مقایسهٔ روش‌ها

	تحلیل مؤلفه‌های اصلی کرنل (Kernel PCA)	Isomap	فشرده‌سازی محلی خطی (LLE)
حوزه	یادگیری ماشین	یادگیری ماشین	یادگیری ماشین
خانواده	Latent structure	Latent structure	Machine learning
سال پیدایش	1998	2000	2000
پدیدآور	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Tenenbaum, J. B.; de Silva, V.; Langford, J. C.	Sam Roweis & Lawrence Saul
نوع	Nonlinear dimensionality reduction via kernel trick	Manifold learning / nonlinear dimensionality reduction	Nonlinear manifold dimensionality reduction
منبع بنیادین	Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319.	Tenenbaum, J. B., de Silva, V. & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319–2323.	Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.
نام‌های دیگر	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	Isomap, isometric feature mapping, geodesic Isomap, nonlinear MDS	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme
مرتبط	5	3	3
خلاصه	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.	Isomap (Isometric Feature Mapping) is a manifold learning algorithm introduced by Tenenbaum, de Silva, and Langford in 2000 that discovers the intrinsic low-dimensional geometry of high-dimensional data by preserving geodesic — rather than straight-line Euclidean — distances between all pairs of points. It was one of the earliest, and most influential, nonlinear dimensionality reduction methods to demonstrate that genuinely curved data manifolds could be unfolded into a faithful low-dimensional coordinate system.	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.