We present libNMF – a computationally efficient high performance library for computing nonnegative matrix factorizations (NMF) written in C. Various algorithms and algorithmic variants for computing NMF are supported. libNMF is based on external routines fromBlas (Basic Linear Algebra Subprograms), Lapack (Linear Algebra package) and Arpack, which provide efficient building blocks for performin...

The need to process and conceptualize large sparse matrices effectively and efficiently (typically via low-rank approximations) is essential for many data mining applications, including document and image analysis, recommendation systems, and gene expression analysis. The nonnegative matrix factorization (NMF) has many advantages to alternative techniques for processing such matrices, but its u...

An alternative to singular value decomposition (SVD) in the information retrieval is the low-rank approximation of an original non-negative matrix A by its non-negative factors U and V . The columns of U are the feature vectors with no non-negative components, and the columns of V store the non-negative weights that serve for the combination of feature vectors. First experiments show that restr...

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image processing, computational biology, etc. In this paper, we explain how algorithms for NMF can be embedded into the framework of multilevel methods in order t...

Abstract—Nonnegative matrix factorization (NMF) is an emerging technique with a wide spectrum of potential applications in data analysis. Mathematically, NMF can be formulated as a minimization problem with nonnegative constraints. This problem is currently attracting much attention from researchers for theoretical reasons and for potential applications. Currently, the most popular approach to ...

Traditional NMF-based signal decomposition relies on the factorization of spectral data which is typically computed by means of the short-time Fourier transform. In this paper we propose to relax the choice of a pre-fixed transform and learn a short-time unitary transform together with the factorization, using a novel block-descent algorithm. This improves the fit between the processed data and...

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 ...

Nonnegative matrix factorization (NMF) is a popular technique for pattern recognition, data analysis, and dimensionality reduction, the goal of which is to decompose nonnegative data matrix X into a product of basis matrix A and encoding variable matrix S with both A and S allowed to have only nonnegative elements. In this paper we consider Amari’s α-divergence as a discrepancy measure and rigo...

Nonnegative matrix factorization (NMF) provides a lower rank approximation of a nonnegative matrix, and has been successfully used as a clustering method. In this paper, we offer some conceptual understanding for the capabilities and shortcomings of NMF as a clustering method. Then, we propose Symmetric NMF (SymNMF) as a general framework for graph clustering, which inherits the advantages of N...

The problem of illumination estimation for color constancy and automatic white balancing of digital color imagery can be viewed as the separation of the image into illumination and reflectance components. We propose using nonnegative matrix factorization with sparseness constraints to separate these components. Since illumination and reflectance are combinedmultiplicatively, the first step is t...