Nonnegative matrix factorization (NMF) and its numerous variants have been extensively studied used in hyperspectral unmixing (HU). With the aid of designed deep structure, NMF-based methods demonstrate advantages exploring hierarchical features complex data. However, a noise corruption problem commonly exists data severely degrades performance when applied to HU. In this study, we propose an ℓ...

This study develops an atlas-based automated framework for segmenting infants’ brains from magnetic resonance imaging (MRI). For the accurate segmentation of different structures infant’s brain at isointense age (6–12 months), our integrates features diffusion tensor (DTI) (e.g., fractional anisotropy (FA)). A (DT) image and its region map are considered samples a Markov–Gibbs random field (MGR...

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 . A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...

Nonnegative Matrix Factorization (NMF) has gathered a lot of attention in the last decade and has been successfully applied in numerous applications. It consists in the factorization of a nonnegative matrix by the product of two low-rank nonnegative matrices: M ≈ VW . In this paper, we attempt to solve NMF problems in a recursive way. In order to do that, we introduce a new variant called Nonne...

Nonnegative Matrix Factorization (NMF) has been widely used in machine learning and data mining. It aims to find two nonnegative matrices whose product can well approximate the nonnegative data matrix, which naturally lead to parts-based representation. In this paper, we present a local learning regularized nonnegative matrix factorization (LLNMF) for clustering. It imposes an additional constr...

Nonnegative matrix factorization (NMF) is a popular data analysis method, the objective of which is to approximate a matrix with all nonnegative components into the product of two nonnegative matrices. In this work, we describe a new simple and efficient algorithm for multi-factor nonnegative matrix factorization (mfNMF) problem that generalizes the original NMF problem to more than two factors...

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. In many applications data are often partially corrupted with large additive n...