Eq. IDs | Equations | References | Note |
---|---|---|---|
1 | \( {S}_{Jaccard}=\frac{a}{a+b+c} \) | ||
2 | \( {S}_{Dice-2}=\frac{a}{2a+b+c} \) | ||
3 | \( {S}_{Dice-1/ Czekanowski}=\frac{2a}{2a+b+c} \) | *** | |
4 | \( {S}_{3W- Jaccard}=\frac{3a}{3a+b+c} \) | ||
5 | \( {S}_{Nei\&Li}=\frac{2a}{\left(a+b\right)+\left(a+c\right)} \) | * | |
6 | \( {S}_{Sokal\& Sneath-1}=\frac{a}{a+2b+2c} \) | ||
7 | \( {S}_{Sokal\& Michener}=\frac{a+d}{a+b+c+d} \) | ||
8 | \( {S}_{Sokal\& Sneath-2}=\frac{2\left(a+d\right)}{2a+b+c+2d} \) | ||
9 | \( {S}_{Roger\& Tanimoto}=\frac{a+d}{a+2\left(b+c\right)+d} \) | ||
10 | \( {S}_{Faith}=\frac{a+0.5d}{a+b+c+d} \) | ||
11 | \( {S}_{Gower\& Legendre}=\frac{a+d}{a+0.5\left(b+c\right)+d} \) | * | |
12 | S Intersection = a | ||
13 | S Innerproduct = a + d | [23] | *** |
14 | \( {S}_{Russell\&Rao}=\frac{a}{a+b+c+d} \) | *** | |
15 | D Hamming = b + c | ||
16 | \( {D}_{Euclid}=\sqrt{b+c} \) | [23] | |
17 | \( {D}_{Squared- euclid}=\sqrt{{\left(b+c\right)}^2} \) | * | |
18 | \( {D}_{Canberra}={\left(b+c\right)}^{\frac{2}{2}} \) | [23] | * |
19 | D Manhattan = b + c | [23] | * |
20 | \( {D}_{Mean- Manhattan}=\frac{b+c}{a+b+c+d} \) | *** | |
21 | D Cityblock = b + c | [23] | * |
22 | \( {D}_{Minkowski}={\left(b+c\right)}^{\frac{1}{1}} \) | [23] | * |
23 | \( {D}_{Vari}=\frac{b+c}{4\left(a+b+c+d\right)} \) | *** | |
24 | \( {D}_{SizeDifference}=\frac{{\left(b+c\right)}^2}{{\left(a+b+c+d\right)}^2} \) | [23] | |
25 | \( {D}_{ShapeDifference}=\frac{n\left(b+c\right)-{\left(b-c\right)}^2}{{\left(a+b+c+d\right)}^2} \) | [23] | |
26 | \( {D}_{PatternDifference}=\frac{4bc}{{\left(a+b+c+d\right)}^2} \) | [23] | |
27 | \( {D}_{Lance\& Williams}=\frac{b+c}{2a+b+c} \) | ||
28 | \( {D}_{Bray\& Curtis}=\frac{b+c}{2a+b+c} \) | [23] | * |
29 | \( {D}_{Hellinger}=2\sqrt{\left(1-\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}}\right)} \) | [23] | |
30 | \( {D}_{Chord}=\sqrt{2\left(1-\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}}\right)} \) | [23] | *** |
31 | \( {S}_{Cosine}=\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}} \) | ||
32 | \( {S}_{Gilbert\& Wells}= \log a- \log n- \log \left(\frac{a+b}{n}\right)- \log \left(\frac{a+c}{n}\right) \) | ** | |
33 | \( {S}_{Ochiai-1}=\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}} \) | * | |
34 | \( {S}_{Forbes-1}=\frac{na}{\left(a+b\right)\left(a+c\right)} \) | ||
35 | \( {S}_{Fossum}=\frac{n{\left(a-0.5\right)}^2}{\left(a+b\right)\left(a+c\right)} \) | ||
36 | \( {S}_{Sorgenfrei}=\frac{a^2}{\left(a+b\right)\left(a+c\right)} \) | ||
37 | \( {S}_{Mountford}=\frac{a}{0.5\left( ab+ac\right)+bc} \) | ** | |
38 | \( {S}_{Otsuka}=\frac{a}{{\left(\left(a+b\right)\left(a+c\right)\right)}^{0.5}} \) | * | |
39 | \( {S}_{McConnaughey}=\frac{a^2-bc}{\left(a+b\right)\left(a+c\right)} \) | ||
40 | \( {S}_{Tarwid}=\frac{na-\left(a+b\right)\left(a+c\right)}{na+\left(a+b\right)\left(a+c\right)} \) | ||
41 | \( {S}_{Kulczynski-2}=\frac{\frac{a}{2}\left(2a+b+c\right)}{\left(a+b\right)\left(a+c\right)} \) | *** | |
42 | \( {S}_{Driver\& Kroeber}=\frac{a}{2}\left(\frac{1}{a+b}+\frac{1}{a+c}\right) \) | *** | |
43 | \( {S}_{Johnson}=\frac{a}{a+b}+\frac{a}{a+c} \) | *** | |
44 | \( {S}_{Dennis}=\frac{ad-bc}{\sqrt{n\left(a+b\right)\left(a+c\right)}} \) | ||
45 | \( {S}_{Simpson}=\frac{a}{ \min \left(a+b,a+c\right)} \) | ||
46 | \( {S}_{Braun\& Banquet}=\frac{a}{ \max \left(a+b,a+c\right)} \) | ||
47 | \( {S}_{Fager\& McGowan}=\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}}-\frac{ \max \left(a+b,a+c\right)}{2} \) | ||
