Similarity coefficients, Tanimoto

Tanimoto similarity coefficient Also known as the Jaccard c. E =1 W/B ... 

The most widely used similarity measure by far is the Tanimoto similarity coefficient SXan, which is given in set-theoretic language as (cf. Eq. 2.13 for the graph-theoretical case)... 

Distances in these spaces should be based upon an Zj or city-block metric (see Eq. 2.18) and not the Z2 or Euclidean metric typically used in many applications. The reasons for this are the same as those discussed in Subheading 2.2.1. for binary vectors. Set-based similarity measures can be adapted from those based on bit vectors using an ansatz borrowed from fuzzy set theory (41,42). For example, the Tanimoto similarity coefficient becomes... 

The inner-product terms (, is the labeled graph corresponding to Zth basis fragment, vA is the labeled graph corresponding to molecule A, and STan(G ,GA) is the chemical graph-theoretical Tanimoto similarity coefficient. 

Compounds were chosen for further testing using Cousin fingerprint descriptors (73) and the Tanimoto similarity coefficient with a 67% similarity cutoff. 

Fig. 7. (see facing page) Comparison of the intramolecular similarity distribution for four compound collections versus the NCI collection. This figure shows the intermol-ecular similarity (calculated using the Tanimoto similarity coefficient using ISIS fingerprint descriptors) between each compound in each library. The first panel shows how the NCI dataset contains many identical compounds (or salts of the same compound) that have been submitted for testing. 

In the NN method, the property F of the target compound is calculated as an average (or weighted average) of that for its NN in the space of descriptors selected for the model. Different metrics (Euclidian distances, Tanimoto similarity coefficients, etc.), can be used to identify the neighbors. Their number k is optimized using a cross-validation procedure for the training set. 

Rogers-Tanimoto similarity coefficient similarity/diversity (Table S9)... 

The following example indicates the bit strings (0/1 means feature absent or present) of two molecules (A and B) with four common features yielding Tanimoto similarity coefficients of 0.5. 

As is well known, the Tanimoto similarity coefficient, which is the most widely used similarity measure, exhibits size-dependent behavior [5, 92-95] that can significantly influence the results of similarity searches. A significant part of the problem can be traced to the terms in the denominator of the Tanimoto function that counts the number of elements that are common to both molecular fingerprints. Thus, when molecules of widely varying sizes are treated, the number of elements in fingerprint... 

Thus, dissimilarity values also lie on the unit interval [0,1], For example, in the case of the Tanimoto similarity coefficient the corresponding dissimilarity coefficient is... 

It was shown by both Fligner et al. [65] and Holhday et al. [67] that the modified Tanimoto coefficient did to a large extent ameliorate size bias associated with the Tanimoto similarity coefficient. More recently, Bajorath and his collaborators [58, 66] successfully introduced a related type of modified similarity measure that weights contributions associated with the presence and absence of substractural features. In their case, however, a Tveiksy-type similarity coefficient was used rather than the Tanimoto expression employed by Fligner et al. [65]. 

The vector-based Tanimoto similarity coefficient corresponding to the FP-based coefficient in Eq. (1.8) is given by... 

Fig. 1.9 Depictions of CSs generated from Tanimoto similarity coefficients computed with respect to binary FPs associated with four different types of descriptors—APF, MACCS key, TGD, and piDAPH4. (Adapted from Medina-Franco Maggiora, Molecular Similarity Analysis [10])...

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