smile.manifold

Class LLE

java.lang.Object

smile.manifold.LLE

All Implemented Interfaces:

java.io.Serializable

public class LLE
extends java.lang.Object
implements java.io.Serializable

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.

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double[][]	coordinates The coordinate matrix in embedding space.
smile.graph.AdjacencyList	graph Nearest neighbor graph.
int[]	index The original sample index.

Constructor Summary

Constructors

Constructor and Description
LLE(int[] index, double[][] coordinates, smile.graph.AdjacencyList graph) Constructor.

Method Summary

Modifier and Type	Method and Description
static LLE	of(double[][] data, int k) Runs the LLE algorithm.
static LLE	of(double[][] data, int k, int d) Runs the LLE algorithm.

Methods inherited from class java.lang.Object

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

Field Detail

index

public final int[] index

The original sample index.

coordinates

public final double[][] coordinates

The coordinate matrix in embedding space.

graph

public smile.graph.AdjacencyList graph

Nearest neighbor graph.

Constructor Detail

LLE

public LLE(int[] index,
           double[][] coordinates,
           smile.graph.AdjacencyList graph)

Constructor.

Parameters:

index - the original sample index.

coordinates - the coordinates.

graph - the nearest neighbor graph.

Method Detail

of

public static LLE of(double[][] data,
                     int k)

Runs the LLE algorithm.

Parameters:

data - the input data.

k - k-nearest neighbor.

of

public static LLE of(double[][] data,
                     int k,
                     int d)

Runs the LLE algorithm.

Parameters:

data - the input data.

d - the dimension of the manifold.

k - k-nearest neighbor.