Package elki.distance.set

Class JaccardSimilarityDistance

java.lang.Object

elki.distance.set.AbstractSetDistance<FeatureVector<?>>

elki.distance.set.JaccardSimilarityDistance

All Implemented Interfaces:

Distance<FeatureVector<?>>, NumberVectorDistance<FeatureVector<?>>, PrimitiveDistance<FeatureVector<?>>, NormalizedPrimitiveSimilarity<FeatureVector<?>>, NormalizedSimilarity<FeatureVector<?>>, PrimitiveSimilarity<FeatureVector<?>>, Similarity<FeatureVector<?>>

@Reference(authors="P. Jaccard",
           title="Distribution de la florine alpine dans la Bassin de Dranses et dans quelques regiones voisines",
           booktitle="Bulletin del la Soci\u00e9t\u00e9 Vaudoise des Sciences Naturelles",
           url="http://data.rero.ch/01-R241574160",
           bibkey="journals/misc/Jaccard1902")
public class JaccardSimilarityDistance
extends AbstractSetDistance<FeatureVector<?>>
implements NormalizedPrimitiveSimilarity<FeatureVector<?>>, NumberVectorDistance<FeatureVector<?>>, PrimitiveDistance<FeatureVector<?>>

A flexible extension of Jaccard similarity to non-binary vectors.

Jaccard coefficient is commonly defined as \(\frac{A\cap B}{A\cup B}\).

We can extend this definition to non-binary vectors as follows: \(\tfrac{|\{i\mid a_i = b_i\}|}{|\{i\mid a_i = 0 \wedge b_i = 0\}|}\)

For binary vectors, this will obviously be the same quantity. However, this version is more useful for categorical data.

Reference:

P. Jaccard
Distribution de la florine alpine dans la Bassin de Dranses et dans quelques regiones voisines
Bulletin del la Société Vaudoise des Sciences Naturelles

Since:

0.6.0

Author:

Erich Schubert

Field Summary

Fields inherited from class elki.distance.set.AbstractSetDistance

DOUBLE_NULL, INTEGER_NULL, STRING_NULL

Constructor Summary

Constructors

Constructor	Description
JaccardSimilarityDistance()	Constructor.

Method Summary

Modifier and Type	Method	Description
double	distance(FeatureVector<?> o1, FeatureVector<?> o2)	Computes the distance between two given DatabaseObjects according to this distance function.
double	distance(NumberVector o1, NumberVector o2)	Computes the distance between two given vectors according to this distance function.
boolean	equals(java.lang.Object obj)
SimpleTypeInformation<? super FeatureVector<?>>	getInputTypeRestriction()	Get the input data type of the function.
int	hashCode()
<T extends FeatureVector<?>> DistanceSimilarityQuery<T>	instantiate(Relation<T> relation)	Instantiate with a representation to get the actual similarity query.
boolean	isMetric()	Is this distance function metric (satisfy the triangle inequality)
boolean	isSymmetric()	Is this function symmetric?
double	similarity(FeatureVector<?> o1, FeatureVector<?> o2)	Computes the similarity between two given DatabaseObjects according to this similarity function.
static double	similarityNumberVector(NumberVector o1, NumberVector o2)	Compute Jaccard similarity for two number vectors.

Methods inherited from class elki.distance.set.AbstractSetDistance

isNull

Methods inherited from class java.lang.Object

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

Methods inherited from interface elki.distance.Distance

isSquared

Constructor Detail

JaccardSimilarityDistance

public JaccardSimilarityDistance()

Constructor. No parameters.

Method Detail

similarity

public double similarity(FeatureVector<?> o1,
                         FeatureVector<?> o2)

Description copied from interface: PrimitiveSimilarity

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

Specified by:

similarity in interface PrimitiveSimilarity<FeatureVector<?>>

Parameters:

o1 - first DatabaseObject

o2 - second DatabaseObject

Returns:

the similarity between two given DatabaseObjects according to this similarity function

similarityNumberVector

public static double similarityNumberVector(NumberVector o1,
                                            NumberVector o2)

Compute Jaccard similarity for two number vectors.

Parameters:

o1 - First vector

o2 - Second vector

Returns:

Jaccard similarity

distance

public double distance(FeatureVector<?> o1,
                       FeatureVector<?> o2)

Description copied from interface: PrimitiveDistance

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

Specified by:

distance in interface PrimitiveDistance<FeatureVector<?>>

Parameters:

o1 - first DatabaseObject

o2 - second DatabaseObject

Returns:

the distance between two given DatabaseObjects according to this distance function

distance

public double distance(NumberVector o1,
                       NumberVector o2)

Description copied from interface: NumberVectorDistance

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

Specified by:

distance in interface NumberVectorDistance<FeatureVector<?>>

Parameters:

o1 - first vector

o2 - second vector

Returns:

the distance between two given vectors according to this distance function

isSymmetric

public boolean isSymmetric()

Description copied from interface: Similarity

Is this function symmetric?

Specified by:

isSymmetric in interface Distance<FeatureVector<?>>

Specified by:

isSymmetric in interface Similarity<FeatureVector<?>>

Returns:

true when symmetric

isMetric

public boolean isMetric()

Description copied from interface: Distance

Is this distance function metric (satisfy the triangle inequality)

Specified by:

isMetric in interface Distance<FeatureVector<?>>

Returns:

true when metric.

getInputTypeRestriction

public SimpleTypeInformation<? super FeatureVector<?>> getInputTypeRestriction()

Description copied from interface: Similarity

Get the input data type of the function.

Specified by:

getInputTypeRestriction in interface Distance<FeatureVector<?>>

Specified by:

getInputTypeRestriction in interface PrimitiveDistance<FeatureVector<?>>

Specified by:

getInputTypeRestriction in interface Similarity<FeatureVector<?>>

Returns:

Type restriction

instantiate

public <T extends FeatureVector<?>> DistanceSimilarityQuery<T> instantiate(Relation<T> relation)

Description copied from interface: Similarity

Instantiate with a representation to get the actual similarity query.

Specified by:

instantiate in interface Distance<FeatureVector<?>>

Specified by:

instantiate in interface PrimitiveDistance<FeatureVector<?>>

Specified by:

instantiate in interface PrimitiveSimilarity<FeatureVector<?>>

Specified by:

instantiate in interface Similarity<FeatureVector<?>>

Parameters:

relation - Representation to use

Returns:

Actual distance query.

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