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package de.lmu.ifi.dbs.elki.distance.distancefunction.histogram;
/*
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.spatial.SpatialComparable;
import de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractSpatialDistanceFunction;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
/**
* Distance function based on histogram matching, i.e. Manhattan distance on the
* cumulative density function.
*
* This distance function assumes there exist a natural order in the vectors,
* i.e. they should be some 1-dimensional histogram.
*
* This is also known as Earth Movers Distance (EMD), 1st Mallows distance or
* 1st Wasserstein metric (also Vasershtein metric), for the special case of a
* one-dimensional histogram, where the cost is linear in the number of bins to
* transport.
*
* Reference:
* <p>
* L.N. Vaserstein<br />
* Markov processes over denumerable products of spaces describing large systems
* of automata <br />
* Problemy Peredachi Informatsii 5.3 / Problems of Information Transmission 5:3
* </p>
*
* @author Erich Schubert
*/
@Reference(authors = "L.N. Vaserstein", //
title = "Markov processes over denumerable products of spaces describing large systems of automata", //
booktitle = "Problemy Peredachi Informatsii 5.3 / Problems of Information Transmission, 5:3", //
url = "http://mi.mathnet.ru/eng/ppi1811")
public class HistogramMatchDistanceFunction extends AbstractSpatialDistanceFunction {
/**
* Static instance. Use this!
*/
public static final HistogramMatchDistanceFunction STATIC = new HistogramMatchDistanceFunction();
/**
* Constructor for the Histogram match distance function.
*
* @deprecated Use static instance!
*/
@Deprecated
public HistogramMatchDistanceFunction() {
super();
}
@Override
public double distance(NumberVector v1, NumberVector v2) {
final int dim = dimensionality(v1, v2);
double xs = 0., ys = 0., agg = 0.;
for(int i = 0; i < dim; i++) {
xs += v1.doubleValue(i);
ys += v2.doubleValue(i);
agg += Math.abs(xs - ys);
}
return agg;
}
@Override
public double minDist(SpatialComparable mbr1, SpatialComparable mbr2) {
final int dim = dimensionality(mbr1, mbr2);
double xmin = 0., xmax = 0., ymin = 0., ymax = 0., agg = 0.;
for(int i = 0; i < dim; i++) {
xmin += mbr1.getMin(i);
xmax += mbr1.getMax(i);
ymin += mbr2.getMin(i);
ymax += mbr2.getMax(i);
agg += (ymin > xmax) ? (ymin - xmax) : (xmin > ymax) ? (xmin - ymax) : 0.;
}
return agg;
}
@Override
public boolean isMetric() {
return true;
}
@Override
public String toString() {
return "HistogramMatchDistanceFunction";
}
@Override
public boolean equals(Object obj) {
if(obj == null) {
return false;
}
if(obj == this) {
return true;
}
if(this.getClass().equals(obj.getClass())) {
return true;
}
return super.equals(obj);
}
/**
* Parameterization class, using the static instance.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
@Override
protected HistogramMatchDistanceFunction makeInstance() {
return STATIC;
}
}
}
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