Tanimoto distance

To demonstrate this, Figure 2.8 shows the comparison of similarity for Daylight structural and biological fingerprints created from a panel of 154 assays from the BioPrint database (measured by pairwise Tanimoto distance for 347 drugs with MW 200-600 60031 points) [6]. Figure 2.8a shows the overall scatter plot of the... 

In order to apply the SA protocol, one of the keys is to design a mathematical function that adequately measures the diversity of a subset of selected molecules. Because each molecule is represented by molecular descriptors, geometrically it is mapped to a point in a multidimensional space. The distance between two points, such as Euclidean distance, Tanimoto distance, and Mahalanobis distance, then measures the dissimilarity between any two molecules. Thus, the diversity function to be designed should be based on all pairwise distances between molecules in the subset. One of the functions is as follows ... 

Another weighted variant of the Jaccard/Tanimoto distance was suggested considering a trade-off between the presence and absence of common features. In effect, the Jaccard/ Tanimoto similarity emphasizes the presence of common features a, neglecting the absence of common features d and it is written as... 

The most popular distance binary measures are Hamming and Tanimoto distances that are listed below (Table SIO), together with other distance measures on binary vectors. 

Tanimoto distance Square root Tanimoto distance Watson nonmetric distance Soergel binary distance... 

It must be noted that comparing distances for binary and continuous variables, the Hamming distance coincides vith the Manhattan distance, square root Hamming distance is the Euclidean distance, Tanimoto distance coincides vdth average Manhattan distance and squared Tanimoto vith the average Euclidean distance. Moreover, the Watson nonmetric distance corresponds to the Lance-Williams distance and is the complement of the Sorenson coefficient the Soergel binary distance corresponds to the Soergel distance and is the complement of the Jaccard/ Tanimoto coefficient. 

Figure 12.1 R graphical representation of Ward clustering of 1.0-tanimoto distances between compounds.

The Hamming distance has some disadvantages for vectors with only a few components containing 1 s. An alternative is the Tanimoto distance which is a normalized Hamming distance C3983. 

The denominator in equation (28) is the number of vector components which contain a 1 at Least in one of the patterns (Logical or) The numerator is the number of vector components with a 1 in both vectors (Logical and/ Table 2). Application of the Tanimoto distance to the classification of infrared spectra yielded better results than the Hamming distance C353T. 

The normalized distance is independent of the number of dimensions C1753 the Hamming and Tanimoto distances are suitable for binary encoded patterns C353, 356, 3573. 

As described before, it is due to the vast amount of possible structures that one can never get an adequate sample of chemical space. One question is if the entire chemical space is relevant for finding pharmacologically active compounds and how to predict this for future targets [19]. Another question is how to sample a part of chemical space in a uniform, systematic fashion. Often, the answer is considered to be a diverse selection. However, what is diversity [20] The usual method to describe diversity is to determine Tanimoto distances. These coefficients are calculated by comparing the number of shared and unique molecular fingerprints within a pair of structures. Usually, compounds with Tanimoto >0.85 are considered to be similar. The lower the Tanimoto coefficients in a compound set are, the more structurally diverse the set can be... 

Lipkus AH (1999) A proof of the triangle inequality for the Tanimoto distance. J Math Chem 26 263-265... 

---