/*
* Created on Jul 15, 2007
*
* Copyright (c) 2007, the JUNG Project and the Regents of the University
* of California
* All rights reserved.
*
* This software is open-source under the BSD license; see either
* "license.txt" or
* http://jung.sourceforge.net/license.txt for a description.
*/
package edu.uci.ics.jung.algorithms.scoring;
import edu.uci.ics.jung.algorithms.scoring.util.ScoringUtils;
import edu.uci.ics.jung.graph.Graph;
import org.apache.commons.collections15.Transformer;
/**
* Assigns hub and authority scores to each vertex depending on the topology of
* the network. The essential idea is that a vertex is a hub to the extent
* that it links to authoritative vertices, and is an authority to the extent
* that it links to 'hub' vertices.
*
*
The classic HITS algorithm essentially proceeds as follows:
*
* assign equal initial hub and authority values to each vertex
* repeat
* for each vertex w:
* w.hub = sum over successors x of x.authority
* w.authority = sum over predecessors v of v.hub
* normalize hub and authority scores so that the sum of the squares of each = 1
* until scores converge
*
*
* HITS is somewhat different from random walk/eigenvector-based algorithms
* such as PageRank in that:
*
* there are two mutually recursive scores being calculated, rather than
* a single value
* the edge weights are effectively all 1, i.e., they can't be interpreted
* as transition probabilities. This means that the more inlinks and outlinks
* that a vertex has, the better, since adding an inlink (or outlink) does
* not dilute the influence of the other inlinks (or outlinks) as in
* random walk-based algorithms.
* the scores cannot be interpreted as posterior probabilities (due to the different
* normalization)
*
*
* This implementation has the classic behavior by default. However, it has
* been generalized somewhat so that it can act in a more "PageRank-like" fashion:
*
* this implementation has an optional 'random jump probability' parameter analogous
* to the 'alpha' parameter used by PageRank. Varying this value between 0 and 1
* allows the user to vary between the classic HITS behavior and one in which the
* scores are smoothed to a uniform distribution.
* The default value for this parameter is 0 (no random jumps possible).
* the edge weights can be set to anything the user likes, and in
* particular they can be set up (e.g. using UniformDegreeWeight
)
* so that the weights of the relevant edges incident to a vertex sum to 1.
* The vertex score normalization has been factored into its own method
* so that it can be overridden by a subclass. Thus, for example,
* since the vertices' values are set to sum to 1 initially, if the weights of the
* relevant edges incident to a vertex sum to 1, then the vertices' values
* will continue to sum to 1 if the "sum-of-squares" normalization code
* is overridden to a no-op. (Other normalization methods may also be employed.)
*
*
* @param the vertex type
* @param the edge type
*
* @see "'Authoritative sources in a hyperlinked environment' by Jon Kleinberg, 1997"
*/
public class HITS extends HITSWithPriors
{
/**
* Creates an instance for the specified graph, edge weights, and alpha
* (random jump probability) parameter.
* @param g the input graph
* @param edge_weights the weights to use for each edge
* @param alpha the probability of a hub giving some authority to all vertices,
* and of an authority increasing the score of all hubs (not just those connected
* via links)
*/
public HITS(Graph g, Transformer edge_weights, double alpha)
{
super(g, edge_weights, ScoringUtils.getHITSUniformRootPrior(g.getVertices()), alpha);
}
/**
* Creates an instance for the specified graph and alpha (random jump probability)
* parameter. The edge weights are all set to 1.
* @param g the input graph
* @param alpha the probability of a hub giving some authority to all vertices,
* and of an authority increasing the score of all hubs (not just those connected
* via links)
*/
public HITS(Graph g, double alpha)
{
super(g, ScoringUtils.getHITSUniformRootPrior(g.getVertices()), alpha);
}
/**
* Creates an instance for the specified graph. The edge weights are all set to 1
* and alpha is set to 0.
* @param g the input graph
*/
public HITS(Graph g)
{
this(g, 0.0);
}
/**
* Maintains hub and authority score information for a vertex.
*/
public static class Scores
{
/**
* The hub score for a vertex.
*/
public double hub;
/**
* The authority score for a vertex.
*/
public double authority;
/**
* Creates an instance with the specified hub and authority score.
*/
public Scores(double hub, double authority)
{
this.hub = hub;
this.authority = authority;
}
@Override
public String toString()
{
return String.format("[h:%.4f,a:%.4f]", this.hub, this.authority);
}
}
}