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package de.lmu.ifi.dbs.elki.algorithm.outlier.spatial;
/*
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.outlier.spatial.neighborhood.NeighborSetPredicate;
import de.lmu.ifi.dbs.elki.data.type.TypeInformation;
import de.lmu.ifi.dbs.elki.data.type.TypeUtil;
import de.lmu.ifi.dbs.elki.database.Database;
import de.lmu.ifi.dbs.elki.database.datastore.DataStoreFactory;
import de.lmu.ifi.dbs.elki.database.datastore.DataStoreUtil;
import de.lmu.ifi.dbs.elki.database.datastore.WritableDoubleDataStore;
import de.lmu.ifi.dbs.elki.database.ids.DBIDIter;
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.query.distance.DistanceQuery;
import de.lmu.ifi.dbs.elki.database.relation.DoubleRelation;
import de.lmu.ifi.dbs.elki.database.relation.MaterializedDoubleRelation;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.distance.distancefunction.PrimitiveDistanceFunction;
import de.lmu.ifi.dbs.elki.logging.Logging;
import de.lmu.ifi.dbs.elki.math.DoubleMinMax;
import de.lmu.ifi.dbs.elki.result.outlier.BasicOutlierScoreMeta;
import de.lmu.ifi.dbs.elki.result.outlier.OutlierResult;
import de.lmu.ifi.dbs.elki.result.outlier.OutlierScoreMeta;
import de.lmu.ifi.dbs.elki.utilities.documentation.Description;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.documentation.Title;
/**
* SLOM: a new measure for local spatial outliers
*
* <p>
* Reference:<br>
* Sanjay Chawla and Pei Sun<br>
* SLOM: a new measure for local spatial outliers<br>
* in Knowledge and Information Systems 9(4), 412-429, 2006
* </p>
*
* This implementation works around some corner cases in SLOM, in particular
* when an object has none or a single neighbor only (albeit the results will
* still not be too useful then), which will result in divisions by zero.
*
* @author Ahmed Hettab
* @since 0.4.0
*
* @param <N> the type the spatial neighborhood is defined over
* @param <O> the type of objects handled by the algorithm
*/
@Title("SLOM: a new measure for local spatial outliers")
@Description("Spatial local outlier measure (SLOM), which captures the local behaviour of datum in their spatial neighbourhood")
@Reference(authors = "Sanjay Chawla and Pei Sun", title = "SLOM: a new measure for local spatial outliers", booktitle = "Knowledge and Information Systems 9(4), 412-429, 2006", url = "http://dx.doi.org/10.1007/s10115-005-0200-2")
public class SLOM<N, O> extends AbstractDistanceBasedSpatialOutlier<N, O> {
/**
* The logger for this class.
*/
private static final Logging LOG = Logging.getLogger(SLOM.class);
/**
* Constructor.
*
* @param npred Neighborhood predicate
* @param nonSpatialDistanceFunction Distance function to use on the
* non-spatial attributes
*/
public SLOM(NeighborSetPredicate.Factory<N> npred, PrimitiveDistanceFunction<O> nonSpatialDistanceFunction) {
super(npred, nonSpatialDistanceFunction);
}
/**
* @param database Database to process
* @param spatial Spatial Relation to use.
* @param relation Relation to use.
