraction and spectral unmixing of hyperspectral images is proposed, which is called as minimum distance constrained nonnegative matrix factorization (MDC-NMF). After being compared with a newly...

Nonnegative matrix factorization (NMF) can be formulated as a minimization problem with bound constraints. Although bound-constrained optimization has been studied extensively in both theory and practice, so far no study has formally applied its techniques to NMF. In this letter, we propose two projected gradient methods for NMF, both of which exhibit strong optimization properties. We discuss ...

Polar organic solvents, such as N-methylformamide (NMF), N,N-dimethylformamide, and dimethyl sulfoxide, have been demonstrated to induce differentiation in a number of neoplastic cell lines, including human colon cancer cells. Although the mechanism of action of these agents is yet unknown, one possibility is that polar solvents induce a change in lateral mobility of membrane lipids, important ...

Introduction One of the goals in human brain mapping is to relate brain areas to psychological functions. Meta-analyses can confirm presumed links and further suggest new directions for hypothesis-testing research [1]. The mounting functional imaging literature calls for new innovative computer assisted meta-analysis schemes. Here we describe a semi-automated data mining method combining text a...

Nonnegative Matrix Factorization (NMF) is one of the famous unsupervised learning models. In this paper, we give a short survey on NMF-related models, including K-means, Probabilistic Latent Semantic Indexing etc. and present a new Posterior Probabilistic Clustering model, and compare their numerical experimental results on five real microarray data. The results show that i) NMF using with K-L ...

There are two problems need to be dealt with for Non-negative Matrix Factorization (NMF): choose a suitable rank of the factorization and provide a good initialization method for NMF algorithms. This paper aims to solve these two problems using Singular Value Decomposition (SVD). At first we extract the number of main components as the rank, actually this method is inspired from [1, 2]. Second,...

Non-negative matrix factorization (NMF) is a relatively new approach to analyze gene expression data that models data by additive combinations of non-negative basis vectors (metagenes). The non-negativity constraint makes sense biologically as genes may either be expressed or not, but never show negative expression. We applied NMF to five different microarray data sets. We estimated the appropr...

Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where prova...