Bhattacharyya distance

In statistics, the Bhattacharyya distance measures the similarity of two discrete probability distributions. It is usually used to measure the separability of classes in classification.

For discrete probability distributions p and q over the same domain X; it is defined as:
 * $$BC(p,q) = \sum_{x\in X} \sqrt{p(x) q(x)}$$

The Bhattacharyya coefficient is a divergence-type measure; it can be seen as the scalar product of the two vectors (one for $$p$$ and one for $$q$$) having as components the square root of the probability of the points x &isin; X. It thereby lends itself to a geometric interpretation: the Bhattacharyya coefficient is the cosine of the angle enclosed between these two vectors.