Jaccard

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) ... 

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

The Jaccard similarity coefficient is then computed with eq. (30.13), where m is now the number of attributes for which one of the two objects has a value of 1. This similarity measure is sometimes called the Tanimoto similarity. The Tanimoto similarity has been used in combinatorial chemistry to describe the similarity of compounds, e.g. based on the functional groups they have in common [9]. Unfortunately, the names of similarity coefficients are not standard, so that it can happen that the same name is given to different similarity measures or more than one name is given to a certain similarity measure. This is the case for the Tanimoto coefficient (see further). 

The most prominent pessimists are C. Campbell, J. Laherrere, R. Bentley and K. Deffeyes there is also a society called the Association for the Study of Peak Oil (ASPO), see www.peakoil.net. So-called optimists include M. Adelman, C. Watkins, M. Lynch, J. Ryan and P. Odell. (For further reading about the peak oil debate, see (CERA, 2006 Deffeyes, 2001 EWG, 2007 Jaccard, 2005 Kagi et al, 2003 OGJ, 2004 or Robelius, 2007).)... 

Jaccard, M. (2005). Sustainable Fossil Fuels. New York Cambridge University Press. 

The awareness that our human culture requires sustainable use of the earth s resources and its biosphere has become generally accepted in those societies that are in a relatively wealthy economic position. It also provides the intuitive justification for many that the use of renewable resources is a necessity. However, several economists (see Jaccard [1], Smil [4], Lomborg [5]) caution that the introduction or transition to renewable resources will also have economic as well as environmental costs, that sometimes reverse the preference for particular raw materials or technologies that at first sight seem to be the best. 

M. Jaccard, Sustainable Fossil Fuels The Unusual Suspect in the Quest for Clean and Enduring Energy, Cambridge University Press, Cambridge (UK), 2005. 

Chemical structures are often characterized by binary vectors in which each vector component (with value 0 or 1) indicates absence or presence of a certain substructure (binary substructure descriptors). An appropriate and widely used similarity measure for such binary vectors is the Tanimoto index (Willett 1987), also called Jaccard similarity coefficient (Vandeginste et al. 1998). Let xA and xB be binary vectors with m components for two chemical structures A and B, respectively. The Tanimoto index fAB is given by... 

Cimasoni G, ishikawa i and Jaccard F (1977) Enzyme activity in the gingival crevice, in The borderland between caries and periodontal disease (ed. Lehner T), pp. 13-41. Academic, London UK. 

R. Cherbuliez, B. Willhelm, O. Espejo, S. Jaccard, and J. Rabino-witz, Helv. Chim. Acta 51, 1440 (1967). 

Liaudet L, Buclin T, Jaccard C, Eckert P. Severe ergotism associated with interaction between ritonavir and ergo-tamine. Br Med J 1999 318 771. 

Reyren N, Thiel S, Caviglia AD, Kourkoutis LF, Hammer G, Richter C, Schneider CW, Kopp T, Riietschid A-S, Jaccard D et al (2007) Science 317 1196... 

Thorburn A (2004) Death receptor-induced cell killing. Cell Signal 16 139-144 Tinel A, Janssens S, Lippens S, Cuenin S, Logette E, Jaccard B, Quadroni M, Tschopp J (2007) Autoproteolysis of PIDD marks the bifurcation between pro-death caspase-2 and pro-survival NF-lappaB pathway. EMBO J 26 197-208... 

For binary descriptors, the most commonly used distance function is the Tanimoto (or Jaccard) coefficient given in (5). Here x and y are two binary sets (encoded molecules). AND is the bitwise and operation (a bit in the result is set if both corresponding bits in the two operands are set), and lOR the bitwise inclusive or operation (a bit in the result is set if either corresponding bits in the two operands is set). The result, T, is a measure of the number of features shared by the two molecules relative to the ones they could have in common. 

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