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package de.lmu.ifi.dbs.elki.distance.distancefunction.probabilistic;
/*
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.data.NumberVector;
import de.lmu.ifi.dbs.elki.data.type.SimpleTypeInformation;
import de.lmu.ifi.dbs.elki.data.type.TypeUtil;
import de.lmu.ifi.dbs.elki.database.query.DistanceSimilarityQuery;
import de.lmu.ifi.dbs.elki.database.query.distance.PrimitiveDistanceSimilarityQuery;
import de.lmu.ifi.dbs.elki.database.relation.Relation;
import de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractNumberVectorDistanceFunction;
import de.lmu.ifi.dbs.elki.distance.similarityfunction.PrimitiveSimilarityFunction;
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.utilities.Alias;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Hellinger kernel / Hellinger distance are used with SIFT vectors, and also
* known as Bhattacharyya distance / coefficient.
*
* This distance is appropriate for histograms, and is equal to A) L1
* normalizing the vectors and then B) using Euclidean distance. As this is
* usually much faster, this is the recommended way of handling such data.
*
* Reference:
* <p>
* E. Hellinger<br />
* Neue Begründung der Theorie quadratischer Formen von unendlichvielen
* Veränderlichen<br />
* Journal für die reine und angewandte Mathematik
* </p>
*
* TODO: support acceleration for sparse vectors
*
* @author Erich Schubert
* @since 0.7.0
*/
@Reference(authors = "E. Hellinger", //
title = "Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen", //
booktitle = "Journal für die reine und angewandte Mathematik ", //
url = "http://resolver.sub.uni-goettingen.de/purl?GDZPPN002166941")
@Alias({ "hellinger", "bhattacharyya" })
public class HellingerDistanceFunction extends AbstractNumberVectorDistanceFunction implements PrimitiveSimilarityFunction<NumberVector> {
/**
* Static instance.
*/
public static final HellingerDistanceFunction STATIC = new HellingerDistanceFunction();
/**
* Hellinger kernel. Use static instance {@link #STATIC}!
*/
@Deprecated
public HellingerDistanceFunction() {
super();
}
@Override
public double distance(final NumberVector fv1, final NumberVector fv2) {
final int dim1 = fv1.getDimensionality(), dim2 = fv2.getDimensionality();
final int mindim = (dim1 < dim2) ? dim1 : dim2;
double agg = 0.;
for(int d = 0; d < mindim; d++) {
final double v = Math.sqrt(fv1.doubleValue(d)) - Math.sqrt(fv2.doubleValue(d));
agg += v * v;
}
for(int d = mindim; d < dim1; d++) {
agg += Math.abs(fv1.doubleValue(d));
}
for(int d = mindim; d < dim2; d++) {
agg += Math.abs(fv2.doubleValue(d));
}
return MathUtil.SQRTHALF * Math.sqrt(agg);
}
@Override
public double similarity(final NumberVector o1, final NumberVector o2) {
// TODO: accelerate sparse!
final int dim1 = o1.getDimensionality(), dim2 = o2.getDimensionality();
final int mindim = (dim1 < dim2) ? dim1 : dim2;
double agg = 0.;
for(int d = 0; d < mindim; d++) {
agg += Math.sqrt(o1.doubleValue(d) * o2.doubleValue(d));
}
return agg;
}
@Override
public boolean isMetric() {
return true; // as this equals Euclidean in sqrt space
}
@Override
public <T extends NumberVector> DistanceSimilarityQuery<T> instantiate(Relation<T> database) {
return new PrimitiveDistanceSimilarityQuery<>(database, this, this);
}
@Override
public SimpleTypeInformation<? super NumberVector> getInputTypeRestriction() {
return TypeUtil.NUMBER_VECTOR_VARIABLE_LENGTH;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected HellingerDistanceFunction makeInstance() {
return HellingerDistanceFunction.STATIC;
}
}
}
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