Jensen-Shannon divergence

Kullback-Leibler Divergence is not symmetric:

$$D_{KL}[p(x)||q(x)]\ne D_{KL}[q(x)||p(x)]$$

The Jensen-Shannon divergence is a measure of distance that is symmetric by construction:

$$D_{JS}[p(x)||q(x)]=\frac{1}{2}{D}_{KL}\left[p(x)\left|\right|\frac{p(x)+q(x)}{2}\right]+\frac{1}{2}{D}_{KL}\left[q(x)\left|\right|\frac{p(x)+q(x)}{2}\right]$$

It is the mean divergence of $p(x)$ and $q(x)$ to the average of the two distributions.