package de.lmu.ifi.dbs.elki.utilities.scaling.outlier;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2012
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.database.ids.DBID;
import de.lmu.ifi.dbs.elki.math.MathUtil;
import de.lmu.ifi.dbs.elki.math.MeanVariance;
import de.lmu.ifi.dbs.elki.math.statistics.distribution.NormalDistribution;
import de.lmu.ifi.dbs.elki.result.outlier.OutlierResult;
import de.lmu.ifi.dbs.elki.utilities.documentation.Reference;
/**
* Scaling that can map arbitrary values to a probability in the range of [0:1].
*
* Transformation is done using the formula max(0, erf(lambda * (x - mean) /
* (stddev * sqrt(2))))
*
* Where mean can be fixed to a given value, and stddev is then computed against
* this mean.
*
* @author Erich Schubert
*/
@Reference(authors="H.-P. Kriegel, P. Kröger, E. Schubert, A. Zimek", title="Interpreting and Unifying Outlier Scores", booktitle="Proc. 11th SIAM International Conference on Data Mining (SDM), Mesa, AZ, 2011", url="http://siam.omnibooksonline.com/2011datamining/data/papers/018.pdf")
public class MinusLogStandardDeviationScaling extends StandardDeviationScaling {
/**
* Constructor.
*
* @param fixedmean
* @param lambda
*/
public MinusLogStandardDeviationScaling(Double fixedmean, Double lambda) {
super(fixedmean, lambda);
}
@Override
public double getScaled(double value) {
assert (factor != 0) : "prepare() was not run prior to using the scaling function.";
final double mlogv = -Math.log(value);
if(mlogv < mean || Double.isNaN(mlogv)) {
return 0.0;
}
return Math.max(0.0, NormalDistribution.erf((mlogv - mean) / factor));
}
@Override
public void prepare(OutlierResult or) {
if(fixedmean == null) {
MeanVariance mv = new MeanVariance();
for(DBID id : or.getScores().iterDBIDs()) {
double val = -Math.log(or.getScores().get(id));
if(!Double.isNaN(val) && !Double.isInfinite(val)) {
mv.put(val);
}
}
mean = mv.getMean();
factor = lambda * mv.getSampleStddev() * MathUtil.SQRT2;
}
else {
mean = fixedmean;
double sqsum = 0;
int cnt = 0;
for(DBID id : or.getScores().iterDBIDs()) {
double val = -Math.log(or.getScores().get(id));
if(!Double.isNaN(val) && !Double.isInfinite(val)) {
sqsum += (val - mean) * (val - mean);
cnt += 1;
}
}
factor = lambda * Math.sqrt(sqsum / cnt) * MathUtil.SQRT2;
}
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends StandardDeviationScaling.Parameterizer {
@Override
protected MinusLogStandardDeviationScaling makeInstance() {
return new MinusLogStandardDeviationScaling(fixedmean, lambda);
}
}
}