What is Jaccard Distance

Jaccard distance is a measure of dissimilarity between two sets. It is calculated as the complement of the Jaccard similarity coefficient and is particularly useful when dealing with binary data or sets. The Jaccard similarity coefficient measures the proportion of shared elements between two sets, and the Jaccard distance is essentially the complement of this coefficient.

The Jaccard similarity coefficient ((J)) is defined as the size of the intersection of two sets divided by the size of the union of the sets. Mathematically, it can be expressed as:

The Jaccard distance ((D_J)) is then calculated as:

In the context of clustering or comparing similarity between two samples, a Jaccard distance of 0 indicates that the sets are identical, while a Jaccard distance of 1 implies no shared elements.

The Jaccard distance is often used in various applications, including information retrieval, data mining, and bioinformatics. It is especially useful when dealing with categorical or binary data, such as document comparison (presence or absence of words) or genetic data (presence or absence of specific genetic markers).