smile.clustering

Class SpectralClustering

java.lang.Object

smile.clustering.SpectralClustering

public class SpectralClustering
extends Object

Spectral Clustering. Given a set of data points, the similarity matrix may be defined as a matrix S where S_ij represents a measure of the similarity between points. Spectral clustering techniques make use of the spectrum of the similarity matrix of the data to perform dimensionality reduction for clustering in fewer dimensions. Then the clustering will be performed in the dimension-reduce space, in which clusters of non-convex shape may become tight. There are some intriguing similarities between spectral clustering methods and kernel PCA, which has been empirically observed to perform clustering.

References

1. A.Y. Ng, M.I. Jordan, and Y. Weiss. On Spectral Clustering: Analysis and an algorithm. NIPS, 2001.
2. Marina Maila and Jianbo Shi. Learning segmentation by random walks. NIPS, 2000.
3. Deepak Verma and Marina Meila. A Comparison of Spectral Clustering Algorithms. 2003.

Author:

Haifeng Li

Constructor Summary

Constructors

Constructor and Description
SpectralClustering(double[][] W, int k) Constructor.
SpectralClustering(double[][] data, int k, double sigma) Constructor.
SpectralClustering(double[][] data, int l, int k, double sigma) Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
double	distortion() Returns the distortion in feature space.
int[]	getClusterLabel() Returns the cluster labels of data.
int[]	getClusterSize() Returns the size of clusters.
double	getGaussianKernelWidth() Returns the width of Gaussian kernel.
int	getNumClusters() Returns the number of clusters.
String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

SpectralClustering

public SpectralClustering(double[][] W,
                  int k)

Constructor. Spectral graph clustering.

Parameters:

W - the adjacency matrix of graph.

k - the number of clusters.

SpectralClustering

public SpectralClustering(double[][] data,
                  int k,
                  double sigma)

Constructor. Spectral clustering the data.

Parameters:

data - the dataset for clustering.

k - the number of clusters.

sigma - the smooth/width parameter of Gaussian kernel, which is a somewhat sensitive parameter. To search for the best setting, one may pick the value that gives the tightest clusters (smallest distortion, see distortion()) in feature space.

SpectralClustering

public SpectralClustering(double[][] data,
                  int l,
                  int k,
                  double sigma)

Constructor. Spectral clustering with Nystrom approximation.

Parameters:

data - the dataset for clustering.

l - the number of random samples for Nystrom approximation.

k - the number of clusters.

sigma - the smooth/width parameter of Gaussian kernel, which is a somewhat sensitive parameter. To search for the best setting, one may pick the value that gives the tightest clusters (smallest distortion, see distortion()) in feature space.

Method Detail

getNumClusters

public int getNumClusters()

Returns the number of clusters.

getClusterLabel

public int[] getClusterLabel()

Returns the cluster labels of data.

getClusterSize

public int[] getClusterSize()

Returns the size of clusters.

getGaussianKernelWidth

public double getGaussianKernelWidth()

Returns the width of Gaussian kernel.

distortion

public double distortion()

Returns the distortion in feature space.

toString

public String toString()

Overrides:

toString in class Object