Table 2. Similarity Coefficients^a.

name	measurement	range	reference(s)
Braun-Blanquet	x/max(y,z)	0 to 1	(53,54)
Cosine		0 to 1	(55,56)
Dice		0 to 1	(57,58)
Dot-product	x	0 to ∞	N/A
Euclidean		0 to 1	N/A
Kulczynski		0 to 1	(59)
McConnaughey		–1 to 1	(60)
Russel/Rao	x/w	0 to 1	(61)
Simpson	x/min(y,z)	0 to 1	(62)
Sokal/Sneath		0 to 1	(63)
Tanimoto		0 to 1	(64,65)
Tullos	XYZ	0 to 1	(66)
Tversky		0 to 1	(67)

^aA total of 13 different similarity coefficients (several of these coefficients were collected by Raymond and Willett)⁵² were compiled for measuring the degree of structural similarity of two compounds described by a given molecular fingerprint encoding. Here, x is the number of bits set in both fingerprints, y is the number of bits set in the first fingerprint, z is the number of bits set in the second fingerprint, and w is the total number of bits in the bit string. For the Tullos similarity coefficient, , , and . For the asymmetric evaluation of the Tversky similarity coefficient, α = 0.9. Here, we assume that the parameters of the Tversky coefficient in its original formulation, , will follow p + q = 1. The Dice and Tanimoto similarity coefficients are two symmetric instances of the Tversky coefficient, where p = q = 0.5 and p = q = 1, respectively.