LLE
Locally Linear Embedding preserves local neighborhood structure by representing each point as a linear combination of neighbors
LLE
Locally Linear Embedding preserves local neighborhood structure by representing each point as a linear combination of neighbors.
When to use:
- Data has non-linear structure
- Want to preserve local relationships
- Have well-sampled manifold
- Visualization of manifold structure
Strengths: Preserves local structure well, single hyperparameter, can reveal manifold geometry Weaknesses: No inference on new data, sensitive to noise, can create topological defects, slow
Model Parameters
N Components (default: 2, required) Embedding dimensions.
N Neighbors (default: 5) Number of neighbors for reconstruction.
- Small (3-8): Fine local structure
- Large (10-20): Smoother, more stable
- Rule: n_neighbors > n_components
Method (default: "standard") LLE variant:
- standard: Classic LLE (default)
- hessian: Hessian-based (better for undersampled manifolds)
- modified: Modified LLE (more stable)
- ltsa: Local Tangent Space Alignment (preserves angles)
Random State (default: 42) Seed for reproducibility.