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,
    int max_iter = 100,
    Scalar tol = 1e-6,
    std::string method = "standard");

Parameters

Parameter	Default	Description
n_components	2	Embedding dimensionality.
n_neighbors	5	Neighbours per point.
reg	1e-3	Regularisation of the local Gram matrix.
method	"standard"	LLE variant: standard, modified, hessian, or ltsa.

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.