SorensenDice

The Sorensen Dice coefficient, often called the Dice coefficient, is a statistic used to measure the similarity between two samples. For two finite sets A and B, it is defined as D = 2|A ∩ B| / (|A| + |B|). If A and B are represented by nonempty binary vectors indicating presence or absence of features, then D = 2c/(a+b), where a and b are the numbers of features present in A and B, and c is the number present in both.

Origin and variants: The Dice coefficient was introduced by Lee R. Dice in 1945; the Sørensen–Dice coefficient combines Dice’s idea with the Sørensen’s approach to produce a symmetric measure of similarity used in ecology, biology, linguistics, and computer science. It ranges from 0 to 1, where 1 indicates identical sets or vectors and 0 indicates no overlap. It is related to the Jaccard index by the relation Dice = 2J/(1+J).

Applications and limitations: Widely used to compare sample agreements in bioinformatics, text retrieval, natural language processing, and image segmentation. It is computationally simple and robust to small differences but can be biased by the size of the sets: large sets with small overlaps can yield low Dice scores than expected. It is not transitive and should be used with care when comparing multiple pairs. For multi-label or weighted data, generalized or adapted Dice coefficients are employed.