In the last decade, non-negative matrix factorization (NMF) has become a widely used method for solving problems in data mining and pattern recognition. The NMF in its present state can be traced back to the work of Paatero and Tapper in 1994 at the University of Helsinki under the name, “positive matrix factorization” [1]. This technique was popularized by Lee and Seung in 1999 under its curre...

The well-known Nonnegative Matrix Factorization (NMF) method can be provided with more flexibility by generalizing the non-normalized Kullback-Leibler divergence to αdivergences. However, the resulting α-NMF method can only achieve mediocre sparsity for the factorizing matrices. We have earlier proposed a variant of NMF, called Projective NMF (PNMF) that has been shown to have superior sparsity...

Nonnegative matrix factorization (NMF) has been widely used for discovering physically meaningful latent components in audio signals to facilitate source separation. Most of the existing NMF algorithms require that the number of latent components is provided a priori, which is not always possible. In this paper, we leverage developments from the Bayesian nonparametrics and compressive sensing l...

Nonnegative matrix factorizations (NMF) have recently assumed an important role in several fields, such as pattern recognition, automated image exploitation, data clustering and so on. They represent a peculiar tool adopted to obtain a reduced representation of multivariate data by using additive components only, in order to learn parts-based representations of data. All algorithms for computin...

Nonnegative matrix factorization (NMF) is one of the most frequently-used matrix factorization models in data analysis. A significant reason to the popularity of NMF is its interpretability and the ‘parts of whole’ interpretation of its components. Recently, max-times, or subtropical, matrix factorization (SMF) has been introduced as an alternative model with equally interpretable ‘winner takes...

We present in this paper an integrated service discovery framework based on Non-negative Matrix Factorization (NMF). NMF provides an effective means to cluster high-dimensional sparse data with both high clustering accuracy and good interpretability of the clustering result. This makes NMF especially suitable for service community discovery by clustering the Web service description data. Nevert...

Nonnegative matrix factorization (NMF) is developed for parts-based representation of nonnegative data with the sparseness constraint. The degree of sparseness plays an important role for model regularization. This paper presents Bayesian group sparse learning for NMF and applies it for single-channel source separation. This method establishes the common bases and individual bases to characteri...

This paper presents a new method to decompose musical spectrograms derived from Non-negative Matrix Factorization (NMF). This method uses time-varying harmonic templates (atoms) which are parametric: these atoms correspond to musical notes. Templates are synthesized from the values of the parameters which are learnt in an NMF framework. This parameterization permits to accurately model some mus...

Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts. However, this decompostion is not generally identifiable (even up to permutation and scaling). While other studies have provide criteria under which NMF is identifiable, we present the first (to our knowledge) characterization of the non-identifiabi...

A connection between the convolutive nonnegative matrix factorization (NMF) and the conventional NMF has been established. As a results, we can convey arbitrary alternating update rules for NMF to update rules for CNMF. In order to illustrate the novel derivation method, a new ALS algorithm for CNMF is proposed based on solving nonnegative quadratic programming problems. The experiment will con...