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.DoubleMinMax;
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;
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.parameterization.Parameterization;
import de.lmu.ifi.dbs.elki.utilities.optionhandling.parameters.DoubleParameter;
/**
* Scaling that can map arbitrary values to a probability in the range of [0:1].
*
* Transformation is done using the formulas
*
* {@code y = sqrt(x - min)}
*
* {@code newscore = max(0, erf(lambda * (y - mean) / (stddev * sqrt(2))))}
*
* Where min and 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 SqrtStandardDeviationScaling implements OutlierScalingFunction {
/**
* Parameter to specify the fixed minimum to use.
* <p>
* Key: {@code -sqrtstddevscale.min}
* </p>
*/
public static final OptionID MIN_ID = OptionID.getOrCreateOptionID("sqrtstddevscale.min", "Fixed minimum to use in sqrt scaling.");
/**
* Parameter to specify a fixed mean to use.
* <p>
* Key: {@code -sqrtstddevscale.mean}
* </p>
*/
public static final OptionID MEAN_ID = OptionID.getOrCreateOptionID("sqrtstddevscale.mean", "Fixed mean to use in standard deviation scaling.");
/**
* Parameter to specify the lambda value
* <p>
* Key: {@code -sqrtstddevscale.lambda}
* </p>
*/
public static final OptionID LAMBDA_ID = OptionID.getOrCreateOptionID("sqrtstddevscale.lambda", "Significance level to use for error function.");
/**
* Field storing the lambda value
*/
protected Double lambda = null;
/**
* Min to use
*/
Double min = null;
/**
* Mean to use
*/
Double mean = null;
/**
* Scaling factor to use (usually: Lambda * Stddev * Sqrt(2))
*/
double factor;
/**
* Constructor.
*
* @param min
* @param mean
* @param lambda
*/
public SqrtStandardDeviationScaling(Double min, Double mean, Double lambda) {
super();
this.min = min;
this.mean = mean;
this.lambda = lambda;
}
@Override
public double getScaled(double value) {
assert (factor != 0) : "prepare() was not run prior to using the scaling function.";
if(value <= min) {
return 0;
}
value = (value <= min) ? 0 : Math.sqrt(value - min);
if(value <= mean) {
return 0;
}
return Math.max(0, NormalDistribution.erf((value - mean) / factor));
}
@Override
public void prepare(OutlierResult or) {
if(min == null) {
DoubleMinMax mm = new DoubleMinMax();
for(DBID id : or.getScores().iterDBIDs()) {
double val = or.getScores().get(id);
if(!Double.isNaN(val) && !Double.isInfinite(val)) {
mm.put(val);
}
}
min = mm.getMin();
}
if(mean == null) {
MeanVariance mv = new MeanVariance();
for(DBID id : or.getScores().iterDBIDs()) {
double val = or.getScores().get(id);
val = (val <= min) ? 0 : Math.sqrt(val - min);
mv.put(val);
}
mean = mv.getMean();
factor = lambda * mv.getSampleStddev() * MathUtil.SQRT2;
}
else {
double sqsum = 0;
int cnt = 0;
for(DBID id : or.getScores().iterDBIDs()) {
double val = or.getScores().get(id);
val = (val <= min) ? 0 : Math.sqrt(val - min);
sqsum += (val - mean) * (val - mean);
cnt += 1;
}
factor = lambda * Math.sqrt(sqsum / cnt) * MathUtil.SQRT2;
}
}
@Override
public double getMin() {
return 0.0;
}
@Override
public double getMax() {
return 1.0;
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractParameterizer {
protected Double min = null;
protected Double mean = null;
protected Double lambda = null;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
DoubleParameter minP = new DoubleParameter(MIN_ID, true);
if(config.grab(minP)) {
min = minP.getValue();
}
DoubleParameter meanP = new DoubleParameter(MEAN_ID, true);
if(config.grab(meanP)) {
mean = meanP.getValue();
}
DoubleParameter lambdaP = new DoubleParameter(LAMBDA_ID, 3.0);
if(config.grab(lambdaP)) {
lambda = lambdaP.getValue();
}
}
@Override
protected SqrtStandardDeviationScaling makeInstance() {
return new SqrtStandardDeviationScaling(min, mean, lambda);
}
}
}