Non-negative matrix factorization (NMF) has proved effective in many clustering and classification tasks. The classic ways to measure the errors between the original and the reconstructed matrix are l2 distance or KullbackLeibler (KL) divergence. However, nonlinear cases are not properly handled when we use these error measures. As a consequence, alternative measures based on nonlinear kernels,...

Non-negative Matrix Factorization (NMF) has been widely exploited to learn latent features from data. However, previous NMF models often assume a fixed number of features, say p features, where p is simply searched by experiments. Moreover, it is even difficult to learn binary features, since binary matrix involves more challenging optimization problems. In this paper, we propose a new Bayesian...

In this paper we introduce MCA-NMF, a computational model of the acquisition of multimodal concepts by an agent grounded in its environment. More precisely our model finds patterns in multimodal sensor input that characterize associations across modalities (speech utterances, images and motion). We propose this computational model as an answer to the question of how some class of concepts can b...

In a previous work, we proposed an informed Non-negative Matrix Factorization (NMF) with a specific parametrization which involves constraints about some known components of the factorization. In this paper we extend the above work by adding some information provided by a physical dispersion model. In particular, we derive a special structure of one of the factorizing matrices, which provides a...

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...

Despite its relative novelty, non-negative matrix factorization (NMF) method knew a huge interest from the scientific community, due to its simplicity and intuitive decomposition. Plenty of applications benefited from it, including image processing (face, medical, etc.), audio data processing or text mining and decomposition. This paper briefly describes the underlaying mathematical NMF theory ...

Reverse-convex programming (RCP) concerns global optimization of a specific class of non-convex optimization problems. We show that a recently proposed model for sparse non-negative matrix factorization (NMF) belongs to this class. Based on this result, we design two algorithms for sparse NMF that solve sequences of convex secondorder cone programs (SOCP). We work out some well-defined modifica...

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at data representations suited to NMF. In this work, we relate TL-NMF the classical joint-diagonalization (JD) problem. We show that, when number of realizations sufficiently large, can be replaced by two-step approach -- termed as JD+NMF estimates through JD, prior NMF computation. contrast, found lim...

In this short note, we focus on the use of the generalized Kullback–Leibler (KL) divergence in the problem of non-negative matrix factorization (NMF). We will show that when using the generalized KL divergence as cost function for NMF, the row sums and the column sums of the original matrix are preserved in the approximation. We will use this special characteristic in several approximation prob...

Clustering algorithms have been applied to the identification of new subtypes of human cancer. Clustering of heterogeneous datasets represents a difficult clustering problem to which some clustering methods cannot be easily extended. Clustering methods based on matrix computations, such as non-negative matrix factorization (NMF), can be modified to deal with this complex problem. In this paper,...