手法を比較

	行列補完	MICE	非負値行列因子分解 (NMF)
分野	機械学習	統計学	機械学習
系統	Machine learning	Process / pipeline	Latent structure
提唱年	2009	2011	1999
提唱者	Emmanuel Candès & Benjamin Recht	Stef van Buuren & Karin Groothuis-Oudshoorn	Lee, D. D. & Seung, H. S.
種類	Convex low-rank recovery	Iterative multiple imputation algorithm	Matrix decomposition with non-negativity constraints
原典	Candès, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6), 717–772.	van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67.	Lee, D. D., & Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755), 788–791.
別名	Nuclear Norm Minimization, Collaborative Filtering via Low-Rank Recovery, Inductive Matrix Completion, Matris Tamamlama	Fully Conditional Specification, Sequential Regression Multivariate Imputation, Chained Equations Imputation, Zincirleme Denklemlerle Çoklu Atama	NMF, NNMF, nonnegative matrix factorization, non-negative matrix approximation
関連	2	3	4
概要	Matrix Completion is a technique for recovering a low-rank matrix from a small, possibly random subset of its entries. Introduced by Emmanuel Candès and Benjamin Recht in 2009, it reformulates the problem as nuclear norm minimization — a convex surrogate for rank minimization — and provides theoretical guarantees that exact recovery is achievable when entries are observed uniformly at random and the matrix satisfies an incoherence condition.	Multivariate Imputation by Chained Equations (MICE) is an iterative procedure for handling missing data in multivariate datasets. Introduced by Stef van Buuren and Karin Groothuis-Oudshoorn through the R package mice (2011), the algorithm fills each missing variable using a separate regression model conditioned on all other variables, cycling through variables repeatedly until the imputed values converge. The result is m completed datasets that are analysed separately and combined using Rubin's rules.	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.