>, BitDistance> {
/**
* Logger for debug.
*/
static Logging logger = Logging.getLogger(PCABasedCorrelationDistanceFunction.class);
/**
* Parameter to specify the threshold for approximate linear dependency: the
* strong eigenvectors of q are approximately linear dependent from the strong
* eigenvectors p if the following condition holds for all strong eigenvectors
* q_i of q (lambda_q < lambda_p): q_i' * M^check_p * q_i <= delta^2, must be
* a double equal to or greater than 0.
*
* Default value: {@code 0.1}
*
*
* Key: {@code -ericdf.delta}
*
*/
public static final OptionID DELTA_ID = OptionID.getOrCreateOptionID("ericdf.delta", "Threshold for approximate linear dependency: " + "the strong eigenvectors of q are approximately linear dependent " + "from the strong eigenvectors p if the following condition " + "holds for all stroneg eigenvectors q_i of q (lambda_q < lambda_p): " + "q_i' * M^check_p * q_i <= delta^2.");
/**
* Parameter to specify the threshold for the maximum distance between two
* approximately linear dependent subspaces of two objects p and q (lambda_q <
* lambda_p) before considering them as parallel, must be a double equal to or
* greater than 0.
*
* Default value: {@code 0.1}
*
*
* Key: {@code -ericdf.tau}
*
*/
public static final OptionID TAU_ID = OptionID.getOrCreateOptionID("ericdf.tau", "Threshold for the maximum distance between two approximately linear " + "dependent subspaces of two objects p and q " + "(lambda_q < lambda_p) before considering them as parallel.");
/**
* Holds the value of {@link #DELTA_ID}.
*/
private double delta;
/**
* Holds the value of {@link #TAU_ID}.
*/
private double tau;
/**
* Constructor.
*
* @param indexFactory Index factory.
* @param delta Delta parameter
* @param tau Tau parameter
*/
public ERiCDistanceFunction(IndexFactory, FilteredLocalPCAIndex>> indexFactory, double delta, double tau) {
super(indexFactory);
this.delta = delta;
this.tau = tau;
}
@Override
public BitDistance getDistanceFactory() {
return BitDistance.FACTORY;
}
@Override
public > Instance instantiate(Relation database) {
// We can't really avoid these warnings, due to a limitation in Java
// Generics (AFAICT)
@SuppressWarnings("unchecked")
FilteredLocalPCAIndex indexinst = (FilteredLocalPCAIndex) indexFactory.instantiate((Relation>) database);
return new Instance(database, indexinst, this, delta, tau);
}
/**
* Returns true, if the strong eigenvectors of the two specified pcas span up
* the same space. Note, that the first pca must have equal ore more strong
* eigenvectors than the second pca.
*
* @param pca1 first PCA
* @param pca2 second PCA
* @return true, if the strong eigenvectors of the two specified pcas span up
* the same space
*/
private boolean approximatelyLinearDependent(PCAFilteredResult pca1, PCAFilteredResult pca2) {
Matrix m1_czech = pca1.dissimilarityMatrix();
Matrix v2_strong = pca2.adapatedStrongEigenvectors();
for(int i = 0; i < v2_strong.getColumnDimensionality(); i++) {
Vector v2_i = v2_strong.getCol(i);
// check, if distance of v2_i to the space of pca_1 > delta
// (i.e., if v2_i spans up a new dimension)
double dist = Math.sqrt(v2_i.transposeTimes(v2_i) - v2_i.transposeTimesTimes(m1_czech, v2_i));
// if so, return false
if(dist > delta) {
return false;
}
}
return true;
}
/**
* Computes the distance between two given DatabaseObjects according to this
* distance function. Note, that the first pca must have equal or more strong
* eigenvectors than the second pca.
