org.simmetrics.metrics

Class Jaccard<T>

java.lang.Object

org.simmetrics.metrics.Jaccard<T>

Type Parameters:

T - type of the token

All Implemented Interfaces:

Distance<Set<T>>, Metric<Set<T>>, SetDistance<T>, SetMetric<T>

public final class Jaccard<T>
extends Object
implements SetMetric<T>, SetDistance<T>

Calculates the Jaccard distance and similarity coefficient over two multisets. The similarity is defined as the size of the intersection divided by the size of the union of the sample sets. The distance is obtained by subtracting the Jaccard coefficient from 1.

similarity(a,b) = ∣a ∩ b∣ / ∣a ∪ b∣
distance(a,b) = 1 - similarity(a,b)

When ∣a ∪ b∣ is empty the multisets have no elements in common. In this case the similarity is 0 by definition.

Unlike the generalized Jaccard index the occurrence (cardinality) of an entry is not taken into account. E.g. [hello, world] and [hello, world, hello, world] would be identical when compared with the Jaccard index but are dissimilar when the generalized version is used.

Similar to the overlap coefficient which divides the intersection by the size of the smaller of the two sets.

Similar to the dice coefficient which divides the shared information (intersection) by sum of cardinalities.

This class is immutable and thread-safe.

See Also:

GeneralizedJaccard, OverlapCoefficient, Dice, Wikipedia - Jaccard index

Constructor Summary

Constructors

Constructor and Description
Jaccard()

Method Summary

Modifier and Type	Method and Description
float	compare(Set<T> a, Set<T> b) Measures the similarity between sets a and b.
float	distance(Set<T> a, Set<T> b) Measures the distance between sets a and b.
String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

Jaccard

public Jaccard()

Method Detail

compare

public float compare(Set<T> a,
                     Set<T> b)

Description copied from interface: SetMetric

Measures the similarity between sets a and b. The measurement results in a value between 0 and 1 inclusive. A value of zero indicates that the sets are dissimilar, a value of 1 indicates they are similar.

Results are undefined if set1 and set2 are sets based on different equivalence relations (as HashSet, TreeSet, and the keySet of an IdentityHashMap all are).

Specified by:

compare in interface Metric<Set<T>>

Specified by:

compare in interface SetMetric<T>

Parameters:

a - set a to compare

b - set b to compare

Returns:

a value between 0 and 1 inclusive indicating similarity

distance

public float distance(Set<T> a,
                      Set<T> b)

Description copied from interface: SetDistance

Measures the distance between sets a and b. The measurement results in a non-negative value. A value of 0.0 indicates that a and b are similar.

Results are undefined if a and b are sets based on different equivalence relations (as HashSet, TreeSet, and the keySet of an IdentityHashMap all are).

Specified by:

distance in interface Distance<Set<T>>

Specified by:

distance in interface SetDistance<T>

Parameters:

a - set a to compare

b - set b to compare

Returns:

a non-negative value

toString

public String toString()

Overrides:

toString in class Object