Since the seminal paper published in 1999 by Lee and Seung, non-negative matrix factorization (NMF) has attracted tremendous research interests over the last decade. The earliest work in NMF is perhaps by (Paatero, 1997) and is then made popular by Lee and Seung due to their elegant multiplicative algorithms (Lee & Seung, 1999, Lee & Seung, 2001). The aim of NMF is to look for latent structures...

In this paper, we propose a novel non-negative matrix factorization (NMF) to the affinity matrix for document clustering, which enforces nonnegativity and orthogonality constraints simultaneously. With the help of orthogonality constraints, this NMF provides a solution to spectral clustering, which inherits the advantages of spectral clustering and presents a much more reasonable clustering int...

A novel approach to single frame multichannel blind image deconvolution is formulated recently as non-negative matrix factorization (NMF) problem with sparseness constraint imposed on the unknown mixing vector. Unlike most of the blind image deconvolution algorithms, the NMF approach requires no a priori knowledge about the blurring kernel and original image. The experimental performance evalua...

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is 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). In this paper we present an algorithm for orthogonal nonn...

Properties of a novel algorithm called non-negative matrix factorization (NMF), are studied. NMF can discover substructures and can provide estimations about the presence or the absence of those, being attractive for completion of missing information. We have studied the working and learning capabilities of NMF networks. Performance was improved by adding sparse code shrinkage (SCS) algorithm t...

We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Betaand Gam...

Multiplicative update algorithms have encountered a great success to solve optimization problems with nonnegativity constraints, such as the famous non-negative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov’s stability theor...

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...

A single channel speech-music separation algorithm based on nonnegative matrix factorization (NMF) with sliding windows and spectral masks is proposed in this work. We train a set of basis vectors for each source signal using NMF in the magnitude spectral domain. Rather than forming the columns of the matrices to be decomposed by NMF of a single spectral frame, we build them with multiple spect...

Nonnegative Matrix Factorization has been proved to be valuable in many fields of data mining, especially in unsupervised learning. In this paper, we will briefly review its variations and applications in image processing, data clustering, semi-supervised clustering, bi-clustering (co-clustering) and financial data mining. Note that we cannot cover all the interesting works on NMF, but generall...