手法を比較

	Locally Linear Embedding (LLE)（局所線形埋め込み）	Isomap	カーネル主成分分析
分野	機械学習	機械学習	機械学習
系統	Machine learning	Latent structure	Latent structure
提唱年	2000	2000	1998
提唱者	Sam Roweis & Lawrence Saul	Tenenbaum, J. B.; de Silva, V.; Langford, J. C.	Schölkopf, B.; Smola, A. J.; Müller, K.-R.
種類	Nonlinear manifold dimensionality reduction	Manifold learning / nonlinear dimensionality reduction	Nonlinear dimensionality reduction via kernel trick
原典	Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.	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.
別名	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme	Isomap, isometric feature mapping, geodesic Isomap, nonlinear MDS	KPCA, kernel PCA, nonlinear PCA via kernel trick, kernel eigenvalue decomposition
関連	3	3	5
概要	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.	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.