*
* @param v1 first DatabaseObject
* @param v2 second DatabaseObject
* @param pca1 first PCA
* @param pca2 second PCA
* @return the distance between two given DatabaseObjects according to this
* distance function
*/
public BitDistance distance(NumberVector v1, NumberVector v2, PCAFilteredResult pca1, PCAFilteredResult pca2) {
if(pca1.getCorrelationDimension() < pca2.getCorrelationDimension()) {
throw new IllegalStateException("pca1.getCorrelationDimension() < pca2.getCorrelationDimension(): " + pca1.getCorrelationDimension() + " < " + pca2.getCorrelationDimension());
}
boolean approximatelyLinearDependent;
if(pca1.getCorrelationDimension() == pca2.getCorrelationDimension()) {
approximatelyLinearDependent = approximatelyLinearDependent(pca1, pca2) && approximatelyLinearDependent(pca2, pca1);
}
else {
approximatelyLinearDependent = approximatelyLinearDependent(pca1, pca2);
}
if(!approximatelyLinearDependent) {
return new BitDistance(true);
}
else {
double affineDistance;
if(pca1.getCorrelationDimension() == pca2.getCorrelationDimension()) {
WeightedDistanceFunction df1 = new WeightedDistanceFunction(pca1.similarityMatrix());
WeightedDistanceFunction df2 = new WeightedDistanceFunction(pca2.similarityMatrix());
affineDistance = Math.max(df1.distance(v1, v2).doubleValue(), df2.distance(v1, v2).doubleValue());
}
else {
WeightedDistanceFunction df1 = new WeightedDistanceFunction(pca1.similarityMatrix());
affineDistance = df1.distance(v1, v2).doubleValue();
}
if(affineDistance > tau) {
return new BitDistance(true);
}
return new BitDistance(false);
}
}
@Override
public boolean equals(Object obj) {
if(obj == null) {
return false;
}
if (!this.getClass().equals(obj.getClass())) {
return false;
}
ERiCDistanceFunction other = (ERiCDistanceFunction) obj;
return (this.delta == other.delta) && (this.tau == other.tau);
}
/**
* The actual instance bound to a particular database.
*
* @author Erich Schubert
*/
public static class Instance> extends AbstractIndexBasedDistanceFunction.Instance, BitDistance, ERiCDistanceFunction> implements FilteredLocalPCABasedDistanceFunction.Instance, BitDistance> {
/**
* Holds the value of {@link #DELTA_ID}.
*/
private final double delta;
/**
* Holds the value of {@link #TAU_ID}.
*/
private final double tau;
/**
* Constructor.
*
* @param database Database
* @param index Index
* @param parent Parent distance
* @param delta Delta parameter
* @param tau Tau parameter
*/
public Instance(Relation database, FilteredLocalPCAIndex index, ERiCDistanceFunction parent, double delta, double tau) {
super(database, index, parent);
this.delta = delta;
this.tau = tau;
}
/**
* Note, that the pca of o1 must have equal ore more strong eigenvectors
* than the pca of o2.
*/
@Override
public BitDistance distance(DBID id1, DBID id2) {
PCAFilteredResult pca1 = index.getLocalProjection(id1);
PCAFilteredResult pca2 = index.getLocalProjection(id2);
V v1 = relation.get(id1);
V v2 = relation.get(id2);
return parent.distance(v1, v2, pca1, pca2);
}
}
/**
* Parameterization class.
*
* @author Erich Schubert
*
* @apiviz.exclude
*/
public static class Parameterizer extends AbstractIndexBasedDistanceFunction.Parameterizer, FilteredLocalPCAIndex>>> {
double delta = 0.0;
double tau = 0.0;
@Override
protected void makeOptions(Parameterization config) {
super.makeOptions(config);
configIndexFactory(config, FilteredLocalPCAIndex.Factory.class, KNNQueryFilteredPCAIndex.Factory.class);
final DoubleParameter deltaP = new DoubleParameter(DELTA_ID, new GreaterEqualConstraint(0), 0.1);
if(config.grab(deltaP)) {
delta = deltaP.getValue();
}
final DoubleParameter tauP = new DoubleParameter(TAU_ID, new GreaterEqualConstraint(0), 0.1);
if(config.grab(tauP)) {
tau = tauP.getValue();
}
}
@Override
protected ERiCDistanceFunction makeInstance() {
return new ERiCDistanceFunction(factory, delta, tau);
}
}
}