方法对比

	随机投影	局部线性嵌入 (LLE)
领域	机器学习	机器学习
方法族	Machine learning	Machine learning
起源年份	1984	2000
提出者	Johnson & Lindenstrauss (lemma); Achlioptas (sparse variant)	Sam Roweis & Lawrence Saul
类型	Linear, data-oblivious dimensionality reduction	Nonlinear manifold dimensionality reduction
开创性文献	Johnson, W. B., & Lindenstrauss, J. (1984). Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics, 26, 189–206.	Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 290(5500), 2323–2326.
别名	random projections, Johnson-Lindenstrauss projection, sparse random projection, rastgele izdüşüm	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme
相关	2	3
摘要	Random projection reduces dimensionality by multiplying the data by a random matrix, relying on the Johnson-Lindenstrauss lemma (1984), which guarantees that projecting onto enough random directions approximately preserves all pairwise distances. Unlike PCA it does not analyze the data at all — the projection is random and data-oblivious — making it extremely cheap and well suited to very high-dimensional data and streaming or privacy-sensitive settings.	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.