/**
* Copyright (c) 2002-2011 "Neo Technology,"
* Network Engine for Objects in Lund AB [http://neotechnology.com]
*
* This file is part of Neo4j.
*
* Neo4j is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as
* published by the Free Software Foundation, either version 3 of the
* License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
package org.neo4j.graphalgo.impl.centrality;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.Map;
import java.util.Random;
import java.util.Set;
import org.neo4j.graphalgo.CostEvaluator;
import org.neo4j.graphalgo.impl.util.MatrixUtil;
import org.neo4j.graphalgo.impl.util.MatrixUtil.DoubleMatrix;
import org.neo4j.graphalgo.impl.util.MatrixUtil.DoubleVector;
import org.neo4j.graphdb.Direction;
import org.neo4j.graphdb.Node;
import org.neo4j.graphdb.Relationship;
/**
* Computing eigenvector centrality with the "Arnoldi iteration". Convergence is
* dependent of the eigenvalues of the input adjacency matrix (the network). If
* the two largest eigenvalues are u1 and u2, a small factor u2/u1 will give a
* faster convergence (i.e. faster computation). NOTE: Currently only works on
* Doubles.
* @complexity The {@link CostEvaluator} is called once for every relationship
* in each iteration. Assuming this is done in constant time, the
* total time complexity is O(j(n + m + i)) when j internal restarts
* are required and i iterations are done in the internal
* eigenvector solving of the H matrix. Typically j = the number of
* iterations / k, where normally k = 3.
* @author Patrik Larsson
*/
public class EigenvectorCentralityArnoldi implements EigenvectorCentrality
{
protected Direction relationDirection;
protected CostEvaluator<Double> costEvaluator;
protected Set<Node> nodeSet;
protected Set<Relationship> relationshipSet;
protected double precision = 0.001;
protected boolean doneCalculation = false;
protected Map<Node,Double> values;
protected int totalIterations = 0;
private int maxIterations = Integer.MAX_VALUE;
/**
* @param relationDirection
* The direction in which the paths should follow the
* relationships.
* @param costEvaluator
* @see CostEvaluator
* @param nodeSet
* The set of nodes the calculation should be run on.
* @param relationshipSet
* The set of relationships that should be processed.
* @param precision
* Precision factor (ex. 0.01 for 1% error). Note that this is
* not the error from the correct values, but the amount of
* change tolerated in one iteration.
*/
public EigenvectorCentralityArnoldi( Direction relationDirection,
CostEvaluator<Double> costEvaluator, Set<Node> nodeSet,
Set<Relationship> relationshipSet, double precision )
{
super();
this.relationDirection = relationDirection;
this.costEvaluator = costEvaluator;
this.nodeSet = nodeSet;
this.relationshipSet = relationshipSet;
this.precision = precision;
}
/**
* This can be used to retrieve the result for every node. Will return null
* if the node is not contained in the node set initially given, or doesn't
* receive a result because no relationship points to it.
* @param node
* @return
*/
public Double getCentrality( Node node )
{
calculate();
return values.get( node );
}
/**
* This resets the calculation if we for some reason would like to redo it.
*/
public void reset()
{
doneCalculation = false;
}
/**
* Internal calculate method that will do the calculation. This can however
* be called externally to manually trigger the calculation.The calculation is
* done the first time this method is run. Upon successive requests, the old
* result is returned, unless the calculation is reset via {@link #reset()}
*/
public void calculate()
{
// Don't do it more than once
if ( doneCalculation )
{
return;
}
doneCalculation = true;
values = new HashMap<Node,Double>();
totalIterations = 0;
// generate a random start vector
Random random = new Random( System.currentTimeMillis() );
for ( Node node : nodeSet )
{
values.put( node, random.nextDouble() );
}
normalize( values );
runIterations( maxIterations );
}
/**
* Stop condition for the iteration.
* @return true if enough precision has been achieved.
*/
private boolean timeToStop( Map<Node,Double> oldValues,
Map<Node,Double> newValues )
{
for ( Node node : oldValues.keySet() )
{
if ( newValues.get( node ) == null )
{
return false;
}
if ( oldValues.get( node ) == 0.0 )
{
if ( Math.abs( newValues.get( node ) ) > precision )
{
return false;
}
continue;
}
double factor = newValues.get( node ) / oldValues.get( node );
factor = Math.abs( factor );
if ( factor - precision > 1.0 || factor + precision < 1.0 )
{
return false;
}
}
return true;
}
/**
* This runs a number of iterations in the computation and stops when enough
* precision has been reached. A maximum number of iterations to perform is
* supplied. NOTE: For maxNrIterations > 0 at least one iteration will be
* run, regardless if good precision has already been reached or not. This
* method also ignores the global limit defined by maxIterations.
* @param maxNrIterations
* The maximum number of iterations to run.
* @return the number of iterations performed. if this is lower than the
* given maxNrIterations the desired precision has been reached.
*/
public int runIterations( int maxNrIterations )
{
if ( maxNrIterations <= 0 )
{
return 0;
}
int localIterations = 0;
while ( localIterations < maxNrIterations )
{
Map<Node,Double> oldValues = values;
localIterations += runInternalArnoldi( 3 );
if ( timeToStop( oldValues, values ) )
{
break;
}
}
// If the first value is negative (possibly the whole vector), negate
// the whole vector
if ( values.get( nodeSet.iterator().next() ) < 0 )
{
for ( Node node : nodeSet )
{
values.put( node, -values.get( node ) );
}
}
return localIterations;
}
/**
* This runs the Arnoldi decomposition in a specified number of steps.
* @param iterations
* The number of steps to perform, i.e. the dimension of the H
* matrix.
* @return The number of iterations actually performed. This can be less
* than the input argument if the starting vector is not linearly
* dependent on that many eigenvectors.
