Question

the union of distance is​

Answer 1

Explanation:

The Jaccard index, also known as Intersection over Union and the Jaccard similarity coefficient (originally given the French name coefficient de communauté by Paul Jaccard), is a statistic used for gauging the similarity and diversity of sample sets. The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union ofsample set

(If A and B are both empty, define J(A,B) = 1.)

The Jaccard distance, which measures dissimilarity between sample sets, is complementary to the Jaccard coefficient and is obtained by subtracting the Jaccard coefficient from 1, or, equivalently, by dividing the difference of the sizes of the union and the intersection of two sets by the size of the union:

An alternative interpretation of the Jaccard distance is as the ratio of the size of the symmetric difference {\displaystyle A\triangle B=(A\cup B)-(A\cap B)} A \triangle B = (A \cup B) - (A \cap B) to the union. Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets.

This distance is a metric on the collection of all finite sets.[1][2][3]

There is also a version of the Jaccard distance for measures, including probability measures. If {\displaystyle \mu } \mu  is a measure on a measurable space , then we define the Jaccard coefficient by

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Answer 2

Answer:

"The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used for gauging the similarity and diversity of sample sets. It was developed by Paul Jaccard, originally giving the French name coefficient de communauté,[1] and independently formulated again by T. Tanimoto.[2] Thus, the Tanimoto index or Tanimoto coefficient are also used in some fields. However, they are identical in generally taking the ratio of Intersection over Union. "