Table 2 Groups of identical equations
Groups | Eliminated Equations | Selected Equations |
|---|---|---|
1 | \( {S}_{Nei\&Li}=\frac{2a}{\left(a+b\right)+\left(a+c\right)} \) (Eq.5) | \( {S}_{Dice-1/ Czekanowski}=\frac{2a}{2a+b+c} \) (Eq.3) |
2 | \( {S}_{Gower\& Legendre}=\frac{a+d}{a+0.5\left(b+c\right)+d} \) (Eq.11) | \( {S}_{Sokal\& Sneath-2}=\frac{2\left(a+d\right)}{2a+b+c+2d} \) (Eq.8) |
3 | \( {D}_{Squared- euclid}=\sqrt{{\left(b+c\right)}^2} \) (Eq.17) | D Hamming  = b + c (Eq.15) |
\( {D}_{Canberra}={\left(b+c\right)}^{\frac{2}{2}} \) (Eq.18) | ||
D Manhattan  = b + c (Eq.19) | ||
D Cityblock  = b + c (Eq.21) | ||
\( {D}_{Minkowski}={\left(b+c\right)}^{\frac{1}{1}} \) (Eq.22) | ||
4 | \( {D}_{Bray\& Curtis}=\frac{b+c}{2a+b+c} \) (Eq.28) | \( {D}_{Lance\& Williams}=\frac{b+c}{2a+b+c} \) (Eq.27) |
5 | \( {S}_{Ochiai-1}=\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}} \) (Eq.33) | \( {S}_{Cosine}=\frac{a}{\sqrt{\left(a+b\right)\left(a+c\right)}} \) (Eq.31) |
\( {S}_{Otsuka}=\frac{a}{{\left(\left(a+b\right)\left(a+c\right)\right)}^{0.5}} \) (Eq.38) | ||
6 | \( {S}_{Ochiai-2}=\frac{ad}{\sqrt{\left(a+b\right)\left(a+c\right)\left(b+d\right)\left(c+d\right)}} \) (Eq.60) | \( {S}_{Sokal\& Sneath-5}=\frac{ad}{\left(a+b\right)\left(a+c\right)\left(b+d\right){\left(c+d\right)}^{0.5}} \) (Eq.57) |
7 | \( {S}_{Tanimoto}=\frac{a}{\left(a+b\right)+\left(a+c\right)-a} \) (Eq.65) | \( {S}_{Jaccard}=\frac{a}{a+b+c} \) (Eq.1) |