Despite its relative novelty, non-negative matrix factorization (NMF) methodknew 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 describesthe underlaying mathematical NMF theory along with some extensions. Several relevantapplications from different scientific areas are also presented. NMF shortcomings and conclusionsare considered.

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