Non-negative matrix factorization

Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation^[1][2] is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms or muscular activity, non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.

NMF finds applications in such fields as astronomy,^[3][4] computer vision, document clustering,^[1] missing data imputation,^[5] chemometrics, audio signal processing, recommender systems,^[6][7] and bioinformatics.^[8]