Methoden vergleichen

	Singuläre Spektralanalyse	Kernel PCA	Singulärwertzerlegung
Fachgebiet	Zeitreihen	Maschinelles Lernen	Numerische Methoden
Familie	Process / pipeline	Latent structure	Machine learning
Entstehungsjahr	1986	1998	1965
Urheber	David Broomhead	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Gene Golub
Typ	Dimension reduction and trend extraction	Nonlinear dimensionality reduction via kernel trick	Linear algebra decomposition
Wegweisende Quelle	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.	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.
Aliasnamen	SSA, SVD-based decomposition	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	SVD, thin SVD, reduced SVD
Verwandt	3	5	0
Zusammenfassung	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.	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.