What is Hellinger Distance and when to use it?
Hellinger distance is a metric to measure the difference between two probability distributions. It is the probabilistic analog of Euclidean distance.

Given two probability distributions, $P$ and $Q$, Hellinger distance is defined as: 

$$h(P,Q) = \frac1{\sqrt2}\cdot \|\sqrt{P}-\sqrt{Q}\|_2$$

It is useful when quantifying the difference between two probability distributions. For example, if you estimate a distribution for users and non-users of a service. If the Hellinger distance is small between those groups for some features, then those features are not statistically useful for segmentation.