LocallyLinearEmbedding
LLE: embeds data by preserving the local linear reconstruction weights of each point from its neighbours.
Algorithm
Each point is expressed as a weighted combination of its k nearest neighbours; the embedding minimises the same reconstruction error in low dimensions via a sparse eigenproblem (standard variant).
Constructor
Skigen::LocallyLinearEmbedding<Scalar> model(int n_components = 2, int n_neighbors = 5, Scalar reg = 1e-3);
Parameters
| Parameter | Default | Description |
|---|---|---|
n_components | 2 | Embedding dimensionality. |
n_neighbors | 5 | Neighbours per point. |
reg | 1e-3 | Regularisation of the local Gram matrix. |
Methods
| Method | Description |
|---|---|
fit_transform(X) | Return the embedding. |
Fitted Attributes
| Accessor | Description |
|---|---|
reconstruction_error() | Embedding reconstruction error. |
Example
Skigen::LocallyLinearEmbedding<double> lle(2, 5);
auto Y = lle.fit_transform(X);
Verified against scikit-learn
This estimator is checked by the parity suite. See the generator tests/parity/generate_manifold_reference.py and the reference fixtures in tests/parity/data/locally_linear_embedding/, exercised by tests/parity/parity_manifold.cpp.
API Reference
For full signatures see the LocallyLinearEmbedding API Reference.