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Square Root Jensen-Shannon Divergence
Let x be the relative abundances of one sample and y be the relative abundances of the other and m be the average relative abundances of the 2 samples.
JSD(x,y)= sqrt(1/2 KLD(x,m)+ 1/2 KLD(y,m))
where KLD is the Kullback-Leibler divergence between x and y defined by:
KLD(x,y)=∑ xi log xi / yi