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/*
* Copyright 2011 David Jurgens
*
* This file is part of the S-Space package and is covered under the terms and
* conditions therein.
*
* The S-Space package is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License version 2 as published
* by the Free Software Foundation and distributed hereunder to you.
*
* THIS SOFTWARE IS PROVIDED "AS IS" AND NO REPRESENTATIONS OR WARRANTIES,
* EXPRESS OR IMPLIED ARE MADE. BY WAY OF EXAMPLE, BUT NOT LIMITATION, WE MAKE
* NO REPRESENTATIONS OR WARRANTIES OF MERCHANT- ABILITY OR FITNESS FOR ANY
* PARTICULAR PURPOSE OR THAT THE USE OF THE LICENSED SOFTWARE OR DOCUMENTATION
* WILL NOT INFRINGE ANY THIRD PARTY PATENTS, COPYRIGHTS, TRADEMARKS OR OTHER
* RIGHTS.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see
*
* - Yong-Yeol Ahn, James P. Bagrow and Sune Lehmann. Link communities
* reveal multiscale complexity in networks. Nature 466, 761–764 (05 August
* 2010). Available online here.
*
*
*
* This algorithm automatically determines the number of clusters based on a
* partition density function. Accordingly, the clustering methods take no
* parameters. Calling the {@code cluster} method with a fixed number of
* elements will still cluster the rows, but will ignore the requester number of
* clusters.
*
* Note that this class is not thread-safe. Each call to clustering
* will cache local information about the clustering result to facilitate the
* {@link #getSolution(int)} and {@link #getSolutionDensity(int)} functions.
*
* This class provides one configurable property:
*
*
* - Property:
{@value #KEEP_SIMILARITY_MATRIX_IN_MEMORY_PROPERTY}
*
* Default: {@code true}
*
* - If {@code true}, this property specifies the
* edge similarity matrix used by {@link
* HierarchicalAgglomerativeClustering} should be computed once and then
* kept in memory, which is the default behavior. If {@code false}, this
* causes the similarity of two edges to be recomputed on-the-fly whenever
* it is requester. By computing these values on-the-fly, the performance
* will be slowed down, depending on the complexity of the edge similarity
* function. However, this on-the-fly setting allows for clustering large
* graphs whose edge similarity matrix would not regularly fit into memory.
* It is advised that users not tune this parameter unless it is known that
* the similarity matrix will not fit in memory.
*
*
*
* @author David Jurgens
*/
public class LinkClustering implements Clustering, java.io.Serializable {
private static final long serialVersionUID = 1L;
/**
* A prefix for specifying properties.
*/
public static final String PROPERTY_PREFIX =
"edu.ucla.sspace.clustering.LinkClustering";
/**
* The property to specify if the edge similarity matrix should be kept in
* memory during clustering, or if its values should be computed on the fly.
*/
public static final String KEEP_SIMILARITY_MATRIX_IN_MEMORY_PROPERTY =
PROPERTY_PREFIX + ".keepSimilarityMatrixInMemory";
/**
* The logger to which clustering status updates will be written.
*/
private static final Logger LOGGER =
Logger.getLogger(LinkClustering.class.getName());
/**
* The work used by all {@code LinkClustering} instances to perform
* multi-threaded operations.
*/
private final WorkQueue workQueue;
/**
* The merges for the prior run of this clustering algorithm
*/
private List mergeOrder;
/**
* The list of edges that were last merged. This list is maintained in the
* same order as the initial cluster ordering.
*/
private List edgeList;
/**
* The number of rows in the input matrix that was last clustered.
*/
private int numRows;
/**
* Instantiates a new {@code LinkClustering} instance.
*/
public LinkClustering() {
mergeOrder = null;
edgeList = null;
numRows = 0;
workQueue = WorkQueue.getWorkQueue();
}
/**
* Ignores the specified number of clusters and returns the
* clustering solution according to the partition density.
*
* @param numClusters this parameter is ignored.
