org.simmetrics.metrics.Jaccard Maven / Gradle / Ivy
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* Copyright (C) 2014 - 2016 Simmetrics Authors
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package org.simmetrics.metrics;
import static org.simmetrics.metrics.Math.intersection;
import java.util.Set;
import org.simmetrics.SetDistance;
import org.simmetrics.SetMetric;
/**
* 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. {@code [hello, world]} and
* {@code [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 GeneralizedJaccard
* @see OverlapCoefficient
* @see Dice
* @see Wikipedia - Jaccard
* index
*
* @param
* type of the token
*
*/
public final class Jaccard implements SetMetric, SetDistance {
@Override
public float compare(Set a, Set b) {
if (a.isEmpty() && b.isEmpty()) {
return 1.0f;
}
if (a.isEmpty() || b.isEmpty()) {
return 0.0f;
}
final int intersection = intersection(a, b).size();
// ∣a ∩ b∣ / ∣a ∪ b∣
// Implementation note: The size of the union of two sets is equal to
// the size of both sets minus the duplicate elements.
return intersection / (float) (a.size() + b.size() - intersection);
}
@Override
public float distance(Set a, Set b) {
return 1.0f - compare(a, b);
}
@Override
public String toString() {
return "Jaccard";
}
}