Contingency table for binary data

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Symmetrical binary variables:

d(x,y)=r+sq+r+s+td(x, y)=\frac{r+s}{q+r+s+t}

Asymmetrical binary variables:

d(x,y)=r+sq+r+sd(x, y)=\frac{r+s}{q+r+s}

Jaccard coefficient for asymmetrical binary similarity:

sim⁡(i,j)=jaccard⁡(i,j)=1−d(i,j)=qq+r+s\operatorname{sim}(i, j)=\operatorname{jaccard}(i, j)=1-d(i, j)=\frac{q}{q+r+s}

Example

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