مقایسهٔ روش‌ها

	تحلیل مؤلفه‌های اصلی کرنل (Kernel PCA)	خودرمزگذار	Isomap	فشرده‌سازی محلی خطی (LLE)	ماشین بردار پشتیبان (طبقه‌بندی)
حوزه	یادگیری ماشین	یادگیری عمیق	یادگیری ماشین	یادگیری ماشین	یادگیری ماشین
خانواده	Latent structure	Machine learning	Latent structure	Machine learning	Machine learning
سال پیدایش	1998	2006	2000	2000	1995
پدیدآور	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Hinton, G.E. & Salakhutdinov, R.R.	Tenenbaum, J. B.; de Silva, V.; Langford, J. C.	Sam Roweis & Lawrence Saul	Cortes, C. & Vapnik, V.
نوع	Nonlinear dimensionality reduction via kernel trick	Neural network (encoder-decoder)	Manifold learning / nonlinear dimensionality reduction	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.	Hinton, G.E. & Salakhutdinov, R.R. (2006). Reducing the Dimensionality of Data with Neural Networks. Science, 313(5786), 504–507.	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.	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	Otokodlayıcı (Autoencoder), otokodlayıcı, auto-encoder, encoder-decoder network	Isomap, isometric feature mapping, geodesic Isomap, nonlinear MDS	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme	Destek Vektör Makinesi (SVM — Sınıflandırma), support-vector network, SVM classifier, maximum-margin classifier
مرتبط	5	4	3	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.	An autoencoder is an encoder-decoder neural network, popularised by Hinton and Salakhutdinov in 2006, that compresses data into a low-dimensional latent code and then reconstructs it, enabling dimensionality reduction and anomaly detection. By learning to rebuild its own input through a narrow bottleneck, it discovers a compact representation of the data.	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.	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.