In PCA based face recognition, the basis images may contain negative pixels and thus do not facilitate physical interpretation. Recently, the technique of nonnegative matrix Factorization (NMF) has been applied to face recognition: the non-negativity constraint of NMF yields a localized parts-based representation which achieves a recognition rate that is on par with the eigenface approach. In t...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n × m matrix M into a product of a nonnegative n × d matrix W and a nonnegative d × m matrix H. Restricted NMF requires in addition that the column spaces of M and W coincide. Finding the minimal inner dimension d is known to be NP-hard, both for NMF and restricted NMF. We show that restricted NMF is closel...

Given a matrix M (not necessarily nonnegative) and a factorization rank r, semi-nonnegative matrix factorization (semi-NMF) looks for a matrix U with r columns and a nonnegative matrix V with r rows such that UV is the best possible approximation of M according to some metric. In this paper, we study the properties of semi-NMF from which we develop exact and heuristic algorithms. Our contributi...

BACKGROUND Filaggrin, coded by FLG, is the main source of several major components of natural moisturizing factor (NMF) in the stratum corneum (SC), including pyrrolidone carboxylic acid (PCA) and urocanic acid (UCA). Loss-offunction mutations in FLG lead to reduced levels of filaggrin degradation products in the SC. It has recently been suggested that expression of filaggrin may additionally b...

Nonnegative Matrix Factorization (NMF) is a popular technique in a variety of fields due to its component-based representation with physical interpretablity. NMF finds a nonnegative hidden structures as oblique bases and coefficients. Recently, Orthogonal NMF (ONMF), imposing an orthogonal constraint into NMF, has been gathering a great deal of attention. ONMF is more appropriate for the cluste...

In applications such as speech and audio denoising, music transcription, music and audio based forensics, it is desirable to decompose a single-channel recording into its respective sources, commonly referred to as blind source separation (BSS). One of the techniques used in BSS is non-negative matrix factorization (NMF). In NMF both supervised and unsupervised mode of operations is used. Among...

We review algorithms developed for nonnegativematrix factorization (NMF) and 1 nonnegative tensor factorization (NTF) from a unified view based on the block coordinate 2 descent (BCD) framework. NMF and NTF are low-rank approximation methods for matri3 ces and tensors in which the low-rank factors are constrained to have only nonnegative 4 elements. The nonnegativity constraints have been shown...

In this paper, a nonnegative matrix factorization (NMF)-based speech enhancement method robust to real and diverse noise is proposed by online NMF dictionary learning without relying on prior knowledge of noise. Conventional NMF-based methods have used a fixed noise dictionary, which often results in performance degradation when the NMF noise dictionary cannot cover noise types that occur in re...

Non-negative matrix factorization (NMF) has become a widely used tool for additive parts-based analysis in a wide range of applications. As NMF is a non-convex problem, the quality of the solution will depend on the initialization of the factor matrices. In this study, the successive projection algorithm (SPA) is proposed as an initialization method for NMF. SPA builds on convex geometry and al...

Abstract—What matrix factorization methods do is reduce the dimensionality of data without losing any important information. In this work, we present Non-negative Matrix Factorization (NMF) method, focusing on its advantages concerning other factorization. We discuss main optimization algorithms, used to solve NMF problem, and their convergence. The paper also contains a comparative study betwe...