* @return Outlier detection result
*/
public OutlierResult run(Database database, Relation<N> spatial, Relation<O> relation) {
final NeighborSetPredicate npred = getNeighborSetPredicateFactory().instantiate(database, spatial);
DistanceQuery<O> distFunc = getNonSpatialDistanceFunction().instantiate(relation);
WritableDoubleDataStore modifiedDistance = DataStoreUtil.makeDoubleStorage(relation.getDBIDs(), DataStoreFactory.HINT_HOT | DataStoreFactory.HINT_TEMP);
// calculate D-Tilde
for(DBIDIter iditer = relation.iterDBIDs(); iditer.valid(); iditer.advance()) {
double sum = 0;
double maxDist = 0;
int cnt = 0;
final DBIDs neighbors = npred.getNeighborDBIDs(iditer);
for(DBIDIter iter = neighbors.iter(); iter.valid(); iter.advance()) {
if(DBIDUtil.equal(iditer, iter)) {
continue;
}
double dist = distFunc.distance(iditer, iter);
sum += dist;
cnt++;
maxDist = Math.max(maxDist, dist);
}
if(cnt > 1) {
modifiedDistance.putDouble(iditer, ((sum - maxDist) / (cnt - 1)));
}
else {
// Use regular distance when the d-tilde trick is undefined.
// Note: this can be 0 when there were no neighbors.
modifiedDistance.putDouble(iditer, maxDist);
}
}
// Second step - compute actual SLOM values
DoubleMinMax slomminmax = new DoubleMinMax();
WritableDoubleDataStore sloms = DataStoreUtil.makeDoubleStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC);
for(DBIDIter iditer = relation.iterDBIDs(); iditer.valid(); iditer.advance()) {
double sum = 0;
int cnt = 0;
final DBIDs neighbors = npred.getNeighborDBIDs(iditer);
for(DBIDIter iter = neighbors.iter(); iter.valid(); iter.advance()) {
if(DBIDUtil.equal(iditer, iter)) {
continue;
}
sum += modifiedDistance.doubleValue(iter);
cnt++;
}
double slom;
if(cnt > 0) {
// With and without the object itself:
double avgPlus = (sum + modifiedDistance.doubleValue(iditer)) / (cnt + 1);
double avg = sum / cnt;
double beta = 0;
for(DBIDIter iter = neighbors.iter(); iter.valid(); iter.advance()) {
final double dist = modifiedDistance.doubleValue(iter);
if(dist > avgPlus) {
beta += 1;
}
else if(dist < avgPlus) {
beta -= 1;
}
}
// Include object itself
if(!neighbors.contains(iditer)) {
final double dist = modifiedDistance.doubleValue(iditer);
if(dist > avgPlus) {
beta += 1;
}
else if(dist < avgPlus) {
beta -= 1;
}
}
beta = Math.abs(beta);
// note: cnt == size of N(x), not N+(x)
if(cnt > 1) {
beta = Math.max(beta, 1.0) / (cnt - 1);
}
else {
// Workaround insufficiency in SLOM paper - div by zero
beta = 1.0;
}
beta = beta / (1 + avg);
slom = beta * modifiedDistance.doubleValue(iditer);
}
else {
// No neighbors to compare to - no score.
slom = 0.0;
}
sloms.putDouble(iditer, slom);
slomminmax.put(slom);
}
DoubleRelation scoreResult = new MaterializedDoubleRelation("SLOM", "slom-outlier", sloms, relation.getDBIDs());
OutlierScoreMeta scoreMeta = new BasicOutlierScoreMeta(slomminmax.getMin(), slomminmax.getMax(), 0.0, Double.POSITIVE_INFINITY);
OutlierResult or = new OutlierResult(scoreMeta, scoreResult);
or.addChildResult(npred);
return or;
}
@Override
protected Logging getLogger() {
return LOG;
}
@Override
public TypeInformation[] getInputTypeRestriction() {
return TypeUtil.array(getNeighborSetPredicateFactory().getInputTypeRestriction(), TypeUtil.NUMBER_VECTOR_FIELD);
}
/**
* Parameterization class.
*
* @author Ahmed Hettab
*
* @apiviz.exclude
*
* @param <N> Neighborhood type
* @param <O> Data Object type
*/
public static class Parameterizer<N, O> extends AbstractDistanceBasedSpatialOutlier.Parameterizer<N, O> {
@Override
protected SLOM<N, O> makeInstance() {
return new SLOM<>(npredf, distanceFunction);
}
}
}
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