smile.manifold

Class LaplacianEigenmap

java.lang.Object

smile.manifold.LaplacianEigenmap

public class LaplacianEigenmap
extends java.lang.Object

Laplacian Eigenmap. Using the notion of the Laplacian of the nearest neighbor adjacency graph, Laplacian Eigenmap computes a low dimensional representation of the dataset that optimally preserves local neighborhood information in a certain sense. The representation map generated by the algorithm may be viewed as a discrete approximation to a continuous map that naturally arises from the geometry of the manifold.

The locality preserving character of the Laplacian Eigenmap algorithm makes it relatively insensitive to outliers and noise. It is also not prone to "short circuiting" as only the local distances are used.

See Also:

IsoMap,

References

1. Mikhail Belkin and Partha Niyogi. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. NIPS, 2001.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double[][]	getCoordinates() Returns the coordinates of projected data.
double	getHeatKernelWidth() Returns the width of heat kernel.
int[]	getIndex() Returns the original sample index.
smile.graph.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

LaplacianEigenmap

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

Constructor. Learn Laplacian Eigenmaps with discrete weights.

Parameters:

data - the dataset.

d - the dimension of the manifold.

k - k-nearest neighbor.

LaplacianEigenmap

public LaplacianEigenmap(double[][] data,
                         int d,
                         int k,
                         double t)

Constructor. Learn Laplacian Eigenmap with Gaussian kernel.

Parameters:

data - the dataset.

d - the dimension of the manifold.

k - k-nearest neighbor.

t - the smooth/width parameter of heat kernel e^{-||x-y||2 / t}. Non-positive value means discrete weights.

Method Detail

getIndex

public int[] getIndex()

Returns the original sample index. Because Laplacian Eigenmap 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 smile.graph.Graph getNearestNeighborGraph()

Returns the nearest neighbor graph.

getHeatKernelWidth

public double getHeatKernelWidth()

Returns the width of heat kernel.