Dice coefficient

Empirically, the Dice coefficient has worked better than cosine similarity in retrieving actives and is the standard choice for use with the ap and tt descriptors. 

In a subsequent study, we examined the influence of seven similarity indices on the enrichment of actives using the topological CATS descriptor and the 12 COBRA datasets [31]. In particular, we evaluated to what extent different similarity measures complement each other in terms of the retrieved active compounds. Retrospective screening experiments were carried out with seven similarity measures Manhattan distance, Euclidian distance, Tanimoto coefficient, Soergel distance, Dice coefficient, cosine coefficient, and spherical distance. Apart from the GPCR dataset, considerable enrichments were achieved. Enrichment factors for the same datasets but different similarity measures differed only slightly. For most of the datasets the Manhattan and the Soergel distance... 

Tanimoto coefficient Dice coefficient Cosine coefficient... 

Other metrics include the Hamming distance metric, given by (6). XOR is the bitwise exclusive or operation (a bit in the result is set if the corresponding bits in the two operands are different), and N the number of bits in each set. The Dice coefficient is defined by (7). 

With respect to metric properties, the Tanimoto coefficient obeys all four properties if dichotomous variables are used. Complement does not obey the triangular inequality in the Dice coefficient. 

Here we will introduce three similarity coefficients that have been widely used for both realvalued (i.e. continuous) and binary (dichotomous) descriptors the Tanimoto coefficient, the Dice coefficient and the Cosine coefficient The formulae used to compute these coefficients are given in Table 12.3, where, for completeness, we have also provided the Euclidean and Hamming expressions that were introduced in Section 9.13. Different expressions are used for real-valued data (where the molecule is represented by a vector containing N real values Xj) and for binary data (where each molecule is represented by N binary values). For binary data, we additionally define a to be the number of bits on in the bitstring for A, b to be the number of bits on in the bitstring for B, and c to be the number of bits that are on in both A and B (calculated using the AND operator). 

There are other coefficients like the Dice coefficient. Cosine coefficient, simple matching coefficient, and Tversky similarity coefficient. 

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