The objective of single-channel source separation is to accurately recover source signals from mixtures. Non-negative matrix factorization (NMF) is a popular approach for this task, yet previous NMF approaches have not optimized directly this objective, despite some efforts in this direction. Our paper introduces discriminative training of the NMF basis functions such that, given the coefficien...

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlin...

Performance of Non-negative Matrix Factorisation (NMF) can be diminished when the underlying factors consist of elements that overlap in the matrix to be factorised. The use of `0 sparsity may improve NMF, however such approaches are generally limited to Euclidean distance. We have previously proposed a stepwise `0 method for Hellinger distance, leading to improved sparse NMF. We extend sparse ...

Abstract: Semi-Nonnegative Matrix Factorization (Semi-NMF), as a variant of NMF, inherits the merit of parts-based representation of NMF and possesses the ability to process mixed sign data, which has attracted extensive attention. However, standard Semi-NMF still suffers from the following limitations. First of all, Semi-NMF fits data in a Euclidean space, which ignores the geometrical structu...

Nonnegative matrix factorization (NMF) approximates a nonnegative matrix by the product of two low-rank nonnegative matrices. Since it gives semantically meaningful result that is easily interpretable in clustering applications, NMF has been widely used as a clustering method especially for document data, and as a topic modeling method. We describe several fundamental facts of NMF and introduce...

BACKGROUND Among the various types of folliculitis, differentiation of Malassezia folliculitis (MF) from other forms of folliculitis is important because it is usually treated with antifungal agents. OBJECTIVE We attempted to find a method to enhance the detection rate of MF, and examined the differences in the clinical manifestation between MF and non-MF (NMF). METHODS We performed a retro...

Active appearance models (AAMs) have been widely used in many face modeling and facial feature extraction methods. One of the problems of AAMs is that it is difficult to model a sufficiently wide range of human facial appearances, the pattern of intensities across a face image patch. Previous researches have used principal component analysis (PCA) for facial appearance modeling, but there has b...

The importance of unsupervised clustering and topic modeling is well recognized with ever-increasing volumes of text data available from numerous sources. Nonnegative matrix factorization (NMF) has proven to be a successful method for cluster and topic discovery in unlabeled data sets. In this paper, we propose a fast algorithm for computing NMF using a divide-and-conquer strategy, called DC-NM...

Non-negative matrix factorization (NMF) has proven to be a useful decomposition technique for multivariate data, where the non-negativity constraint is necessary to have a meaningful physical interpretation. NMF reduces the dimensionality of non-negative data by decomposing it into two smaller non-negative factors with physical interpretation for class discovery. The NMF algorithm, however, ass...

The complexes between trans-N-methylformamide (t-NMF) and Ar, N(2), CO, H(2)O have been studied by infrared matrix isolation spectroscopy and/or ab initio calculations. The infrared spectra of NMF/Ne, NMF/Ar and NMF/N(2)(CO,H(2)O)/Ar matrices have been measured and the effect of the complexation on the perturbation of t-NMF frequencies was analyzed. The geometries of the complexes formed betwee...