*
* @throws IllegalArgumentException if {@code matrix} is not square, or is
* not an instance of {@link SparseMatrix}
*/
public Assignments cluster(Matrix matrix,
int numClusters,
Properties props) {
LOGGER.warning("Link clustering does not take a specified number of " +
"clusters. Clustering the matrix anyway.");
return cluster(matrix, props);
}
/**
* {@inheritDoc}
*
* @throws IllegalArgumentException if {@code matrix} is not square, or is
* not an instance of {@link SparseMatrix}
*/
public Assignments cluster(Matrix matrix, Properties props) {
if (matrix.rows() != matrix.columns())
throw new IllegalArgumentException("Input matrix is not square. " +
"Matrix is expected to be a square matrix whose values (i,j) " +
"denote an edge from row i to row j");
if (!(matrix instanceof SparseMatrix)) {
throw new IllegalArgumentException("Input matrix must be a " +
"sparse matrix.");
}
SparseMatrix sm = (SparseMatrix)matrix;
String inMemProp =
props.getProperty(KEEP_SIMILARITY_MATRIX_IN_MEMORY_PROPERTY);
boolean keepSimMatrixInMem = (inMemProp != null)
? Boolean.parseBoolean(inMemProp) : true;
// IMPLEMENTATION NOTE: Ahn et al. used single-linkage HAC, which can be
// efficiently implemented in O(n^2) time as a special case of HAC.
// However, we currently don't optimize for this special case and
// instead use our HAC class. Because of the complexity of the edge
// similarity function, we build our own similarity matrix and then pass
// it in, rather than passing in the edge matrix directly.
final int rows = sm.rows();
numRows = rows;
LOGGER.fine("Generating link similarity matrix for " + rows + " nodes");
// Rather than create an O(row^3) matrix for representing the edges,
// compress the edge matrix by getting a mapping for each edge to a row
// in the new matrix.
final List edgeList = new ArrayList();
this.edgeList = edgeList;
for (int r = 0; r < rows; ++r) {
SparseDoubleVector row = sm.getRowVector(r);
int[] edges = row.getNonZeroIndices();
for (int col : edges) {
// Always add edges from the upper triangular
if (r > col)
edgeList.add(new Edge(r, col));
// Otherwise, we only add the edge from the lower triangular if
// it wasn't present in the upper. This avoids counting
// duplicate edges.
else if (r < col && sm.get(col, r) == 0)
edgeList.add(new Edge(r, col));
}
}
final int numEdges = edgeList.size();
LOGGER.fine("Number of edges to cluster: " + numEdges);
Matrix edgeSimMatrix =
getEdgeSimMatrix(edgeList, sm, keepSimMatrixInMem);
LOGGER.fine("Computing single linkage link clustering");
final List mergeOrder =
new HierarchicalAgglomerativeClustering().
buildDendrogram(edgeSimMatrix, ClusterLinkage.SINGLE_LINKAGE);
this.mergeOrder = mergeOrder;
LOGGER.fine("Calculating partition densitities");
// Set up a concurrent map that each thread will update once it has
// calculated the densitites of each of its partitions. This map is
// only written to once per thread.
