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Non-negative matrix factorization (NMF), also non-negative matrix approximation〔 is a group of algorithms in multivariate analysis and linear algebra where a matrix is factorized into (usually) two matrices and , 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 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 computer vision, document clustering,〔 chemometrics, audio signal processing and recommender systems. == History == In chemometrics non-negative matrix factorization has a long history under the name "self modeling curve resolution". In this framework the vectors in the right matrix are continuous curves rather than discrete vectors. Also early work on non-negative matrix factorizations was performed by a Finnish group of researchers in the middle of the 1990s under the name ''positive matrix factorization''. It became more widely known as ''non-negative matrix factorization'' after Lee and Seung investigated the properties of the algorithm and published some simple and useful algorithms for two types of factorizations. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「nonnegative matrix factorization」の詳細全文を読む スポンサード リンク
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