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	カーネル主成分分析	特異値分解
分野	機械学習	数値解析
系統	Latent structure	Machine learning
提唱年	1998	1965
提唱者	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Gene Golub
種類	Nonlinear dimensionality reduction via kernel trick	Linear algebra decomposition
原典	Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319.	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	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	SVD, thin SVD, reduced SVD
関連	5	0
概要	Kernel Principal Component Analysis (Kernel PCA) is a nonlinear dimensionality-reduction method introduced by Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller in 1997–1998. It extends classical linear PCA to curved, non-linear data manifolds by implicitly mapping input data into a high-dimensional feature space via a kernel function, then performing standard PCA in that space — all without ever computing the mapping explicitly.	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.