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.

Author:

Haifeng Li

See Also:

IsoMap,

References

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

Constructor Summary

Constructors

Constructor and Description
LLE(double[][] data, int d, int k) Constructor.

Method Summary

Modifier and Type	Method and Description
double[][]	getCoordinates() Returns the coordinates of projected data.
int[]	getIndex() Returns the original sample index.
Graph	getNearestNeighborGraph() Returns the nearest neighbor graph.

Methods inherited from class java.lang.Object

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

Constructor Detail

LLE

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

Constructor.

Parameters:

data - the dataset.

d - the dimension of the manifold.

k - k-nearest neighbor.

Method Detail

getIndex

public int[] getIndex()

Returns the original sample index. Because LLE is applied to the largest connected component of k-nearest neighbor graph, we record the the original indices of samples in the largest component.

getCoordinates

public double[][] getCoordinates()

Returns the coordinates of projected data.

getNearestNeighborGraph

public Graph getNearestNeighborGraph()

Returns the nearest neighbor graph.