方法对比

	核主成分分析	奇异值分解
领域	机器学习	数值方法
方法族	Latent structure	Machine learning
起源年份	1998	1965
提出者	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Gene Golub
类型	Nonlinear dimensionality reduction via kernel trick	Linear algebra decomposition
开创性文献	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.
别名	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	SVD, thin SVD, reduced SVD
相关	5	0
摘要	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.