Package elki.distance.minkowski

Class LPNormDistance

java.lang.Object

elki.distance.minkowski.LPNormDistance

All Implemented Interfaces:

Distance<NumberVector>, Norm<NumberVector>, NumberVectorDistance<NumberVector>, PrimitiveDistance<NumberVector>, SpatialPrimitiveDistance<NumberVector>

Direct Known Subclasses:

LPIntegerNormDistance, MaximumDistance, WeightedLPNormDistance

@Priority(200)
@Alias({"lp","minkowski","p"})
public class LPNormDistance
extends java.lang.Object
implements SpatialPrimitiveDistance<NumberVector>, NumberVectorDistance<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 ManhattanDistance, for p = 2 the standard EuclideanDistance.

Since:

0.1

Author:

Arthur Zimek

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	LPNormDistance.Par	Parameterization class.

Field Summary

Fields

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

Constructor Summary

Constructors

Constructor	Description
LPNormDistance(double p)	Constructor, internal version.

Method Summary

Modifier and Type	Method	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	getInvP()	Get the functions 1/p parameter.
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 elki.distance.Distance

isSquared, isSymmetric

Methods inherited from interface elki.distance.SpatialPrimitiveDistance

instantiate

Field Detail

p

protected double p

p parameter and its inverse.

invp

protected double invp

p parameter and its inverse.

Constructor Detail

LPNormDistance

public LPNormDistance(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: PrimitiveDistance

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

Specified by:

distance in interface NumberVectorDistance<NumberVector>

Specified by:

distance in interface PrimitiveDistance<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: SpatialPrimitiveDistance

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

Specified by:

minDist in interface SpatialPrimitiveDistance<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: Distance

Is this distance function metric (satisfy the triangle inequality)

Specified by:

isMetric in interface Distance<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

getInvP

public double getInvP()

Get the functions 1/p parameter.

Returns:

1/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: Distance

Get the input data type of the function.

Specified by:

getInputTypeRestriction in interface Distance<NumberVector>

Specified by:

getInputTypeRestriction in interface PrimitiveDistance<NumberVector>

Returns:

Type restriction