Locally Linear Embedding (LLE) — how does it work?
hardAnswer
- (1) Find k nearest neighbors for each point.
- (2) Reconstruct each point as linear combination of neighbors: minimize || ||² with Σ .
- (3) Find embedding minimizing || ||² preserving the same weights.
- Captures non-linear structure with a linear reconstruction locally.
- Sensitive to k.
- Modern: superseded by UMAP but still cited in manifold-learning theory.
Check yourself — multiple choice
- Same as PCA
- Reconstruct each point from neighbors with weights w; embed preserving same weights → non-linear DR with local linearity
- Random
- Not real
LLE: local linear reconstruction weights preserved in embedding.
#dimensionality-reduction
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