48 | \( {S}_{Forbes-2}=\frac{na-\left(a+b\right)\left(a+c\right)}{n \min \left(a+b,a+c\right)-\left(a+b\right)\left(a+c\right)} \) | ||
49 | \( {S}_{Sokal\& Sneath-4}=\frac{\frac{a}{\left(a+b\right)}+\frac{a}{\left(a+c\right)}+\frac{d}{\left(b+d\right)}+\frac{d}{\left(c+d\right)}}{4} \) | ||
50 | \( {S}_{Gower}=\frac{a+d}{\sqrt{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) | [23] | |
51 | \( {S}_{Pearson-1}={\chi}^2=\frac{n{\left( ad-bc\right)}^2}{\left(a+b\right)\left(a+c\right)\left(c+d\right)\left(b+d\right)} \) | ||
52 | \( {S}_{Pearson-2}={\left(\frac{\chi^2}{n+{\chi}^2}\right)}^{\frac{1}{2}} \) | ||
53 | \( {S}_{Pearson-3}={\left(\frac{\rho }{n+\rho}\right)}^{\frac{1}{2}} \) \( \mathrm{where}\kern0.75em \rho =\frac{ad-bc}{\sqrt{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) | [23] | ** |
54 | \( {S}_{Pearson\& Heron-1}=\frac{ad-bc}{\sqrt{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) | ||
55 | \( {S}_{Pearson\& Heron-2}= \cos \left(\frac{\pi \sqrt{bc}}{\sqrt{ad}+\sqrt{bc}}\right) \) | ||
56 | \( {S}_{Sokal\& Sneath-3}=\frac{a+d}{b+c} \) | ** | |
57 | \( {S}_{Sokal\& Sneath-5}=\frac{ad}{\left(a+b\right)\left(a+c\right)\left(b+d\right){\left(c+d\right)}^{0.5}} \) | ||
58 | \( {S}_{Cole}=\frac{\sqrt{2}\left( ad-bc\right)}{\sqrt{{\left( ad-bc\right)}^2-\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) | ** | |
59 | \( {S}_{Stiles}={ \log}_{10}\frac{n{\left(\left| ad-bc\right|-\frac{n}{2}\right)}^2}{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)} \) | ||
60 | \( {S}_{Ochiai-2}=\frac{ad}{\sqrt{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) | * | |
61 | \( {S}_{Yuleq}=\frac{ad-bc}{ad+bc} \) | ||
62 | \( {D}_{Yuleq}=\frac{2bc}{ad+bc} \) | [23] | |
63 | \( {S}_{Yulew}=\frac{\sqrt{ad}-\sqrt{bc}}{\sqrt{ad}+\sqrt{bc}} \) | ||
64 | \( {S}_{Kulczynski-1}=\frac{a}{b+c} \) | ** | |
65 | \( {S}_{Tanimoto}=\frac{a}{\left(a+b\right)+\left(a+c\right)-a} \) | * | |
66 | \( {S}_{Disperson}=\frac{ad-bc}{{\left(a+b+c+d\right)}^2} \) | ||
67 | \( {S}_{Hamann}=\frac{\left(a+d\right)-\left(b+c\right)}{a+b+c+d} \) | *** | |
68 | \( {S}_{Michael}=\frac{4\left( ad-bc\right)}{{\left(a+d\right)}^2+{\left(b+c\right)}^2} \) | ||
69 | \( {S}_{Goodman\& Kruskal}=\frac{\sigma -{\sigma}^{\hbox{'}}}{2n-{\sigma}^{\hbox{'}}} \) \( \begin{array}{l}\mathrm{where}\;\sigma = \max \left(a,b\right)+ \max \left(c,d\right)+ \max \left(a,c\right)+ \max \left(b,d\right)\\ {}\kern1.56em {\sigma}^{\hbox{'}}= \max \left(a+c,b+d\right)+ \max \left(a+b,c+d\right)\end{array} \) | [23] | ** |
70 | \( {S}_{Anderberg}=\frac{\sigma -{\sigma}^{\hbox{'}}}{2n} \) | [23] | ** |
71 | \( {S}_{Baroni- Urbani\& Buser-1}=\frac{\sqrt{ad}+a}{\sqrt{ad}+a+b+c} \) | ||
72 | \( {S}_{Baroni- Urbani\& Buser-2}=\frac{\sqrt{ad}+a-\left(b+c\right)}{\sqrt{ad}+a+b+c} \) | *** | |
73 | \( {S}_{Peirce}=\frac{ab+bc}{ab+2bc+ cd} \) | ** | |
74 | \( {S}_{Eyraud}=\frac{n^2\left(na-\left(a+b\right)\left(a+c\right)\right)}{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)} \) | [23] | |
75 | \( {S}_{Tarantula}=\frac{\frac{a}{\left(a+b\right)}}{\frac{c}{\left(c+d\right)}}=\frac{a\left(c+d\right)}{c\left(a+b\right)} \). | [23] | ** |
76 | \( {S}_{Ample}=\left|\frac{\frac{a}{\left(a+b\right)}}{\frac{c}{\left(c+d\right)}}\right|=\left|\frac{a\left(c+d\right)}{c\left(a+b\right)}\right| \). | [23] | ** |
77 | \( {S}_{Derived\_ Rusell-Rao}=\frac{ \log \left(1+a\right)}{ \log \left(1+n\right)} \). | ||
78 | \( {S}_{Derived\_ Jaccard}=\frac{ \log \left(1+a\right)}{ \log \left(1+a+b+c\right)} \) | ||
79 | \( {S}_{Var\_ of\_ Correlation}=\frac{ \log \left(1+ ad\right)- \log \left(1+bc\right)}{ \log \left(1+{n}^2/4\right)} \) |