Jaccardetäisyys

Jaccardetäisyys, also known as the Jaccard distance or Jaccard dissimilarity, is a statistic used for gauging the similarity and diversity of sample sets. It is defined as the size of the intersection divided by the size of the union of the sample sets. Mathematically, for two sets A and B, the Jaccard index is calculated as |A ∩ B| / |A ∪ B|. The Jaccard distance is then defined as 1 minus the Jaccard index, or 1 - (|A ∩ B| / |A ∪ B|). This means the distance is the size of the difference of the sets divided by the size of the union of the sets.

The Jaccard distance ranges from 0 to 1. A Jaccard distance of 0 indicates that the two sets are identical, meaning they have exactly the same elements. A Jaccard distance of 1 signifies that the two sets are completely dissimilar, possessing no common elements whatsoever. This metric is particularly useful in fields such as data mining, information retrieval, and machine learning for tasks like cluster analysis, document similarity comparison, and recommendation systems. It is sensitive to the presence or absence of elements and is often employed when dealing with binary data or sets where the order of elements does not matter.