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package de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.meta;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2013
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.math.statistics.distribution.Distribution;
import de.lmu.ifi.dbs.elki.math.statistics.distribution.estimator.DistributionEstimator;
import de.lmu.ifi.dbs.elki.utilities.datastructures.QuickSelect;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.ArrayLikeUtil;
import de.lmu.ifi.dbs.elki.utilities.datastructures.arraylike.NumberArrayAdapter;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.AbstractParameterizer;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.OptionID;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.constraints.CommonConstraints;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.ObjectParameter;
/**
* Winsorising or Georgization estimator. Similar to trimming, this is expected
* to be more robust to outliers. However, instead of removing the extreme
* values, they are instead replaced with the cutoff value. This keeps the
* quantity of the data the same, and will have a lower impact on variance and
* similar measures.
*
* Reference:
* <p>
* C. Hastings, F. Mosteller, J. W. Tukey, C. P. Winsor<br />
* Low moments for small samples: a comparative study of order statistics.<br />
* The Annals of Mathematical Statistics, 18(3) *
* </p>
*
* @author Erich Schubert
*
* @apiviz.uses DistributionEstimator
*
* @param <D> Distribution type
*/
@Reference(authors = "C. Hastings, F. Mosteller, J. W. Tukey, C. P. Winsor", title = "Low moments for small samples: a comparative study of order statistics", booktitle = "The Annals of Mathematical Statistics, 18(3)", url = "http://dx.doi.org/10.1214/aoms/1177730388")
public class WinsorisingEstimator<D extends Distribution> implements DistributionEstimator<D> {
/**
* Distribution estimator to use.
*/
private DistributionEstimator<D> inner;
/**
* Amount of data to winsorize.
*/
private double winsorize;
/**
* Constructor.
*
* @param inner Inner estimator.
* @param winsorize Winsorize parameter.
*/
public WinsorisingEstimator(DistributionEstimator<D> inner, double winsorize) {
super();
this.inner = inner;
this.winsorize = winsorize;
}
@Override
public <A> D estimate(A data, NumberArrayAdapter<?, A> adapter) {
// We first need the basic parameters:
int len = adapter.size(data);
final int cut = ((int) (len * winsorize)) >> 1;
// X positions of samples
double[] x = new double[len];
for(int i = 0; i < len; i++) {
final double val = adapter.getDouble(data, i);
x[i] = val;
}
// Partially sort our copy.
double min = QuickSelect.quickSelect(x, 0, len, cut);
double max = QuickSelect.quickSelect(x, cut, len, len - 1 - cut);
// Winsorize by replacing the smallest and largest values.
// QuickSelect ensured that these are correctly in place.
for(int i = 0, j = len - 1; i < cut; i++, j--) {
x[i] = min;
x[j] = max;
}
return inner.estimate(x, ArrayLikeUtil.DOUBLEARRAYADAPTER);
}
@Override
public Class<? super D> getDistributionClass() {
return inner.getDistributionClass();
}
@Override
public String toString() {
return this.getClass().getSimpleName() + "(" + inner.toString() + ", trim=" + winsorize + ")";
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*
* @param <D> Distribution type
*/
public static class Parameterizer<D extends Distribution> extends AbstractParameterizer {
/**
* Option for the class to use on the winsorized sample.
*/
public static final OptionID INNER_ID = new OptionID("winsorize.inner", "Estimator to use on the winsorized data.");
/**
* Option for specifying the amount of data to winsorize.
*/
public static final OptionID WINSORIZE_ID = new OptionID("winsorize.winsorize", "Relative amount of data to winsorize on each end, must be 0 < winsorize < 0.5");
/**
* Distribution estimator to use.
*/
private DistributionEstimator<D> inner;
/**
* Amount of data to winsorize.
*/
private double winsorize;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
ObjectParameter<DistributionEstimator<D>> innerP = new ObjectParameter<>(INNER_ID, DistributionEstimator.class);
if(config.grab(innerP)) {
inner = innerP.instantiateClass(config);
}
DoubleParameter trimP = new DoubleParameter(WINSORIZE_ID);
trimP.addConstraint(CommonConstraints.GREATER_THAN_ZERO_DOUBLE);
trimP.addConstraint(CommonConstraints.LESS_THAN_HALF_DOUBLE);
if(config.grab(trimP)) {
winsorize = trimP.doubleValue();
}
}
@Override
protected WinsorisingEstimator<D> makeInstance() {
return new WinsorisingEstimator<>(inner, winsorize);
}
}
}
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