مقایسهٔ روش‌ها

	تحلیل مؤلفه‌های اصلی کرنل (Kernel PCA)	فشرده‌سازی محلی خطی (LLE)	ماشین بردار پشتیبان (طبقه‌بندی)
حوزه	یادگیری ماشین	یادگیری ماشین	یادگیری ماشین
خانواده	Latent structure	Machine learning	Machine learning
سال پیدایش	1998	2000	1995
پدیدآور	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Sam Roweis & Lawrence Saul	Cortes, C. & Vapnik, V.
نوع	Nonlinear dimensionality reduction via kernel trick	Nonlinear manifold dimensionality reduction	Maximum-margin classifier (kernel method)
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.	Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.	Cortes, C. & Vapnik, V. (1995). Support-Vector Networks. Machine Learning, 20, 273–297.
نام‌های دیگر	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme	Destek Vektör Makinesi (SVM — Sınıflandırma), support-vector network, SVM classifier, maximum-margin classifier
مرتبط	5	3	5
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.	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.	The Support Vector Machine, introduced by Corinna Cortes and Vladimir Vapnik in 1995, is a classifier that finds the optimal separating hyperplane between classes in a high-dimensional space. It chooses the boundary that leaves the widest possible margin to the nearest training points, which makes its decisions robust on new data.