Package org.nlpub.watset.util

Class Matrices

java.lang.Object

org.nlpub.watset.util.Matrices

public final class Matrices
extends Object

Utilities for working with matrices.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	Matrices.ColumnNormalizeVisitor	Visitor that normalizes columns.
static class	Matrices.ColumnSumVisitor	Visitor that computes column sums.
static class	Matrices.InflateVisitor	Visitor that raises each element to the specified power.
static class	Matrices.RowNormalizeVisitor	Visitor that normalizes rows.

Method Summary

Modifier and Type	Method	Description
static <V,E> org.apache.commons.math3.linear.RealMatrix	buildAdjacencyMatrix(org.jgrapht.Graph<V,E> graph, org.jgrapht.util.VertexToIntegerMapping<V> mapping, boolean addLoops)	Construct an adjacency matrix for the given graph.
static <V,E> org.apache.commons.math3.linear.RealMatrix	buildDegreeMatrix(org.jgrapht.Graph<V,E> graph, org.jgrapht.util.VertexToIntegerMapping<V> mapping)	Construct a degree matrix for the given graph.
static org.apache.commons.math3.linear.RealMatrix	buildSymmetricLaplacian(org.apache.commons.math3.linear.RealMatrix degree, org.apache.commons.math3.linear.RealMatrix adjacency)	Construct a symmetric Laplacian for the given graph.
static org.apache.commons.math3.linear.RealVector	computeRowNorms(org.apache.commons.math3.linear.RealMatrix matrix)	Compute row norms of the given matrix.
static <V> List<NodeEmbedding<V>>	computeSpectralEmbedding(org.apache.commons.math3.linear.RealMatrix laplacian, org.jgrapht.util.VertexToIntegerMapping<V> mapping, int k)	Compute spectral embedding of the graph nodes using the pre-computed Laplacian.
static <V> List<NodeEmbedding<V>>	computeSpectralEmbedding(org.jgrapht.Graph<V,?> graph, org.jgrapht.util.VertexToIntegerMapping<V> mapping, int k)	Compute spectral embedding of the graph nodes.

Methods inherited from class java.lang.Object

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

Method Detail

buildAdjacencyMatrix

public static <V,E> org.apache.commons.math3.linear.RealMatrix buildAdjacencyMatrix(org.jgrapht.Graph<V,E> graph,
                                                                                          org.jgrapht.util.VertexToIntegerMapping<V> mapping,
                                                                                          boolean addLoops)

Construct an adjacency matrix for the given graph.

Note that the loops in the graph are ignored.

Type Parameters:

V - the type of nodes in the graph

E - the type of edges in the graph

Parameters:

graph - the graph

mapping - the mapping

addLoops - should self-loops be added

Returns:

an adjacency matrix

buildDegreeMatrix

public static <V,E> org.apache.commons.math3.linear.RealMatrix buildDegreeMatrix(org.jgrapht.Graph<V,E> graph,
                                                                                       org.jgrapht.util.VertexToIntegerMapping<V> mapping)

Construct a degree matrix for the given graph.

Type Parameters:

V - the type of nodes in the graph

E - the type of edges in the graph

Parameters:

graph - the graph

mapping - the mapping

Returns:

a degree matrix

buildSymmetricLaplacian

public static org.apache.commons.math3.linear.RealMatrix buildSymmetricLaplacian(org.apache.commons.math3.linear.RealMatrix degree,
                                                                                 org.apache.commons.math3.linear.RealMatrix adjacency)

Construct a symmetric Laplacian for the given graph.

Parameters:

degree - the degree matrix

adjacency - the adjacency matrix

Returns:

a symmetric Laplacian

computeRowNorms

public static org.apache.commons.math3.linear.RealVector computeRowNorms(org.apache.commons.math3.linear.RealMatrix matrix)

Compute row norms of the given matrix.

Parameters:

matrix - the matrix

Returns:

a vector with row norms

computeSpectralEmbedding

public static <V> List<NodeEmbedding<V>> computeSpectralEmbedding(org.apache.commons.math3.linear.RealMatrix laplacian,
                                                                  org.jgrapht.util.VertexToIntegerMapping<V> mapping,
                                                                  int k)

Compute spectral embedding of the graph nodes using the pre-computed Laplacian.

Type Parameters:

V - the type of nodes in the graph

Parameters:

laplacian - the graph Laplacian

mapping - the mapping

k - the number of dimensions

Returns:

spectral embeddings of the graph nodes

See Also:

Shi & Malik (IEEE PAMI 22:8), Ng et al. (NIPS 2002), von Luxburg (Statistics and Computing 17:4), sklearn.manifold.SpectralEmbedding

computeSpectralEmbedding

public static <V> List<NodeEmbedding<V>> computeSpectralEmbedding(org.jgrapht.Graph<V,?> graph,
                                                                  org.jgrapht.util.VertexToIntegerMapping<V> mapping,
                                                                  int k)

Compute spectral embedding of the graph nodes.

Type Parameters:

V - the type of nodes in the graph

Parameters:

graph - the graph

mapping - the mapping

k - the number of dimensions

Returns:

spectral embeddings of the graph nodes

See Also:

Shi & Malik (IEEE PAMI 22:8), Ng et al. (NIPS 2002), von Luxburg (Statistics and Computing 17:4), sklearn.manifold.SpectralEmbedding