Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...

Introduction Non-invasive Fluorescent Reflectance Imaging (FRI) is used for accessing physiological and molecular processes in biological media. The aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using SVD, Jacobi SVD, and NMF methods in the FRI mode. Materials and Methods In this article, a tissue-like phantom and an optical...

In this paper, we analyze character recognition performance of three different nonnegative matrix factorization (NMF) algorithms. These are multiplicative update (MU) rule known as standard NMF, alternating least square (NMF-ALS) and projected gradient descent (NMF-PGD). They are most preferred approaches in the literature. There are lots of application areas for NMF such as robotics, bioinform...

Nonnegative Matrix Factorization (NMF) was first introduced as a low-rank matrix approximation technique, and has enjoyed a wide area of applications. Although NMF does not seem related to the clustering problem at first, it was shown that they are closely linked. In this report, we provide a gentle introduction to clustering and NMF before reviewing the theoretical relationship between them. W...

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at data representations suited to NMF. In this work, we relate TL-NMF the classical joint-diagonalization (JD) problem. We show that, when number of realizations sufficiently large, can be replaced by two-step approach -- termed as JD+NMF estimates through JD, prior NMF computation. contrast, found lim...

Nonnegative Matrix Factorization (NMF) algorithms have been utilized in a wide range of real applications. NMF is done by several researchers to its part based representation property especially in the facial expression recognition problem. It decomposes a face image into its essential parts (e.g. nose, lips, etc.) but in all previous attempts, it is neglected that all features achieved by NMF ...

Non-negative Matrix Factorization (NMF) can learn interpretable parts-based representations of natural data, and is widely applied in data mining and machine learning area. However, NMF does not always achieve good performances as the non-negative constraint leads learned features to be non-orthogonal and overlap in semantics. How to improve the semantic independence of latent features without ...

This paper proposes a discriminative layered nonnegative matrix factorization (DL-NMF) for monaural speech separation. The standard NMF conducts the parts-based representation using a single-layer of bases which was recently upgraded to the layered NMF (L-NMF) where a tree of bases was estimated for multi-level or multi-aspect decomposition of a complex mixed signal. In this study, we develop t...

This paper proposes a ping-pong document clustering method using NMF and the linkage based refinement alternately, in order to improve the clustering result of NMF. The use of NMF in the ping-pong strategy can be expected effective for document clustering. However, NMF in the ping-pong strategy often worsens performance because NMF often fails to improve the clustering result given as the initi...

Recently there has been significant development in the use of non-negative matrix factorization (NMF) methods for various clustering tasks. NMF factorizes an input nonnegative matrix into two nonnegative matrices of lower rank. Although NMF can be used for conventional data analysis, the recent overwhelming interest in NMF is due to the newly discovered ability of NMF to solve challenging data ...