Package 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.
4. Kai Zhang, Nathan R. Zemke, Ethan J. Armand and Bing Ren. A fast, scalable and versatile tool for analysis of single-cell omics data. 2024.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	SpectralClustering.Options	Spectral clustering hyperparameters.

Method Summary

Modifier and Type	Method	Description
static double[][]	embed(double[][] data, int d, double sigma)	Returns the embedding for spectral clustering.
static double[][]	embed(Matrix W, int d)	Returns the embedding for spectral clustering.
static double[][]	embed(SparseIntArray[] data, int p, int d)	Returns the embedding for the nonnegative count data with cosine similarity.
static CentroidClustering<double[],double[]>	fit(double[][] data, SpectralClustering.Options options)	Spectral clustering the data.
static CentroidClustering<double[],double[]>	fit(SparseIntArray[] data, int p, Clustering.Options options)	Spectral clustering the nonnegative count data with cosine similarity.
static CentroidClustering<double[],double[]>	nystrom(double[][] data, SpectralClustering.Options options)	Spectral clustering with Nystrom approximation.

Methods inherited from class java.lang.Object

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

Method Details

fit

public static CentroidClustering<double[],double[]> fit(SparseIntArray[] data,
 int p,
 Clustering.Options options)

Spectral clustering the nonnegative count data with cosine similarity.

Parameters:

data - the nonnegative count matrix.

p - the number of features.

options - the hyperparameters.

Returns:

the model.

fit

public static CentroidClustering<double[],double[]> fit(double[][] data,
 SpectralClustering.Options options)

Spectral clustering the data.

Parameters:

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

options - the hyperparameters.

Returns:

the model.

nystrom

public static CentroidClustering<double[],double[]> nystrom(double[][] data,
 SpectralClustering.Options options)

Spectral clustering with Nystrom approximation.

Parameters:

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

options - the hyperparameters.

Returns:

the model.

embed

public static double[][] embed(Matrix W,
 int d)

Returns the embedding for spectral clustering.

Parameters:

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

d - the dimension of feature space.

Returns:

the embedding.

embed

public static double[][] embed(double[][] data,
 int d,
 double sigma)

Returns the embedding for spectral clustering.

Parameters:

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

d - the dimension of feature space.

sigma - the smooth/width parameter of Gaussian kernel.

Returns:

the embedding.

embed

public static double[][] embed(SparseIntArray[] data,
 int p,
 int d)

Returns the embedding for the nonnegative count data with cosine similarity.

Parameters:

data - the nonnegative count matrix.

p - the number of features.

d - the dimension of feature space.

Returns:

the embedding.