*/
protected int runInternalArnoldi( int iterations )
{
// Create a list of the nodes, in order to quickly translate an index
// into a node.
ArrayList<Node> nodes = new ArrayList<Node>( nodeSet.size() );
for ( Node node : nodeSet )
{
nodes.add( node );
}
DoubleMatrix hMatrix = new DoubleMatrix();
DoubleMatrix qMatrix = new DoubleMatrix();
for ( int i = 0; i < nodes.size(); ++i )
{
qMatrix.set( 0, i, values.get( nodes.get( i ) ) );
}
int localIterations = 1;
// The main arnoldi iteration loop
while ( true )
{
++totalIterations;
Map<Node,Double> newValues = new HashMap<Node,Double>();
// "matrix multiplication"
for ( Relationship relationship : relationshipSet )
{
if ( relationDirection.equals( Direction.BOTH )
|| relationDirection.equals( Direction.OUTGOING ) )
{
processRelationship( newValues, relationship, false );
}
if ( relationDirection.equals( Direction.BOTH )
|| relationDirection.equals( Direction.INCOMING ) )
{
processRelationship( newValues, relationship, true );
}
}
// Orthogonalize
for ( int j = 0; j < localIterations; ++j )
{
DoubleVector qj = qMatrix.getRow( j );
// vector product
double product = 0;
for ( int i = 0; i < nodes.size(); ++i )
{
Double d1 = newValues.get( nodes.get( i ) );
Double d2 = qj.get( i );
if ( d1 != null && d2 != null )
{
product += d1 * d2;
}
}
hMatrix.set( j, localIterations - 1, product );
if ( product != 0.0 )
{
// vector subtraction
for ( int i = 0; i < nodes.size(); ++i )
{
Node node = nodes.get( i );
Double value = newValues.get( node );
if ( value == null )
{
value = 0.0;
}
Double qValue = qj.get( i );
if ( qValue != null )
{
newValues.put( node, value - product * qValue );
}
}
}
}
double normalizeFactor = normalize( newValues );
values = newValues;
DoubleVector qVector = new DoubleVector();
for ( int i = 0; i < nodes.size(); ++i )
{
qVector.set( i, newValues.get( nodes.get( i ) ) );
}
qMatrix.setRow( localIterations, qVector );
if ( normalizeFactor == 0.0 || localIterations >= nodeSet.size()
|| localIterations >= iterations )
{
break;
}
hMatrix.set( localIterations, localIterations - 1, normalizeFactor );
++localIterations;
}
// employ the power method to find eigenvector to h
Random random = new Random( System.currentTimeMillis() );
DoubleVector vector = new DoubleVector();
for ( int i = 0; i < nodeSet.size(); ++i )
{
vector.set( i, random.nextDouble() );
}
MatrixUtil.normalize( vector );
boolean powerDone = false;
int its = 0;
double powerPrecision = 0.1;
while ( !powerDone )
{
DoubleVector newVector = MatrixUtil.multiply( hMatrix, vector );
MatrixUtil.normalize( newVector );
powerDone = true;
for ( Integer index : vector.getIndices() )
{
if ( newVector.get( index ) == null )
{
continue;
}
double factor = Math.abs( newVector.get( index )
/ vector.get( index ) );
if ( factor - powerPrecision > 1.0
|| factor + powerPrecision < 1.0 )
{
powerDone = false;
break;
}
}
vector = newVector;
++its;
if ( its > 100 )
{
break;
}
}
// multiply q and vector to get a ritz vector
DoubleVector ritzVector = new DoubleVector();
for ( int r = 0; r < nodeSet.size(); ++r )
{
for ( int c = 0; c < localIterations; ++c )
{
ritzVector.incrementValue( r, vector.get( c )
* qMatrix.get( c, r ) );
}
}
for ( int i = 0; i < nodeSet.size(); ++i )
{
values.put( nodes.get( i ), ritzVector.get( i ) );
}
normalize( values );
return localIterations;
}
/**
* Internal method used in the "matrix multiplication" in each iteration.
*/
protected void processRelationship( Map<Node,Double> newValues,
Relationship relationship, boolean backwards )
{
Node startNode = relationship.getStartNode();
if ( backwards )
{
startNode = relationship.getEndNode();
}
Node endNode = relationship.getOtherNode( startNode );
Double newValue = newValues.get( endNode );
if ( newValue == null )
{
newValue = 0.0;
}
if ( values.get( startNode ) != null )
{
newValue += values.get( startNode )
* costEvaluator.getCost( relationship,
backwards ? Direction.INCOMING
: Direction.OUTGOING );
}
newValues.put( endNode, newValue );
}
/**
* Normalizes a vector represented as a Map.
* @param vector
* @return the initial length of the vector.
*/
protected double normalize( Map<Node,Double> vector )
{
// Compute vector length
double sum = 0;
for ( Node node : vector.keySet() )
{
Double d = vector.get( node );
if ( d == null )
{
d = 0.0;
vector.put( node, 0.0 );
}
sum += d * d;
}
sum = Math.sqrt( sum );
// Divide all components
if ( sum > 0.0 )
{
for ( Node node : vector.keySet() )
{
vector.put( node, vector.get( node ) / sum );
}
}
return sum;
}
/**
* @return the number of iterations made.
*/
public int getTotalIterations()
{
return totalIterations;
}
/**
* @return the maxIterations
*/
public int getMaxIterations()
{
return maxIterations;
}
/**
* Limit the maximum number of iterations to run. Per default,
* the maximum iterations are set to Integer.MAX_VALUE, which should
* be limited to 50-100 normally.
* @param maxIterations
* the maxIterations to set
*/
public void setMaxIterations( int maxIterations )
{
this.maxIterations = maxIterations;
}
}