Methoden vergleichen

	Lokal Lineare Einbettung (LLE)	Kernel PCA
Fachgebiet	Maschinelles Lernen	Maschinelles Lernen
Familie	Machine learning	Latent structure
Entstehungsjahr	2000	1998
Urheber	Sam Roweis & Lawrence Saul	Schölkopf, B.; Smola, A. J.; Müller, K.-R.
Typ	Nonlinear manifold dimensionality reduction	Nonlinear dimensionality reduction via kernel trick
Wegweisende Quelle	Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.	Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319.
Aliasnamen	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition
Verwandt	3	5
Zusammenfassung	Locally linear embedding, introduced by Sam Roweis and Lawrence Saul in 2000, is a manifold-learning method for nonlinear dimensionality reduction. It assumes that although data may curve through a high-dimensional space, each point and its neighbours lie approximately on a flat patch. LLE captures each point as a weighted combination of its neighbours and then finds a low-dimensional layout that preserves those same local relationships, unrolling curved structure into a faithful low-dimensional map.	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.