手法を比較

	Locally Linear Embedding (LLE)（局所線形埋め込み）	Isomap
分野	機械学習	機械学習
系統	Machine learning	Latent structure
提唱年	2000	2000
提唱者	Sam Roweis & Lawrence Saul	Tenenbaum, J. B.; de Silva, V.; Langford, J. C.
種類	Nonlinear manifold dimensionality reduction	Manifold learning / nonlinear dimensionality reduction
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.
別名	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme	Isomap, isometric feature mapping, geodesic Isomap, nonlinear MDS
関連	3	3
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.