lle-weight-constraints-rotation-translation-invariance
IN premise — summaries/2026/08/24/wiki-Nonlinear_dimensionality_reduction-chunk-1.md
Created 2026-08-24T17:11:20+00:00
LLE reconstruction weights are constrained so that Wᵢⱼ = 0 for non-neighbors and Σⱼ Wᵢⱼ = 1 for each point, ensuring invariance to rotation and translation.
Summary
The reconstruction in Locally Linear Embedding only mixes each point with its immediate neighbors, and those neighbor weights always add up to one, forming a local average. This design means the computed low-dimensional layout stays the same no matter how you rotate or shift the entire dataset in space, so the method captures intrinsic shape rather than absolute position.