Is Tanimoto a metric?

Abstract

No. However, here we show how to generate a metric consistent with the Tanimoto similarity. We also explore new properties of this index, and how it relates to other popular alternatives.

Keywords: Tanimoto; consistency; metric; similarity.

Figure 1:

Function $\tau$ (see Eq. (24)) for different ${\text{r}}_{\text{y}},{\text{r}}_{\text{z}}$, and $\theta$ values. Subfigure A shows $\tau$ for fixed ${\text{r}}_{\text{y}}$ between 1 and 10000. Subfigures B and C depict $\tau$ for fixed ${\text{r}}_{\text{z}}$. In B ${\text{r}}_{\text{z}}$ is in the range of 0 to 1, whereas in C ${\text{r}}_{\text{z}}$ is between 1 and 10000.

Figure 2.

Variation of the Kendall $\tau$ in similarity rankings of all possible combinations of similarity counters filtering only instances with $d$ lower than a threshold $d^{\prime }$.