Tanimoto

The tanimoto function is used to compute the Tanimoto similarity of two bitstrings. The input bit strings would have been computed with the publicl66keys function or another equivalent fragment key or fingerprint function. 

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Maeda K, Terazima M, Azumi T and Tanimoto Y 1991 CIDNP and CIDEP studies on intramolecular hydrogen abstraction reaction of polymethylene-linked xanthone and xanthene. Determination of the... 

Consequently, we can construct a similarity measure intuitively in the following way all matches c -i- d relative to all possibilities, i.e., matches plus mismatches (c+ d) + (a -I- h), yields (c -t- d) / a + b+ c + d), which is called the simple matching coefficient [18], and equal weight is given to matches and mismatches. (Normalized similarity measures are called similarity indices or coefficients see, e.g.. Ref. [19].) When absence of a feature in both objects is deemed to convey no information, then d should not occur in a similarity measure. Omitting d from the above similarity measure, one obtains the Tanimoto (alias Jaccard) similarity measure (Eq. (8) see Ref. [16] and the citations therein) ... 

For examples of different types of similarity measures, see Table 6-2. The Tanimoto similarity measure is monotonic with that of Dice (alias Sorensen, Czekanowski), which uses an arithmetic-mean normaJizer, and gives double weight to the present matches. Russell/Rao (Table 6-2) add the matching absences to the nor-malizer in Tanimoto the cosine similarity measure [19] (alias Ochiai) uses a geometric mean normalizer. 

We should mention here that using just similarity or dissimilarity in a similarity measure might be misleading. Therefore, some composite measures using both similarity and dissimilarity have been developed. These are the Hamann and the Yule measures (Table 6-2). A simple product of (1 - Tanimoto) and squared Eucli-... 

Asymmetry in a similarity measure is the result of asymmetrical weighing of a dissimilarity component - multiplication is commutative by definition, difference is not. By weighing a and h, one obtains asymmetric similarity measures, including the Tversky similarity measure c j aa 4- fih + c), where a and fi are user-defined constants. The Tversky measure can be regarded as a generalization of the Tanimoto and Dice similarity measures like them, it does not consider the absence matches d. A particular case is c(a + c), which measures the number of common features relative to all the features present in A, and gives zero weight to h. 

If the binary descriptors for the objects s and t are substructure keys the Hamming distance Eq. (6)) gives the number of different substructures in s and t (components that are 1 in either s or but not in both). On the other hand, the Tanimoto coefficient (Eq. (7)) is a measure of the number of substructures that s and t have in common (i.e., the frequency a) relative to the total number of substructures they could share (given by the number of components that are 1 in either s or t). 

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

Another important feature of the Tanimoto coefficient when used with bitstring data is that small molecules, which tend to have fewer bits set, will have only a small number of bits in common and so can tend to give inherently low similarity values. This can be important when selecting dissimilar compounds, as a bias towards small molecules can result. 

Tanimoto, A.K., Kobayashi, K. and Fujita, S., 1964. Overall crystallization rate of copper sulfate pentahydrate in an agitated vessel. International Chemical Engineering, 4(1), 153. 

The similarity matrices are constructed by one in-house program developed inside CHIRBASE using the application development kit of ISIS. They contain the similarity coefficients as expressed by the Tanimoto method. In ISIS, the Tanimoto coefficients are calculated from a set of binary descriptors or molecular keys coding the structural fragments of the molecules. 

These structural key descriptors incorporate a remarkable amount of pertinent molecular arrangements covering each type of interaction involved in ligand-receptor bindings [26]. Since every structure in a database is represented by one or more of the 960 key codes available in ISIS, suppose that two molecules include respectively A and B key codes, then the Tanimoto coefficient is given by ... 

Mori, S., M. Kataya, and A. Tanimoto, Performance of Counter-flows, Parallel Plate Heat Exchangers Under Laminar Flow Conditions, Heat Trans. Eng, V. 2, July-Sept. (1980) p. 29. 

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