smile.clustering

Class SpectralClustering

java.lang.Object

smile.clustering.PartitionClustering

smile.clustering.SpectralClustering

All Implemented Interfaces:

java.io.Serializable

public class SpectralClustering
extends PartitionClustering
implements java.io.Serializable

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.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
double	distortion The distortion in feature space.

Fields inherited from class smile.clustering.PartitionClustering

k, OUTLIER, size, y

Constructor Summary

Constructors

Constructor and Description
SpectralClustering(double distortion, int k, int[] y) Constructor.

Method Summary

Modifier and Type	Method and Description
static SpectralClustering	fit(smile.math.matrix.DenseMatrix W, int k) Spectral graph clustering.
static SpectralClustering	fit(smile.math.matrix.DenseMatrix W, int k, int maxIter, double tol) Spectral graph clustering.
static SpectralClustering	fit(double[][] data, int k, double sigma) Spectral clustering the data.
static SpectralClustering	fit(double[][] data, int k, double sigma, int maxIter, double tol) Spectral clustering the data.
static SpectralClustering	fit(double[][] data, int k, int l, double sigma) Spectral clustering with Nystrom approximation.
static SpectralClustering	fit(double[][] data, int k, int l, double sigma, int maxIter, double tol) Spectral clustering with Nystrom approximation.

Methods inherited from class smile.clustering.PartitionClustering

run, seed, toString

Methods inherited from class java.lang.Object

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

Field Detail

distortion

public final double distortion

The distortion in feature space.

Constructor Detail

SpectralClustering

public SpectralClustering(double distortion,
                          int k,
                          int[] y)

Constructor.

Parameters:

distortion - the total distortion.

k - the number of clusters.

y - the cluster labels.

Method Detail

fit

public static SpectralClustering fit(smile.math.matrix.DenseMatrix W,
                                     int k)

Spectral graph clustering.

Parameters:

W - the adjacency matrix of graph, which will be modified.

k - the number of clusters.

fit

public static SpectralClustering fit(smile.math.matrix.DenseMatrix W,
                                     int k,
                                     int maxIter,
                                     double tol)

Spectral graph clustering.

Parameters:

W - the adjacency matrix of graph, which will be modified.

k - the number of clusters.

maxIter - the maximum number of iterations for k-means.

tol - the tolerance of k-means convergence test.

fit

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

Spectral clustering the data.

Parameters:

data - the input data of which each row is an observation.

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) in feature space.

fit

public static SpectralClustering fit(double[][] data,
                                     int k,
                                     double sigma,
                                     int maxIter,
                                     double tol)

Spectral clustering the data.

Parameters:

data - the input data of which each row is an observation.

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) in feature space.

maxIter - the maximum number of iterations for k-means.

tol - the tolerance of k-means convergence test.

fit

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

Spectral clustering with Nystrom approximation.

Parameters:

data - the input data of which each row is an observation.

k - the number of clusters.

l - the number of random samples for Nystrom approximation.

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) in feature space.

fit

public static SpectralClustering fit(double[][] data,
                                     int k,
                                     int l,
                                     double sigma,
                                     int maxIter,
                                     double tol)

Spectral clustering with Nystrom approximation.

Parameters:

data - the input data of which each row is an observation.

k - the number of clusters.

l - the number of random samples for Nystrom approximation.

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) in feature space.

maxIter - the maximum number of iterations for k-means.

tol - the tolerance of k-means convergence test.