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Hellinger Distance
cjrd edited this page Jun 13, 2012
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The Hellinger Distance is a metric used to compare two probability distributions, see e.g. Wikipedia. The TMA only computes the Hellinger distance between multinomials (vectors). Given two multinomials of the same length, (\mathbf{a}, \mathbf{b} ) the Hellinger distance is defined as:
[ hd(\mathbf{a},\mathbf{b}) = \left(\sum_i \left(\sqrt{a_i} - \sqrt{b_i}\right)^2 \right)^{\frac{1}{2}} ]