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) 2011
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.algorithm.outlier.spatial.neighborhood.NeighborSetPredicate.Factory;
import de.lmu.ifi.dbs.elki.data.NumberVector;
import de.lmu.ifi.dbs.elki.data.type.TypeInformation;
import de.lmu.ifi.dbs.elki.data.type.TypeUtil;
import de.lmu.ifi.dbs.elki.data.type.VectorFieldTypeInformation;
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.WritableDataStore;
import de.lmu.ifi.dbs.elki.database.ids.DBID;
import de.lmu.ifi.dbs.elki.database.relation.MaterializedRelation;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.logging.Logging;
import de.lmu.ifi.dbs.elki.math.DoubleMinMax;
import de.lmu.ifi.dbs.elki.math.Mean;
import de.lmu.ifi.dbs.elki.math.MeanVariance;
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;
/**
* Moran scatterplot outliers, based on the standardized deviation from the
* local and global means. In contrast to the definition given in the reference,
* we use this as a ranking outlier detection by not applying the signedness test,
* but by using the score (- localZ) * (Average localZ of Neighborhood) directly.
* This allows us to differentiate a bit between stronger and weaker outliers.
*
* <p>
* Reference: <br>
* S. Shekhar and C.-T. Lu and P. Zhang <br>
* A Unified Approach to Detecting Spatial Outliers <br>
* in GeoInformatica 7-2, 2003
*
* <p>
* Moran scatterplot is a plot of normalized attribute values against the
* neighborhood average of normalized attribute values. Spatial Objects on the
* upper left or lower right are Spatial Outliers.
*
* @author Ahmed Hettab
*
* @param <N> Neighborhood type
*/
@Title("Moran Scatterplot Outlier")
@Description("Spatial Outlier detection based on the standardized deviation from the local means.")
@Reference(authors = "S. Shekhar and C.-T. Lu and P. Zhang", title = "A Unified Approach to Detecting Spatial Outliers", booktitle = "GeoInformatica 7-2, 2003", url="http://dx.doi.org/10.1023/A:1023455925009")
public class CTLuMoranScatterplotOutlier<N> extends AbstractNeighborhoodOutlier<N> {
/**
* The logger for this class.
*/
private static final Logging logger = Logging.getLogger(CTLuMoranScatterplotOutlier.class);
/**
* Constructor
*
* @param npredf Neighborhood
*/
public CTLuMoranScatterplotOutlier(Factory<N> npredf) {
super(npredf);
}
/**
* Main method
*
* @param nrel Neighborhood relation
* @param relation Data relation (1d!)
* @return Outlier detection result
*/
public OutlierResult run(Relation<N> nrel, Relation<? extends NumberVector<?, ?>> relation) {
final NeighborSetPredicate npred = getNeighborSetPredicateFactory().instantiate(nrel);
// Compute the global mean and variance
MeanVariance globalmv = new MeanVariance();
for(DBID id : relation.iterDBIDs()) {
globalmv.put(relation.get(id).doubleValue(1));
}
DoubleMinMax minmax = new DoubleMinMax();
WritableDataStore<Double> scores = DataStoreUtil.makeStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC, Double.class);
// calculate normalized attribute values
// calculate neighborhood average of normalized attribute values.
for(DBID id : relation.iterDBIDs()) {
// Compute global z score
final double globalZ = (relation.get(id).doubleValue(1) - globalmv.getMean()) / globalmv.getNaiveStddev();
// Compute local average z score
Mean localm = new Mean();
for(DBID n : npred.getNeighborDBIDs(id)) {
if(id.equals(n)) {
continue;
}
localm.put((relation.get(n).doubleValue(1) - globalmv.getMean()) / globalmv.getNaiveStddev());
}
// if neighors.size == 0
final double localZ;
if(localm.getCount() > 0) {
localZ = localm.getMean();
}
else {
// if s has no neighbors => Wzi = zi
localZ = globalZ;
}
// compute score
// Note: in the original moran scatterplot, any object with a score < 0 would be an outlier.
final double score = Math.max(-globalZ * localZ, 0);
minmax.put(score);
scores.put(id, score);
}
Relation<Double> scoreResult = new MaterializedRelation<Double>("MoranOutlier", "Moran Scatterplot Outlier", TypeUtil.DOUBLE, scores, relation.getDBIDs());
OutlierScoreMeta scoreMeta = new BasicOutlierScoreMeta(minmax.getMin(), minmax.getMax(), Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY, 0);
OutlierResult or = new OutlierResult(scoreMeta, scoreResult);
or.addChildResult(npred);
return or;
}
@Override
public TypeInformation[] getInputTypeRestriction() {
return TypeUtil.array(getNeighborSetPredicateFactory().getInputTypeRestriction(), VectorFieldTypeInformation.get(NumberVector.class, 1));
}
@Override
protected Logging getLogger() {
return logger;
}
/**
* Parameterization class
*
* @author Ahmed Hettab
*
* @apiviz.exclude
*
* @param <N> Neighborhood object type
*/
public static class Parameterizer<N> extends AbstractNeighborhoodOutlier.Parameterizer<N> {
@Override
protected CTLuMoranScatterplotOutlier<N> makeInstance() {
return new CTLuMoranScatterplotOutlier<N>(npredf);
}
}
}