The Hellinger distance measures the similarity of two probability

histogram_dist.cc

// The Hellinger distance measures the similarity of two probability
// distributions Reference: https://en.wikipedia.org/wiki/Hellinger_distance
double HellingerDistance(
    const std::vector<double>& histogram1,
    const std::vector<double>& histogram2) {
  const int histogram_size = histogram1.size();
  CHECK_GT(histogram_size, 0);
  CHECK_EQ(histogram_size, histogram2.size());
  const double mean1 =
      std::accumulate(histogram1.begin(), histogram1.end(), 0.0) /
      histogram_size;
  const double mean2 =
      std::accumulate(histogram2.begin(), histogram2.end(), 0.0) /
      histogram_size;
  double distance = 0.0;
  for (int i = 0; i < histogram_size; ++i) {
    distance += std::sqrt(histogram1[i] * histogram2[i]);
  }
  distance = std::sqrt(
      1.0 - (1.0 / std::sqrt(mean1 * mean2 * histogram_size * histogram_size)) *
                distance);
  return distance;
}