Tanimoto

The term "Tanimoto" commonly refers to either the Tanimoto coefficient or the Tanimoto distance, both of which are measures of similarity and dissimilarity, respectively, between two sets. They are widely used in information retrieval, data mining, and chemoinformatics, particularly for comparing the similarity of chemical structures based on the presence or absence of specific features.

• Tanimoto Coefficient: The Tanimoto coefficient, also known as the Jaccard index, is a statistic used for gauging the similarity between two sample sets. It is calculated as the size of the intersection of the sets divided by the size of the union of the sets. Formally, given two sets A and B, the Tanimoto coefficient is calculated as |A ∩ B| / |A ∪ B|. The result is a value between 0 and 1, where 0 indicates no similarity and 1 indicates complete similarity.

• Tanimoto Distance: The Tanimoto distance is a measure of dissimilarity derived from the Tanimoto coefficient. It is calculated as 1 minus the Tanimoto coefficient. Formally, the Tanimoto distance between sets A and B is 1 - (|A ∩ B| / |A ∪ B|). The result is a value between 0 and 1, where 0 indicates perfect similarity (and thus no distance) and 1 indicates complete dissimilarity.

The original formulation of these measures is attributed to Taffee T. Tanimoto, who developed them in the context of information retrieval and pattern recognition. While the term "Jaccard Index" is mathematically equivalent and often used interchangeably with "Tanimoto Coefficient," the term "Tanimoto" remains prevalent, especially within the fields of chemoinformatics and drug discovery. In these fields, binary vectors are often used to represent the presence or absence of specific substructures within a molecule, and the Tanimoto coefficient or distance is then used to assess the structural similarity between different molecules.