Non-negative matrix factorization (NMF), as a useful decomposition method for multivariate data, has been widely used in pattern recognition, information retrieval and computer vision. NMF is an effective algorithm to find the latent structure of the data and leads to a parts-based representation. However, NMF is essentially an unsupervised method and can not make use of label information. In t...

This paper combines linear sparse coding and nonnegative matrix factorization into sparse non-negative matrix factorization. In contrast to non-negative matrix factorization, the new model can leam much sparser representation via imposing sparseness constraints explicitly; in contrast to a close model non-negative sparse coding, the new model can learn parts-based representation via fully multi...

This paper addresses the well-known problem of recognizing faces under several unfavorable situations. We have analyzed situations with changes in expression, in illumination and occlusions such as faces wearing sunglasses or scarfs. We have introduced the use of the Non-negative Matrix Factorization (NMF) technique in the context of classification of face images and we have directly compared p...

This article surveys recent research on Non-Negative Matrix Factorization (NNMF), a relatively new technique for dimensionality reduction. It is based on the idea that in many data-processing tasks, negative numbers are physically meaningless. The NNMF technique addresses this problem by placing non-negativity constraints on the data model. I discuss the applications of NNMF, the algorithms and...

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...

In order to solve the problem of algorithm convergence in projective non-negative matrix factorization (P-NMF), a method, called convergent projective non-negative matrix factorization (CP-NMF), is proposed. In CP-NMF, an objective function of Frobenius norm is defined. The Taylor series expansion and the Newton iteration formula of solving root are used. An iterative algorithm for basis matrix...

A well designed and reliable prevention system for non-payment event is very important for the telecom company. Monitoring is especially needed in case the client exceeds the level of his standard payments what can lead to his financial problems. In this paper, we propose a system describing client's behavior and informing about possible problems in advance. In this approach we apply novel ense...

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...