final ConcurrentNavigableMap partitionDensities
= new ConcurrentSkipListMap();
// Register a task group for calculating all of the partition
// densitities
Object key = workQueue.registerTaskGroup(mergeOrder.size());
for (int p = 0; p < mergeOrder.size(); ++p) {
final int part = p;
workQueue.add(key, new Runnable() {
public void run() {
// Get the merges for this particular partitioning of
// the links
List mergeSteps = mergeOrder.subList(0, part);
// Convert the merges to a specific cluster labeling
MultiMap clusterToElements =
convertMergesToAssignments(mergeSteps, numEdges);
// Based on the link partitioning, calculate the
// partition density for each cluster
double partitionDensitySum = 0d;
for (Integer cluster : clusterToElements.keySet()) {
Set linkPartition =
clusterToElements.get(cluster);
int numLinks = linkPartition.size();
BitSet nodesInPartition = new BitSet(rows);
for (Integer linkIndex : linkPartition) {
Edge link = edgeList.get(linkIndex);
nodesInPartition.set(link.from);
nodesInPartition.set(link.to);
}
int numNodes = nodesInPartition.cardinality();
// This reflects the density of this particular
// cluster
double partitionDensity =
(numLinks - (numNodes - 1d))
/ (((numNodes * (numNodes - 1d)) / 2d)
- (numLinks - 1));
partitionDensitySum += partitionDensity;
}
// Compute the density for the total partitioning
// solution
double partitionDensity =
(2d / numEdges) * partitionDensitySum;
LOGGER.log(Level.FINER, "Partition solution {0} had "
+ "density {1}",
new Object[] { part, partitionDensity });
// Update the thread-shared partition density map with
// this task's calculation
partitionDensities.put(partitionDensity, part);
}
});
}
// Wait for all the partition densities to be calculated
workQueue.await(key);
Map.Entry densest = partitionDensities.lastEntry();
LOGGER.fine("Partition " + densest.getValue() +
" had the highest density: " + densest.getKey());
int partitionWithMaxDensity = densest.getValue();
// Select the solution with the highest partition density and assign
// nodes accordingly
MultiMap bestEdgeAssignment =
convertMergesToAssignments(
mergeOrder.subList(0, partitionWithMaxDensity), numEdges);
List> nodeClusters = new ArrayList>(rows);
for (int i = 0; i < rows; ++i)
nodeClusters.add(new HashSet());
// Ignore the original partition labeling, and use our own cluster
// labeling to ensure that the IDs are contiguous.
int clusterId = 0;
// For each of the partitions, add the partion's cluster ID to all the
// nodes that are connected by one of the partition's edges
for (Integer cluster : bestEdgeAssignment.keySet()) {
Set edgePartition = bestEdgeAssignment.get(cluster);
for (Integer edgeId : edgePartition) {
Edge e = edgeList.get(edgeId);
nodeClusters.get(e.from).add(clusterId);
nodeClusters.get(e.to).add(clusterId);
}
// Update the cluster id
clusterId++;
}
int numClusters = 0;
Assignment[] nodeAssignments = new Assignment[rows];
for (int i = 0; i < nodeAssignments.length; ++i) {
nodeAssignments[i] =
new SoftAssignment(nodeClusters.get(i));
}
return new Assignments(numClusters, nodeAssignments, matrix);
}
/**
* Returns the edge similarity matrix for the edges in the provided sparse
* matrix.
*/
private Matrix getEdgeSimMatrix(List edgeList, SparseMatrix sm,
boolean keepSimilarityMatrixInMemory) {
return (keepSimilarityMatrixInMemory)
? calculateEdgeSimMatrix(edgeList, sm)
: new LazySimilarityMatrix(edgeList, sm);
}
/**
* Calculates the similarity matrix for the edges. The similarity matrix is
* symmetric.
*
* @param edgeList the list of all edges known to the system
* @param sm a square matrix whose values denote edges between the rows.
*
* @return the similarity matrix
*/
private Matrix calculateEdgeSimMatrix(
final List edgeList, final SparseMatrix sm) {
final int numEdges = edgeList.size();
final Matrix edgeSimMatrix =
new SparseSymmetricMatrix(
new SparseHashMatrix(numEdges, numEdges));
Object key = workQueue.registerTaskGroup(numEdges);
for (int i = 0; i < numEdges; ++i) {
final int row = i;
workQueue.add(key, new Runnable() {
public void run() {
for (int j = row; j < numEdges; ++j) {
Edge e1 = edgeList.get(row);
Edge e2 = edgeList.get(j);
double sim = getEdgeSimilarity(sm, e1, e2);
if (sim > 0) {
// The symmetric matrix handles the (j,i) case
edgeSimMatrix.set(row, j, sim);
}
}
}
});
}
workQueue.await(key);
return edgeSimMatrix;
}
/**
* Converts a series of merges to cluster assignments. Cluster assignments
* are assumed to start at 0.
*
* @param merges the merge steps, in order
* @param numOriginalClusters how many clusters are present prior to
* merging. This is typically the number of rows in the matrix being
* clustered
*
* @returns a mapping from a cluster to all the elements contained within it.
