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package de.lmu.ifi.dbs.elki.algorithm.clustering.gdbscan;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2015
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program 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/>.
*/
import de.lmu.ifi.dbs.elki.algorithm.clustering.correlation.FourC;
import de.lmu.ifi.dbs.elki.algorithm.clustering.gdbscan.PreDeConNeighborPredicate.PreDeConModel;
import de.lmu.ifi.dbs.elki.data.NumberVector;
import de.lmu.ifi.dbs.elki.data.type.SimpleTypeInformation;
import de.lmu.ifi.dbs.elki.database.Database;
import de.lmu.ifi.dbs.elki.database.QueryUtil;
import de.lmu.ifi.dbs.elki.database.datastore.DataStore;
import de.lmu.ifi.dbs.elki.database.ids.DBIDIter;
import de.lmu.ifi.dbs.elki.database.ids.DBIDRef;
import de.lmu.ifi.dbs.elki.database.ids.DBIDUtil;
import de.lmu.ifi.dbs.elki.database.ids.DBIDs;
import de.lmu.ifi.dbs.elki.database.ids.DoubleDBIDList;
import de.lmu.ifi.dbs.elki.database.ids.HashSetModifiableDBIDs;
import de.lmu.ifi.dbs.elki.database.query.distance.DistanceQuery;
import de.lmu.ifi.dbs.elki.database.query.range.RangeQuery;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.database.relation.RelationUtil;
import de.lmu.ifi.dbs.elki.distance.distancefunction.minkowski.EuclideanDistanceFunction;
import de.lmu.ifi.dbs.elki.logging.Logging;
import de.lmu.ifi.dbs.elki.math.MeanVariance;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Matrix;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Vector;
import de.lmu.ifi.dbs.elki.math.linearalgebra.pca.LimitEigenPairFilter;
import de.lmu.ifi.dbs.elki.math.linearalgebra.pca.PCAFilteredResult;
import de.lmu.ifi.dbs.elki.math.linearalgebra.pca.PCAFilteredRunner;
import de.lmu.ifi.dbs.elki.math.linearalgebra.pca.StandardCovarianceMatrixBuilder;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
/**
* 4C identifies local subgroups of data objects sharing a uniform correlation.
* The algorithm is based on a combination of PCA and density-based clustering
* (DBSCAN).
* <p>
* Reference: Christian Böhm, Karin Kailing, Peer Kröger, Arthur Zimek:
* Computing Clusters of Correlation Connected Objects. <br>
* In Proc. ACM SIGMOD Int. Conf. on Management of Data, Paris, France, 2004.
* </p>
*
* @author Arthur Zimek
* @author Erich Schubert
* @since 0.7.0
*
* @param <V> the type of NumberVector handled by this Algorithm
*/
@Reference(authors = "C. Böhm, K. Kailing, P. Kröger, A. Zimek", //
title = "Computing Clusters of Correlation Connected Objects", //
booktitle = "Proc. ACM SIGMOD Int. Conf. on Management of Data, Paris, France, 2004, 455-466", //
url = "http://dx.doi.org/10.1145/1007568.1007620")
public class FourCNeighborPredicate<V extends NumberVector> extends AbstractRangeQueryNeighborPredicate<V, PreDeConNeighborPredicate.PreDeConModel> {
/**
* The logger for this class.
*/
private static final Logging LOG = Logging.getLogger(FourCNeighborPredicate.class);
/**
* 4C settings class.
*/
private FourC.Settings settings;
/**
* Tool to help with parameterization.
*/
private MeanVariance mvSize = new MeanVariance(),
mvSize2 = new MeanVariance(), mvCorDim = new MeanVariance();
/**
* The Filtered PCA Runner
*/
private PCAFilteredRunner pca;
/**
* Constructor.
