| (1) | \tau(x,y) = \frac{2}{n(n-1)} \sum_{i=1}^{n-1} \sum_{j=i+1} {\rm sgn} \big( rg(x_i)-rg(x_j) \big) \cdot {\rm sgn} \big( rg(y_i)-rg(y_j) \big) |
where rg(x_i) and rg(x_i) are the ranks of elements x_i and y_i.
The Kendall correlation coefficient is similar to Spearmen correlation coefficient in nature but sometimes has advantage by a more reliable pick up a correlation in noisy data.
The computational cost for Kendall correlation coefficient is higher than that of Spearmen correlation coefficient and the selection between the tow should be done based on the practical considerations.
See also
Formal science / Mathematics / Statistics / Statistical correlation
[ Statistical correlation metrics @ review ] [ Pearson correlation ] [ Spearmen Correlation ] [ Fehner correlation ]