# 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.

Part of a series on |

Machine learning and data mining |
---|

Problems |

Learning with humans |

Model diagnostics |

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: