de.lmu.ifi.dbs.elki.distance.distancefunction.minkowski

Class LPNormDistanceFunction

java.lang.Object

de.lmu.ifi.dbs.elki.distance.distancefunction.minkowski.LPNormDistanceFunction

All Implemented Interfaces:

DistanceFunction<NumberVector>, Norm<NumberVector>, NumberVectorDistanceFunction<NumberVector>, PrimitiveDistanceFunction<NumberVector>, SpatialPrimitiveDistanceFunction<NumberVector>

Direct Known Subclasses:

LPIntegerNormDistanceFunction, MaximumDistanceFunction, WeightedLPNormDistanceFunction

@Priority(value=200)
 @Alias(value={"lp","minkowski","p","de.lmu.ifi.dbs.elki.distance.distancefunction.LPNormDistanceFunction"})
public class LPNormDistanceFunction
extends java.lang.Object
implements SpatialPrimitiveDistanceFunction<NumberVector>, NumberVectorDistanceFunction<NumberVector>, Norm<NumberVector>

L_p-Norm (Minkowski norms) are a family of distances for NumberVectors.

The L_p distance is defined as: \[ L_p(\vec{x},\vec{y}) := \left(\sum\nolimits_i (x_i-y_i)\right)^{1/p} \]

For p >= 1 this is a metric. For p=1, this yields the well known ManhattanDistanceFunction, for p = 2 the standard EuclideanDistanceFunction.

Since:

0.1

Author:

Arthur Zimek

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	LPNormDistanceFunction.Parameterizer Parameterization class.

Field Summary

Fields

Modifier and Type	Field and Description
protected double	invp p parameter and its inverse.
protected double	p p parameter and its inverse.

Constructor Summary

Constructors

Constructor and Description
LPNormDistanceFunction(double p) Constructor, internal version.

Method Summary

Modifier and Type	Method and Description
double	distance(NumberVector v1, NumberVector v2) Computes the distance between two given DatabaseObjects according to this distance function.
boolean	equals(java.lang.Object obj)
SimpleTypeInformation<? super NumberVector>	getInputTypeRestriction() Get the input data type of the function.
double	getP() Get the functions p parameter.
int	hashCode()
boolean	isMetric() Is this distance function metric (satisfy the triangle inequality)
double	minDist(SpatialComparable mbr1, SpatialComparable mbr2) Computes the distance between the two given MBRs according to this distance function.
double	norm(NumberVector v) Compute the norm of object obj.
private double	preDistance(NumberVector v1, NumberVector v2, int start, int end) Compute unscaled distance in a range of dimensions.
private double	preDistanceMBR(SpatialComparable mbr1, SpatialComparable mbr2, int start, int end) Compute unscaled distance in a range of dimensions.
private double	preDistanceVM(NumberVector v, SpatialComparable mbr, int start, int end) Compute unscaled distance in a range of dimensions.
private double	preNorm(NumberVector v, int start, int end) Compute unscaled norm in a range of dimensions.
private double	preNormMBR(SpatialComparable mbr, int start, int end) Compute unscaled norm in a range of dimensions.
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

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

instantiate

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

isSquared, isSymmetric

Field Detail

p

protected double p

p parameter and its inverse.

invp

protected double invp

p parameter and its inverse.

Constructor Detail

LPNormDistanceFunction

public LPNormDistanceFunction(double p)

Constructor, internal version.

Parameters:

p - Parameter p

Method Detail

preDistance

private double preDistance(NumberVector v1,
                           NumberVector v2,
                           int start,
                           int end)

Compute unscaled distance in a range of dimensions.

Parameters:

v1 - First object

v2 - Second object

start - First dimension

end - Exclusive last dimension

Returns:

Aggregated values.

preDistanceVM

private double preDistanceVM(NumberVector v,
                             SpatialComparable mbr,
                             int start,
                             int end)

Compute unscaled distance in a range of dimensions.

Parameters:

v - First vector

mbr - Second MBR

start - First dimension

end - Exclusive last dimension

Returns:

Aggregated values.

preDistanceMBR

private double preDistanceMBR(SpatialComparable mbr1,
                              SpatialComparable mbr2,
                              int start,
                              int end)

Compute unscaled distance in a range of dimensions.

Parameters:

mbr1 - First MBR

mbr2 - Second MBR

start - First dimension

end - Exclusive last dimension

Returns:

Aggregated values.

preNorm

private double preNorm(NumberVector v,
                       int start,
                       int end)

Compute unscaled norm in a range of dimensions.

Parameters:

v - Data object

start - First dimension

end - Exclusive last dimension

Returns:

Aggregated values.

preNormMBR

private double preNormMBR(SpatialComparable mbr,
                          int start,
                          int end)

Compute unscaled norm in a range of dimensions.

Parameters:

mbr - Data object

start - First dimension

end - Exclusive last dimension

Returns:

Aggregated values.

distance

public double distance(NumberVector v1,
                       NumberVector v2)

Description copied from interface: PrimitiveDistanceFunction

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

Specified by:

distance in interface NumberVectorDistanceFunction<NumberVector>

Specified by:

distance in interface PrimitiveDistanceFunction<NumberVector>

Parameters:

v1 - first DatabaseObject

v2 - second DatabaseObject

Returns:

the distance between two given DatabaseObjects according to this distance function

norm

public double norm(NumberVector v)

Description copied from interface: Norm

Compute the norm of object obj.

Specified by:

norm in interface Norm<NumberVector>

Parameters:

v - Object

Returns:

Norm

minDist

public double minDist(SpatialComparable mbr1,
                      SpatialComparable mbr2)

Description copied from interface: SpatialPrimitiveDistanceFunction

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

Specified by:

minDist in interface SpatialPrimitiveDistanceFunction<NumberVector>

Parameters:

mbr1 - the first MBR object

mbr2 - the second MBR object

Returns:

the distance between the two given MBRs according to this distance function

isMetric

public boolean isMetric()

Description copied from interface: DistanceFunction

Is this distance function metric (satisfy the triangle inequality)

Specified by:

isMetric in interface DistanceFunction<NumberVector>

Returns:

true when metric.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

getP

public double getP()

Get the functions p parameter.

Returns:

p

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

getInputTypeRestriction

public SimpleTypeInformation<? super NumberVector> getInputTypeRestriction()

Description copied from interface: DistanceFunction

Get the input data type of the function.

Specified by:

getInputTypeRestriction in interface DistanceFunction<NumberVector>

Specified by:

getInputTypeRestriction in interface PrimitiveDistanceFunction<NumberVector>

Returns:

Type restriction