*
* @param settings 4C settings
*/
public FourCNeighborPredicate(FourC.Settings settings) {
super(settings.epsilon, EuclideanDistanceFunction.STATIC);
this.settings = settings;
this.pca = new PCAFilteredRunner(new StandardCovarianceMatrixBuilder(), new LimitEigenPairFilter(settings.delta, settings.absolute), settings.kappa, 1);
}
@SuppressWarnings("unchecked")
@Override
public <T> NeighborPredicate.Instance<T> instantiate(Database database, SimpleTypeInformation<?> type) {
DistanceQuery<V> dq = QueryUtil.getDistanceQuery(database, distFunc);
Relation<V> relation = (Relation<V>) dq.getRelation();
RangeQuery<V> rq = database.getRangeQuery(dq);
mvSize.reset();
mvSize2.reset();
mvCorDim.reset();
DataStore<PreDeConModel> storage = preprocess(PreDeConModel.class, relation, rq);
if(LOG.isVerbose()) {
LOG.verbose("Average neighborhood size: " + mvSize.toString());
LOG.verbose("Average correlation dimensionality: " + mvCorDim.toString());
LOG.verbose("Average correlated neighborhood size: " + mvSize2.toString());
final int dim = RelationUtil.dimensionality(relation);
if(mvSize.getMean() < 5 * dim) {
LOG.verbose("The epsilon parameter may be chosen too small.");
}
else if(mvSize.getMean() > .5 * relation.size()) {
LOG.verbose("The epsilon parameter may be chosen too large.");
}
else if(mvSize2.getMean() < 10) {
LOG.verbose("The epsilon parameter may be chosen too large, or delta too small.");
}
else if(mvSize2.getMean() < settings.minpts) {
LOG.verbose("The minPts parameter may be chosen too large.");
}
else {
LOG.verbose("As a first guess, you can try minPts < " + ((int) mvSize2.getMean()) //
+ ", but you will need to experiment with these parameters and epsilon.");
}
}
return (NeighborPredicate.Instance<T>) new Instance(dq.getRelation().getDBIDs(), storage);
}
@Override
protected PreDeConModel computeLocalModel(DBIDRef id, DoubleDBIDList neighbors, Relation<V> relation) {
mvSize.put(neighbors.size());
PCAFilteredResult pcares = pca.processIds(neighbors, relation);
int cordim = pcares.getCorrelationDimension();
Matrix m_hat = pcares.similarityMatrix();
Vector obj = relation.get(id).getColumnVector();
// To save computing the square root below.
double sqeps = settings.epsilon * settings.epsilon;
HashSetModifiableDBIDs survivors = DBIDUtil.newHashSet(neighbors.size());
for(DBIDIter iter = neighbors.iter(); iter.valid(); iter.advance()) {
// Compute weighted / projected distance:
Vector diff = relation.get(iter).getColumnVector().minusEquals(obj);
double dist = diff.transposeTimesTimes(m_hat, diff);
if(dist <= sqeps) {
survivors.add(iter);
}
}
if(cordim <= settings.lambda) {
mvSize2.put(survivors.size());
}
mvCorDim.put(cordim);
return new PreDeConModel(cordim, survivors);
}
@Override
Logging getLogger() {
return LOG;
}
@Override
public SimpleTypeInformation<?>[] getOutputType() {
return new SimpleTypeInformation[] { new SimpleTypeInformation<>(PreDeConModel.class) };
}
/**
* Instance for a particular data set.
*
* @author Erich Schubert
*/
public static class Instance extends AbstractRangeQueryNeighborPredicate.Instance<PreDeConModel, PreDeConModel> {
/**
* Constructor.
*
* @param ids IDs this is defined for.
* @param storage Stored models
*/
public Instance(DBIDs ids, DataStore<PreDeConModel> storage) {
super(ids, storage);
}
@Override
public PreDeConModel getNeighbors(DBIDRef reference) {
final PreDeConModel asymmetric = storage.get(reference);
// Check for mutual preference reachability:
HashSetModifiableDBIDs ids = DBIDUtil.newHashSet(asymmetric.ids.size());
for(DBIDIter neighbor = asymmetric.ids.iter(); neighbor.valid(); neighbor.advance()) {
if(storage.get(neighbor).ids.contains(reference)) {
ids.add(neighbor);
}
}
return new PreDeConModel(asymmetric.pdim, ids);
}
@Override
public DBIDIter iterDBIDs(PreDeConModel neighbors) {
return neighbors.ids.iter();
}
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer<O extends NumberVector> extends AbstractParameterizer {
/**
* 4C settings.
*/
protected FourC.Settings settings;
@Override
protected void makeOptions(Parameterization config) {
settings = config.tryInstantiate(FourC.Settings.class);
}
@Override
protected FourCNeighborPredicate<O> makeInstance() {
return new FourCNeighborPredicate<>(settings);
}
}
}
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