de.lmu.ifi.dbs.elki.distance.distancefunction
Class KernelBasedLocallyWeightedDistanceFunction<V extends NumberVector<V,?>,P extends LocalPCAPreprocessor<V>>

java.lang.Object
  de.lmu.ifi.dbs.elki.logging.AbstractLoggable
      de.lmu.ifi.dbs.elki.distance.AbstractMeasurementFunction<O,D>
          de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractDistanceFunction<O,DoubleDistance>
              de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractLocallyWeightedDistanceFunction<V,P>
                  de.lmu.ifi.dbs.elki.distance.distancefunction.KernelBasedLocallyWeightedDistanceFunction<V,P>

Type Parameters:

V - the type of NumberVector to compute the distances in between

P - the type of Preprocessor used

All Implemented Interfaces:

DistanceFunction<V,DoubleDistance>, LocalPCAPreprocessorBasedDistanceFunction<V,P,DoubleDistance>, PreprocessorBasedDistanceFunction<V,P,DoubleDistance>, MeasurementFunction<V,DoubleDistance>, PreprocessorBasedMeasurementFunction<V,P,DoubleDistance>, PreprocessorClient<P,V>, Parameterizable

public class KernelBasedLocallyWeightedDistanceFunction<V extends NumberVector<V,?>,P extends LocalPCAPreprocessor<V>>
extends AbstractLocallyWeightedDistanceFunction<V,P>

Provides a kernel based locally weighted distance function. It is defined as follows: result = max{dist_P(P,Q), dist_Q(Q,P)}, where dist_P(P,Q) computes the quadratic form distance on the weak eigenvectors of the kernel matrix of P between two vectors P and Q in feature space. Computation of the distance component of the weak eigenvectors is done indirectly by computing the difference between the complete kernel distance and the distance component of the strong eigenvectors: dist_P(P,Q) = dist_{P_weak}(P,Q) = sqrt(dist_{P_complete}(P,Q)^2 - dist_{P_strong}(P,Q)^2) K_{P_complete}(P,Q) is the kernel derived distance between P and Q. The distance component of the strong eigenvectors K_{P_strong}(P,Q) is computed as follows: First, the vectors P and Q are projected onto the strong eigenvectors of the kernel matrix of P, which results in the two vectors P_p and Q_p. Then, the euclidean distance is used to compute the distance between P_p and Q_p. In case of the linear kernel function, this distance is identical to those computed by the LocallyWeightedDistanceFunction with parameters big = 1.0 and small = 0.0

Author:

Simon Paradies

Field Summary

static Class<?>	DEFAULT_KERNEL_FUNCTION_CLASS The default kernel function.
static OptionID	KERNEL_FUNCTION_ID OptionID for KERNEL_FUNCTION_PARAM
private ObjectParameter<KernelFunction<V,DoubleDistance>>	KERNEL_FUNCTION_PARAM Parameter for the kernel function
private KernelFunction<V,DoubleDistance>	kernelFunction The kernel function that is used.
private KernelMatrix<V>	kernelMatrix The global precomputed kernel matrix

Fields inherited from class de.lmu.ifi.dbs.elki.distance.AbstractMeasurementFunction

distanceFactory

Fields inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debug, logger

Constructor Summary

KernelBasedLocallyWeightedDistanceFunction(Parameterization config)
Constructor, adhering to Parameterizable

Method Summary

private double	computeDistance(V v1, V v2) Computes the distance between two given real vectors according to this distance function.
DoubleDistance	distance(V v1, V v2) Computes the distance between two given DatabaseObjects according to this distance function.
AssociationID<Matrix>	getAssociationID() Returns the association ID for the association to be set by the preprocessor.
void	setDatabase(Database<V> database) Set the database that holds the associations for the DatabaseObject for which the measurements should be computed.

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractLocallyWeightedDistanceFunction

getDefaultPreprocessorClass, getPreprocessorDescription, getPreprocessorSuperClass

Methods inherited from class de.lmu.ifi.dbs.elki.distance.distancefunction.AbstractDistanceFunction

distance, distance

Methods inherited from class de.lmu.ifi.dbs.elki.distance.AbstractMeasurementFunction

getDatabase, getDistanceFactory, infiniteDistance, nullDistance, undefinedDistance, valueOf

Methods inherited from class de.lmu.ifi.dbs.elki.logging.AbstractLoggable

debugFine, debugFiner, debugFinest, exception, progress, verbose, warning

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.distancefunction.DistanceFunction

distance, distance

Methods inherited from interface de.lmu.ifi.dbs.elki.distance.MeasurementFunction

getDistanceFactory, infiniteDistance, nullDistance, undefinedDistance, valueOf

Field Detail

DEFAULT_KERNEL_FUNCTION_CLASS

public static final Class<?> DEFAULT_KERNEL_FUNCTION_CLASS

The default kernel function.

KERNEL_FUNCTION_ID

public static final OptionID KERNEL_FUNCTION_ID

OptionID for KERNEL_FUNCTION_PARAM

KERNEL_FUNCTION_PARAM

private ObjectParameter<KernelFunction<V extends NumberVector<V,?>,DoubleDistance>> KERNEL_FUNCTION_PARAM

Parameter for the kernel function

kernelFunction

private KernelFunction<V extends NumberVector<V,?>,DoubleDistance> kernelFunction

The kernel function that is used.

kernelMatrix

private KernelMatrix<V extends NumberVector<V,?>> kernelMatrix

The global precomputed kernel matrix

Constructor Detail

KernelBasedLocallyWeightedDistanceFunction

public KernelBasedLocallyWeightedDistanceFunction(Parameterization config)

Constructor, adhering to Parameterizable

Parameters:

config - Parameterization

Method Detail

distance

public DoubleDistance distance(V v1,
                               V v2)

Computes the distance between two given DatabaseObjects according to this distance function.

Parameters:

v1 - first DatabaseObject

v2 - second DatabaseObject

Returns:

the distance between two given DatabaseObjects according to this distance function

computeDistance

private double computeDistance(V v1,
                               V v2)

Computes the distance between two given real vectors according to this distance function.

Parameters:

v1 - first FeatureVector

v2 - second FeatureVector

Returns:

the distance between two given real vectors according to this distance function

setDatabase

public void setDatabase(Database<V> database)

Description copied from interface: MeasurementFunction

Set the database that holds the associations for the DatabaseObject for which the measurements should be computed.

Specified by:

setDatabase in interface MeasurementFunction<V extends NumberVector<V,?>,DoubleDistance>

Overrides:

setDatabase in class AbstractLocallyWeightedDistanceFunction<V extends NumberVector<V,?>,P extends LocalPCAPreprocessor<V>>

Parameters:

database - Database

getAssociationID

public AssociationID<Matrix> getAssociationID()

Returns the association ID for the association to be set by the preprocessor.

Returns:

the association ID for the association to be set by the preprocessor, which is AssociationID.STRONG_EIGENVECTOR_MATRIX .