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Proximity Measure for Binary Attributes

  • A contingency table for binary data

  • Distance measure for symmetric binary variables: 
\[ d(i,j)=\frac{r+s}{q+r+s+t} \]
  • Distance measure for asymmetric binary variables: 

\[ d(i,j)=\frac{r+s}{q+r+s} \]

  • Jaccard coefficient (similarity measure for asymmetric binary variables):

\[ sim_{Jaccard}(i,j)=\frac{q}{q+r+s} \]

  • Note: Jaccard coefficient is the same as “coherence”:

\[ coherence(i,j)=\frac{sup(i,j)}{sup(i)+sup(j)-sup(i,j)}=\frac{q}{(q+r)(q+s)-q} \]

Speaker notes:

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