also considered the symmetrized function:
which they referred to as the "divergence", though today the "KL divergence" refers to the asymmetric function (see  for the evolution of the term). This function is symmetric and nonnegative, and had already been defined and used by Harold Jeffreys in 1948; it is accordingly called the Jeffreys divergence.
This quantity has sometimes been used for feature selection in classification problems, where  and  are the conditional pdfs of a feature under two different classes. In the Banking and Finance industries, this quantity is referred to as Population Stability Index (PSI), and is used to assess distributional shifts in model features through time.
An alternative is given via the -divergence,
which can be interpreted as the expected information gain about  from discovering which probability distribution  is drawn from,  or , if they currently have probabilities  and  respectively. 
The value  gives the Jensen–Shannon divergence, defined by
where  is the average of the two distributions,
We can also interpret  as the capacity of a noisy information channel with two inputs giving the output distributions  and . The Jensen–Shannon divergence, like all -divergences, is locally proportional to the Fisher information metric. It is similar to the Hellinger metric (in the sense that it induces the same affine connection on a statistical manifold).
Furthermore, the Jensen–Shannon divergence can be generalized using abstract statistical M-mixtures relying on an abstract mean M.