The nonnegative matrix factorization (NMF) is a boundconstrained low-rank approximation technique for nonnegative multivariate data. NMF has been studied extensively over the last years, but an important aspect which only has received little attention so far is a proper initialization of the NMF factors in order to achieve a faster error reduction. Since the NMF objective function is usually no...

The Non-negative Matrix Factorization technique (NMF) has been recently proposed for dimensionality reduction. NMF is capable to produce a regionor partbased representation of objects and images. The positive space defined with NMF lacks of a suitable metric and this paper experimentally compares NMF to Principal Component Analysis (PCA) in the context of classification trying to determine the ...

This paper proposes a layered nonnegative matrix factorization (L-NMF) algorithm for speech separation. The standard NMF method extracts parts-based bases out of nonnegative training data and is often used to separate mixed spectrograms. The proposed L-NMF algorithm comprises of several layers of standard NMF blocks. During training, each layer of the L-NMF is initialized separately and then fi...

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as product two smaller matrices, $W$ and $H$. In this paper, we introduce a general framework to design multiplicative updates (MU) for NMF based on $\beta$-divergences ($\beta$-NMF) with disjoint equality constraints, penalty terms in objective function. By disjoint, mean that each variable...

Properties of Nonnegative Matrix Factorization (NMF) as a clustering method are studied by relating its formulation to other methods such as K-means clustering. We show how interpreting the objective function of K-means as that of a lower rank approximation with special constraints allows comparisons between the constraints of NMF and K-means and provides the insight that some constraints can b...

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of high-dimensional data as it automatically extracts sparse and meaningful features from a set of nonnegative data vectors. We first illustrate this property of NMF on three applications, in image processing, text mining and hyperspectral imaging –this is the why. Then we address the problem of solving NMF, w...

Recently suggested non-negative matrix factorization (NMF) seems to overcome fundamental limitations of factor analysis at least in theoretical aspect. NMF cost function uses Poisson statistics as a noise model, rather than the Gaussian statistics, and provides a simple learning rule, in contrast to the tricky optimization in factor analysis. To study the feasibility of NMF for the analysis of ...

We propose a new method to incorporate statistical priors on the solution of the nonnegative matrix factorization (NMF) for single-channel source separation (SCSS) applications. The Gaussian mixture model (GMM) is used as a log-normalized gain prior model for the NMF solution. The normalization makes the prior models energy independent. In NMF based SCSS, NMF is used to decompose the spectra of...

Non-negative matrix factorization (NMF) is a recently developed method for finding parts-based representation of non-negative data such as face images. Although it has successfully been applied in several applications, directly using NMF for face recognition often leads to low performance. Moreover, when performing on large databases, NMF needs considerable computational costs. In this paper, w...