SörensenDice

The Sørensen–Dice coefficient, often referred to as the Dice coefficient, is a statistic used to measure the similarity between two samples. It produces a value between 0 and 1, where 1 denotes identical samples and 0 indicates no overlap. The measure is widely used for binary data and set-based comparisons.

For two sets A and B, the coefficient is defined as DSC = 2|A ∩ B| / (|A| + |B|). For binary vectors x and y of length n, it can be computed as DSC = 2 Σ_i min(x_i, y_i) / (Σ_i x_i + Σ_i y_i). The formula emphasizes overlap between the samples, effectively counting common elements twice.

The Dice coefficient is related to the Jaccard index J by the relation Dice = 2J / (1 + J), where J = |A ∩ B| / |A ∪ B|. This relationship connects two common similarity measures used in set theory, information retrieval, and clustering.

Applications of the Sørensen–Dice coefficient span ecology, bioinformatics, and computer science. It is used to compare species composition between sites, assess similarity of binary feature representations, evaluate image segmentation results, and measure text or document similarity in information retrieval and natural language processing.

Historically, the index was introduced by Thorvald Sørensen in 1948 and, independently, the Dice coefficient was proposed by Lee R. Dice in 1945. The combined name reflects its dual attribution. Limitations include sensitivity to sample size and its binary-or-count-based nature; extensions exist for weighted or probabilistic data, but interpretation requires care.