Linganisha mbinu

	Njia ya Kuratibu Nasibu	Ufumbuzi wa Kina wa Kienyeji (LLE)
Nyanja	Ujifunzaji wa Mashine	Ujifunzaji wa Mashine
Familia	Machine learning	Machine learning
Mwaka wa asili	1984	2000
Mwanzilishi	Johnson & Lindenstrauss (lemma); Achlioptas (sparse variant)	Sam Roweis & Lawrence Saul
Aina	Linear, data-oblivious dimensionality reduction	Nonlinear manifold dimensionality reduction
Chanzo asilia	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.
Majina mbadala	random projections, Johnson-Lindenstrauss projection, sparse random projection, rastgele izdüşüm	LLE, manifold learning, nonlinear dimensionality reduction, yerel doğrusal gömme
Zinazohusiana	2	3
Muhtasari	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.