Non-negative matrix factorization (NMF) is becoming a popular tool for decomposition of data in the field of signal and image processing like Independent Component Analysis (ICA). In this study we are relaxing the requirement of non-negative data for NMF making the update equations simple and thus making it Matrix Factorization (MF) and implementing it on simulated Functional Magnetic Resonance...

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...

This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering objective, so clustering aspect of the NMF has a solid justification. Different from previous approaches which usually discard the nonnegativity constraints, our appr...

This paper proposes a new Bayesian nonnegative matrix factorization (NMF) for speech and music separation. We introduce the Poisson likelihood for NMF approximation and the exponential prior distributions for the factorized basis matrix and weight matrix. A variational Bayesian (VB) EM algorithm is developed to implement an efficient solution to variational parameters and model parameters for B...

We exploit the biconvex nature of the Euclidean non-negative matrix factorization (NMF) optimization problem to derive optimization schemes based on sequential quadratic and second order cone programming. We show that for ordinary NMF, our approach performs as well as existing stateof-the-art algorithms, while for sparsity-constrained NMF, as recently proposed by P. O. Hoyer in JMLR 5 (2004), i...

Many bioinformatics problems deal with chemical concentrations that should be non-negative. Non-negative matrix factorization (NMF) is an approach to take advantage of non-negativity in data. We have recently developed sparse NMF algorithms via alternating nonnegativity-constrained least squares in order to obtain sparser basis vectors or sparser mixing coefficients for each sample, which lead ...

In recent years, Nonnegative Matrix Factorization (NMF) has received considerable interest from the data mining and information retrieval fields. NMF has been successfully applied in document clustering, image representation, and other domains. This study proposes an online NMF (ONMF) algorithm to efficiently handle very large-scale and/or streaming datasets. Unlike conventional NMF solutions w...

The Nonnegative Matrix Factorization (NMF) is widely used in audio source separation tasks. However, the separation quality of NMF varies a lot depending on the mixture. In this paper, we analyze the use of NMF in source separation tasks and show how separation results can be significantly improved by using the Nonnegative Matrix Factor 2D Deconvolution (NMF2D). NMF2D was originally proposed as...

Clustering analysis is an effective method to discover and identify tumor classes. So, this paper proposes a Fuzzy C-Means clustering (FCM) algorithm based on Non-negative matrix factorization (NMF). Firstly, gene expression profiling (GEP) is simply processed through mean and variance of gene expression, which can then be mapped into a low dimensional space by NMF method. Finally, for discover...

We propose a new method to incorporate rich statistical priors, modeling temporal gain sequences in the solutions of nonnegative matrix factorization (NMF). The proposed method can be used for single-channel source separation (SCSS) applications. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vector...