/**
* Run the algorithm
*
* @param relation Data relation
* @return Outlier result
*/
public OutlierResult run(Relation<V> relation) {
DoubleMinMax mm = new DoubleMinMax();
// resulting scores
WritableDoubleDataStore oscores =
DataStoreUtil.makeDoubleStorage(
relation.getDBIDs(), DataStoreFactory.HINT_TEMP | DataStoreFactory.HINT_HOT);
// Compute mean and covariance Matrix
CovarianceMatrix temp = CovarianceMatrix.make(relation);
double[] mean = temp.getMeanVector(relation).toArray();
// debugFine(mean.toString());
Matrix covarianceMatrix = temp.destroyToNaiveMatrix();
// debugFine(covarianceMatrix.toString());
Matrix covarianceTransposed =
covarianceMatrix.cheatToAvoidSingularity(SINGULARITY_CHEAT).inverse();
// Normalization factors for Gaussian PDF
final double fakt =
(1.0
/ (Math.sqrt(
MathUtil.powi(MathUtil.TWOPI, RelationUtil.dimensionality(relation))
* covarianceMatrix.det())));
// for each object compute Mahalanobis distance
for (DBIDIter iditer = relation.iterDBIDs(); iditer.valid(); iditer.advance()) {
double[] x = minusEquals(relation.get(iditer).toArray(), mean);
// Gaussian PDF
final double mDist = transposeTimesTimes(x, covarianceTransposed, x);
final double prob = fakt * Math.exp(-mDist * .5);
mm.put(prob);
oscores.putDouble(iditer, prob);
}
final OutlierScoreMeta meta;
if (invert) {
double max = mm.getMax() != 0 ? mm.getMax() : 1.;
for (DBIDIter iditer = relation.iterDBIDs(); iditer.valid(); iditer.advance()) {
oscores.putDouble(iditer, (max - oscores.doubleValue(iditer)) / max);
}
meta = new BasicOutlierScoreMeta(0.0, 1.0);
} else {
meta = new InvertedOutlierScoreMeta(mm.getMin(), mm.getMax(), 0.0, Double.POSITIVE_INFINITY);
}
DoubleRelation res =
new MaterializedDoubleRelation(
"Gaussian Model Outlier Score", "gaussian-model-outlier", oscores, relation.getDBIDs());
return new OutlierResult(meta, res);
}
/**
* Compute optimal kernel bandwidth
*
* @param dim Dimensionality of subspace
* @return optimal bandwidth
*/
protected double optimalBandwidth(int dim) {
// Pi in the publication is redundant and cancels out!
double hopt = 8 * GammaDistribution.gamma(dim / 2.0 + 1) * (dim + 4) * MathUtil.powi(2, dim);
return hopt * Math.pow(relation.size(), (-1. / (dim + 4)));
}