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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) 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.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.ids.DBIDs;
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.math.linearalgebra.CovarianceMatrix;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Matrix;
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;
/**
* Scatterplot-outlier is a spatial outlier detection method that performs a
* linear regression of object attributes and their neighbors average value.
*
* <p>
* Reference: <br>
* S. Shekhar and C.-T. Lu and P. Zhang <br>
* A Unified Approach to Detecting Spatial Outliers<br>
* in in GeoInformatica 7-2, 2003.
* </p>
*
* <p>
* Scatterplot shows attribute values on the X-axis and the average of the
* attribute values in the neighborhood on the Y-axis. Best fit regression line
* is used to identify spatial outliers. Vertical difference of a data point
* tells about outlierness.
* </p>
*
* @author Ahmed Hettab
*
* @param <N> Neighborhood object type
*/
@Title("Scatterplot Spatial Outlier")
@Description("Spatial Outlier Detection Algorithm using linear regression of attributes and the mean of their neighbors.")
@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 CTLuScatterplotOutlier<N> extends AbstractNeighborhoodOutlier<N> {
/**
* The logger for this class.
*/
private static final Logging logger = Logging.getLogger(CTLuScatterplotOutlier.class);
/**
* Constructor
*
* @param npredf Neighborhood predicate
*/
public CTLuScatterplotOutlier(NeighborSetPredicate.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);
WritableDataStore<Double> means = DataStoreUtil.makeStorage(relation.getDBIDs(), DataStoreFactory.HINT_TEMP, Double.class);
// Calculate average of neighborhood for each object and perform a linear
// regression using the covariance matrix
CovarianceMatrix covm = new CovarianceMatrix(2);
for(DBID id : relation.iterDBIDs()) {
final double local = relation.get(id).doubleValue(1);
// Compute mean of neighbors
Mean mean = new Mean();
DBIDs neighbors = npred.getNeighborDBIDs(id);
for(DBID n : neighbors) {
if(id.equals(n)) {
continue;
}
mean.put(relation.get(n).doubleValue(1));
}
final double m;
if(mean.getCount() > 0) {
m = mean.getMean();
}
else {
// if object id has no neighbors ==> avg = non-spatial attribute of id
m = local;
}
// Store the mean for the score calculation
means.put(id, m);
covm.put(new double[] { local, m });
}
// Finalize covariance matrix, compute linear regression
final double slope, inter;
{
double[] meanv = covm.getMeanVector().getArrayRef();
Matrix fmat = covm.destroyToSampleMatrix();
final double covxx = fmat.get(0, 0);
final double covxy = fmat.get(0, 1);
slope = covxy / covxx;
inter = meanv[1] - slope * meanv[0];
}
// calculate mean and variance for error
WritableDataStore<Double> scores = DataStoreUtil.makeStorage(relation.getDBIDs(), DataStoreFactory.HINT_STATIC, Double.class);
MeanVariance mv = new MeanVariance();
for(DBID id : relation.iterDBIDs()) {
// Compute the error from the linear regression
double y_i = relation.get(id).doubleValue(1);
double e = means.get(id) - (slope * y_i + inter);
scores.put(id, e);
mv.put(e);
}
// Normalize scores
DoubleMinMax minmax = new DoubleMinMax();
{
final double mean = mv.getMean();
final double variance = mv.getNaiveStddev();
for(DBID id : relation.iterDBIDs()) {
double score = Math.abs((scores.get(id) - mean) / variance);
minmax.put(score);
scores.put(id, score);
}
}
// build representation
Relation<Double> scoreResult = new MaterializedRelation<Double>("SPO", "Scatterplot-Outlier", TypeUtil.DOUBLE, scores, relation.getDBIDs());
OutlierScoreMeta scoreMeta = new BasicOutlierScoreMeta(minmax.getMin(), minmax.getMax(), 0.0, Double.POSITIVE_INFINITY, 0);
OutlierResult or = new OutlierResult(scoreMeta, scoreResult);
or.addChildResult(npred);
return or;
}
@Override
protected Logging getLogger() {
return logger;
}
@Override
public TypeInformation[] getInputTypeRestriction() {
return TypeUtil.array(getNeighborSetPredicateFactory().getInputTypeRestriction(), VectorFieldTypeInformation.get(NumberVector.class, 1));
}
/**
* Parameterization class
*
* @author Ahmed Hettab
*
* @apiviz.exclude
*
* @param <N> Neighborhood object type
*/
public static class Parameterizer<N> extends AbstractNeighborhoodOutlier.Parameterizer<N> {
@Override
protected CTLuScatterplotOutlier<N> makeInstance() {
return new CTLuScatterplotOutlier<N>(npredf);
}
}
}
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