*/
private static MultiMap convertMergesToAssignments(
List merges, int numOriginalClusters) {
MultiMap clusterToElements =
new HashMultiMap();
for (int i = 0; i < numOriginalClusters; ++i)
clusterToElements.put(i, i);
for (Merge m : merges) {
clusterToElements.putMany(m.remainingCluster(),
clusterToElements.remove(m.mergedCluster()));
}
return clusterToElements;
}
/**
* Computes the similarity of the two edges as the Jaccard index of the
* neighbors of two impost nodes. The impost nodes are the two nodes the
* edges do not have in common. Subclasses may override this method to
* define a new method for computing edge similarity.
*
* Implementation Note: Subclasses that wish to override this
* behavior should be aware that this method is likely to be called by
* multiple threads and therefor should make provisions to be thread safe.
* In addition, this method may be called more than once per edge pair if
* the similarity matrix is being computed on-the-fly.
*
* @param sm a matrix containing the connections between edges. A non-zero
* value in location (i,j) indicates a node i is connected to
* node j by an edge.
* @param e1 an edge to be compared with {@code e2}
* @param e2 an edge to be compared with {@code e1}
*
* @return the similarity of the edges.a
*/
protected double getEdgeSimilarity(SparseMatrix sm, Edge e1, Edge e2) {
// Determing the keystone (shared) node by the edges and the other two
// impost (unshared) nodes.
int keystone = -1;
int impost1 = -1;
int impost2 = -1;
if (e1.from == e2.from) {
keystone = e1.from;
impost1 = e1.to;
impost2 = e2.to;
}
else if (e1.from == e2.to) {
keystone = e1.from;
impost1 = e1.to;
impost2 = e2.from;
}
else if (e2.to == e1.from) {
keystone = e1.from;
impost1 = e1.to;
impost2 = e2.from;
}
else if (e1.to == e2.to) {
keystone = e1.to;
impost1 = e1.from;
impost2 = e2.from;
}
else
return 0d;
// Determine the overlap between the neighbors of the impost nodes
int[] impost1edges = getImpostNeighbors(sm, impost1);
int[] impost2edges = getImpostNeighbors(sm, impost2);
double similarity = Similarity.jaccardIndex(impost1edges, impost2edges);
return similarity;
}
/**
* Returns an array containing the row indices of the neighbors of the
* impost node and the row index of the impost node itself.
*/
private static int[] getImpostNeighbors(SparseMatrix sm, int rowIndex) {
int[] impost1edges = sm.getRowVector(rowIndex).getNonZeroIndices();
int[] neighbors = Arrays.copyOf(impost1edges, impost1edges.length + 1);
neighbors[neighbors.length - 1] = rowIndex;
return neighbors;
}
/**
* Returns the partition density of the clustering solution.
*/
public double getSolutionDensity(int solutionNum) {
if (solutionNum < 0 || solutionNum >= mergeOrder.size()) {
throw new IllegalArgumentException(
"not a valid solution: " + solutionNum);
}
if (mergeOrder == null || edgeList == null) {
throw new IllegalStateException(
"initial clustering solution is not valid yet");
}
int numEdges = edgeList.size();
// Get the merges for this particular partitioning of the links
List mergeSteps =
mergeOrder.subList(0, solutionNum);
// Convert the merges to a specific cluster labeling
MultiMap clusterToElements =
convertMergesToAssignments(mergeSteps, numEdges);
// Based on the link partitioning, calculate the node partition density
double partitionDensitySum = 0d;
for (Integer cluster : clusterToElements.keySet()) {
Set linkPartition = clusterToElements.get(cluster);
int numLinks = linkPartition.size();
BitSet nodesInPartition = new BitSet(numRows);
for (Integer linkIndex : linkPartition) {
Edge link = edgeList.get(linkIndex);
nodesInPartition.set(link.from);
nodesInPartition.set(link.to);
}
int numNodes = nodesInPartition.cardinality();
// This reflects the density of this particular cluster within the
// total partitioning
double partitionDensity = (numLinks - (numNodes - 1d))
/ (((numNodes * (numNodes - 1d)) / 2d) - (numLinks - 1));
partitionDensitySum += partitionDensity;
}
// Compute the density for the total partitioning solution
double partitionDensity = (2d / numEdges) * partitionDensitySum;
return partitionDensity;
}
/**
* Returns the clustering solution after the specified number of merge
* steps.
