The Non-negative Matrix Factorization (NMF) is a special low-rank approximation which allows for an additive parts-based and interpretable representation of the data. This article presents efforts to improve the convergence, approximation quality, and classification accuracy of NMF using five different meta-heuristics based on swarm intelligence. Several properties of the NMF objective function...

The Noisy Non-negative Matrix factorization (NMF) is: given a data matrix A (d × n), find non-negative matrices B,C (d × k, k × n respy.) so that A = BC + N , where N is a noise matrix. Existing polynomial time algorithms with proven error guarantees require each column N·,j to have l1 norm much smaller than ||(BC)·,j ||1, which could be very restrictive. In important applications of NMF such a...

Non-negative Matrix Factorization (NMF) has received considerable attentions in various areas for its psychological and physiological interpretation of naturally occurring data whose representation may be parts-based in the human brain. Despite its good practical performance, one shortcoming of original NMF is that it ignores intrinsic structure of data set. On one hand, samples might be on a m...

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 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...

Today, the need of large data collection processing increase. Such type of data can has very large dimension and hidden relationships. Analyzing this type of data leads to many errors and noise, therefore, dimension reduction techniques are applied. Many techniques of reduction were developed, e.g. SVD, SDD, PCA, ICA and NMF. Non-negative matrix factorization (NMF) has main advantage in process...

In this paper we introduce a supervised, maximum margin framework for linear and non-linear Non-negative Matrix Factorization. By contrast to existing methods in which the matrix factorization phase (i.e. the feature extraction phase) and the classification phase are separated, we incorporate the maximum margin classification constraints within the NMF formulation. This results to a non-convex ...