Сравнение методов

	Изомап	Кернел PCA	Анализ главных компонент
Область	Машинное обучение	Машинное обучение	Машинное обучение
Семейство	Latent structure	Latent structure	Machine learning
Год появления	2000	1998	2002
Автор метода	Tenenbaum, J. B.; de Silva, V.; Langford, J. C.	Schölkopf, B.; Smola, A. J.; Müller, K.-R.	Jolliffe, I.T. (textbook); Pearson & Hotelling (origins)
Тип	Manifold learning / nonlinear dimensionality reduction	Nonlinear dimensionality reduction via kernel trick	Unsupervised dimensionality reduction
Основополагающий источник	Tenenbaum, J. B., de Silva, V. & Langford, J. C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290(5500), 2319–2323.	Schölkopf, B., Smola, A. J., & Müller, K.-R. (1998). Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5), 1299–1319.	Jolliffe, I.T. (2002). Principal Component Analysis (2nd ed.). Springer.
Другие названия	Isomap, isometric feature mapping, geodesic Isomap, nonlinear MDS	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition	Temel Bileşenler Analizi (PCA), PCA, principal components analysis, Karhunen-Loève transform
Связанные	3	5	3
Сводка	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.	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.	Principal Component Analysis (PCA) is an unsupervised dimensionality-reduction method — given its modern textbook treatment by Ian Jolliffe (2002) — that compresses high-dimensional data into fewer dimensions while preserving the maximum possible variance. It re-expresses correlated variables as a small set of uncorrelated principal components ordered by how much of the data's variation each one captures.