Non-negative matrix factorization

Algorithms for matrix decomposition / From Wikipedia, the free encyclopedia

Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Non-negative matrix factorization?

Summarize this article for a 10 year old


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.

Illustration of approximate non-negative matrix factorization: the matrix V is represented by the two smaller matrices W and H, which, when multiplied, approximately reconstruct V.

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]

Oops something went wrong: