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	非負値行列因子分解 (NMF)	特異値分解
分野	機械学習	数値解析
系統	Latent structure	Machine learning
提唱年	1999	1965
提唱者	Lee, D. D. & Seung, H. S.	Gene Golub
種類	Matrix decomposition with non-negativity constraints	Linear algebra decomposition
原典	Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788–791.	Golub, G. H., & Kahan, W. (1970). Calculating the singular values and pseudo-inverse of a matrix. Journal of the SIAM Series B: Numerical Analysis, 2(2), 205–224.
別名	NMF, NNMF, nonnegative matrix factorization, non-negative matrix approximation	SVD, thin SVD, reduced SVD
関連	4	0
概要	Non-negative Matrix Factorization (NMF) is a family of algorithms, introduced by Lee and Seung in their landmark 1999 Nature paper, that decomposes a non-negative data matrix V into the product of two lower-rank non-negative matrices W (basis components) and H (encoding coefficients). Unlike PCA or SVD, the non-negativity constraint forces the algorithm to learn strictly additive, parts-based representations, making the factors directly interpretable as building blocks of the original data.	Singular Value Decomposition (SVD) is a fundamental matrix factorization technique that decomposes any m × n matrix A into the product A = U Σ V^T, where U and V are orthogonal matrices and Σ is a diagonal matrix of singular values. Developed by Gene Golub and others in the 1960s–1970s, SVD is the most robust method for analyzing matrix structure and solving linear systems.