Theory and applications of nonnegative matrix factorization – TANGERINE

Data is often nonnegative by nature, consider for example pixel intensities, amplitude spectra, occurrence counts, food consumption, user scores or stock market values. Optimal processing of such data may call for processing under nonnegativity constraints. Nonnegative matrix factorization (NMF) is a linear regression technique with effervescent popularity in the fields of machine learning and signal/image processing. It basically consists of approximating a data matrix with nonnegative entries as the product of two other nonnegative matrices, where one matrix acts as dictionary of learnt features and the other one acts as a matrix of activation coefficients. NMF has been applied to diverse problems (such as pattern recognition, clustering, mining, source separation and collaborative filtering) in many areas (for example bioinformatics, multimedia processing, finance). NMF, and its extension to nonnegative tensor factorization (NTF), are young research topics that call for answers to many open problems. The general aim of TANGERINE is to bring theoretical and methodological research contributions to NMF and NTF. The more specific aims of the project are 1) to carry out NMF/NTF research concerning model selection, factorizations with structural constraints and fast algorithms in high dimension, and in particular from novel statistical viewpoints, 2) to apply the developed methodology to three specific applications, underlying different sources of problems : identification of dietary behaviors, audio source separation for remastering and video content structuring, 3) to publish our work in high standard journals and conferences and make our code available in a publicly downloadable MATLAB toolbox, 4) to make up for the lack of significant NMF research in France and to put a French research team on the map of global NMF research, 5) to contribute to the dissemination of this novel machine learning technique at national and international levels through the organization of special sessions in conferences and special journal issues. The project is bore by a team of three young researchers of Laboratoire Traitement et Communication de l'Information (CNRS & TELECOM ParisTech) and a young researcher from Metarisk (INRA). They all together gather expertise in applied mathematics, statistical learning and signal processing, as well as experience with applications in multimedia processing (audio, image, video) and bioscience.