手法を比較

	特異スペクトル解析	カーネル主成分分析
分野	時系列解析	機械学習
系統	Process / pipeline	Latent structure
提唱年	1986	1998
提唱者	David Broomhead	Schölkopf, B.; Smola, A. J.; Müller, K.-R.
種類	Dimension reduction and trend extraction	Nonlinear dimensionality reduction via kernel trick
原典	Broomhead, D. S., & King, G. P. (1986). Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena, 20(2–3), 217–236.	Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319.
別名	SSA, SVD-based decomposition	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition
関連	3	5
概要	Singular Spectrum Analysis (SSA) is a nonparametric method for time-series decomposition and forecasting based on singular value decomposition (SVD) of a time-lagged embedding matrix. Introduced by Broomhead and King (1986) and developed further by Vautard, Yiou, and Ghil (1992), SSA decomposes time series into trend, oscillatory, and noise components without assuming any underlying model. It is particularly effective for short, noisy non-stationary signals where parametric approaches fail.	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.