Kendall’s Tau is a measure of rank correlation between two list of rank vectors. This metric's time complexity is O(n log(n)), which can be slow when used in pairwise comparison tasks like clustering. There is an approximated way to calculate it in constant time, which is described in the work "Sketching Algorithms For Approximating Rank Correlations In Collaborative Filtering Systems". I also include a write up in the repo to simplify the descriptions.
Just clone the package and put sketch.py to your working directory.
from sketch import KTSketch
x1 = [1,3,2,4,5]
x2 = [3,2,1,5,4]
epsilon = 0.05 #accuracy as the abs. error <= epsilon
CI = 0.95 #confidence interval as P(abs. error <= epsilon) >= CI
dimension = 5 #size of vector
ktsketch = KTSketch(epsilon=epsilon,CI=CI,dim=dimension,seed=0)
ktsketch.correlation(x1,x2)