*
* @param solutionNum the number of merge steps to take prior to returning
* the clustering solution.
*
* @throws IllegalArgumentException if {@code solutionNum} is less than 0 or
* is greater than or equal to {@link #numberOfSolutions()}.
* @throws IllegalStateException if this instance has not yet finished a
* clustering solution.
*/
public Assignments getSolution(int solutionNum) {
if (solutionNum < 0 || solutionNum >= mergeOrder.size()) {
throw new IllegalArgumentException(
"not a valid solution: " + solutionNum);
}
if (mergeOrder == null || edgeList == null) {
throw new IllegalStateException(
"initial clustering solution is not valid yet");
}
int numEdges = edgeList.size();
// Select the solution and all merges necessary to solve it
MultiMap bestEdgeAssignment =
convertMergesToAssignments(
mergeOrder.subList(0, solutionNum), numEdges);
List> nodeClusters = new ArrayList>(numRows);
for (int i = 0; i < numRows; ++i)
nodeClusters.add(new HashSet());
// Ignore the original partition labeling, and use our own cluster
// labeling to ensure that the IDs are contiguous.
int clusterId = 0;
// For each of the partitions, add the partion's cluster ID to all the
// nodes that are connected by one of the partition's edges
for (Integer cluster : bestEdgeAssignment.keySet()) {
Set edgePartition = bestEdgeAssignment.get(cluster);
for (Integer edgeId : edgePartition) {
Edge e = edgeList.get(edgeId);
nodeClusters.get(e.from).add(clusterId);
nodeClusters.get(e.to).add(clusterId);
}
// Update the cluster id
clusterId++;
}
Assignment[] nodeAssignments = new Assignment[numRows];
for (int i = 0; i < nodeAssignments.length; ++i)
nodeAssignments[i] = new SoftAssignment(nodeClusters.get(i));
return new Assignments(clusterId, nodeAssignments);
}
/**
* Returns the number of clustering solutions found by this instances for
* the prior clustering run.
*
* @returns the number of solutions, or {@code 0} if no solutions are
* available.
*/
public int numberOfSolutions() {
return (mergeOrder == null) ? 0 : mergeOrder.size();
}
/**
* A utility data structure for representing a directed edge between two
* ordinally labeled nodes.
*/
protected static class Edge {
public final int from;
public final int to;
public Edge(int from, int to) {
this.from = from;
this.to = to;
}
public boolean equals(Object o) {
if (o instanceof Edge) {
Edge e = (Edge)o;
return e.from == from && e.to == to;
}
return false;
}
public int hashCode() {
return from ^ to;
}
public String toString() {
return "(" + from + "->" + to + ")";
}
}
/**
* A utility class that represents the edge similarity matrix, where the
* similarity values are lazily computed on demand, rather than stored
* internally. While computationally more expensive, this class provides an
* enormous benefit for clustering a graph where the similarity matrix
* cannot fit into memory.
*/
private class LazySimilarityMatrix extends AbstractMatrix {
private final List edgeList;
private final SparseMatrix sm;
public LazySimilarityMatrix(List edgeList, SparseMatrix sm) {
this.edgeList = edgeList;
this.sm = sm;
}
public int columns() {
return edgeList.size();
}
public double get(int row, int column) {
Edge e1 = edgeList.get(row);
Edge e2 = edgeList.get(column);
double sim = getEdgeSimilarity(sm, e1, e2);
return sim;
}
public DoubleVector getRowVector(int row) {
int cols = columns();
DoubleVector vec = new DenseVector(cols);
for (int c = 0; c < cols; ++c) {
vec.set(c, get(row, c));
}
return vec;
}
public int rows() {
return edgeList.size();
}
public void set(int row, int columns, double val) {
throw new UnsupportedOperationException();
}
}
}