Package smile.manifold

Class LLE

java.lang.Object

smile.manifold.LLE

public class LLE
extends Object

Locally Linear Embedding. It has several advantages over Isomap, including faster optimization when implemented to take advantage of sparse matrix algorithms, and better results with many problems. LLE also begins by finding a set of the nearest neighbors of each point. It then computes a set of weights for each point that best describe the point as a linear combination of its neighbors. Finally, it uses an eigenvector-based optimization technique to find the low-dimensional embedding of points, such that each point is still described with the same linear combination of its neighbors. LLE tends to handle non-uniform sample densities poorly because there is no fixed unit to prevent the weights from drifting as various regions differ in sample densities.

See Also:

• IsoMap
• LaplacianEigenmap

• References

  1. Sam T. Roweis and Lawrence K. Saul. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science 290(5500):2323-2326, 2000.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	LLE.Options	LLE hyperparameters.

Method Summary

Modifier and Type	Method	Description
static double[][]	fit(double[][] data, NearestNeighborGraph nng, int d)	Runs the LLE algorithm.
static double[][]	fit(double[][] data, LLE.Options options)	Runs the LLE algorithm.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

fit

public static double[][] fit(double[][] data,
 LLE.Options options)

Runs the LLE algorithm.

Parameters:

data - the input data.

options - the hyperparameters.

Returns:

the embedding coordinates.

fit

public static double[][] fit(double[][] data,
 NearestNeighborGraph nng,
 int d)

Runs the LLE algorithm.

Parameters:

data - the input data.

nng - the k-nearest neighbor graph.

d - the dimension of the manifold.

Returns:

the embedding coordinates.