Earth mover's distance

emd_example.py

import pyemd # https://github.com/garydoranjr/pyemd. Install by running 'pip install pyemd'.
from scipy.spatial.distance import pdist, squareform

x_bins = range(10) # Assume histogram has 10 bins for each axis
y_bins = range(10)
z_bins = range(10)

xs, ys, zs = np.meshgrid(x_bins, y_bins, z_bins)
xs = xs.flatten()
ys = ys.flatten()
zs = zs.flatten()
xyzs = np.column_stack([xs, ys, zs])

D = squareform(pdist(xyzs, metric='euclidean'))

unnormalized_histogram1 = np.random.randint(1, 10, 8) # replace with actual histogram.
histogram1 = unnormalized_histogram1 / unnormalized_histogram1.sum()

unnormalized_histogram2 = np.random.randint(1, 10, 8) # replace with actual histogram.
histogram2 = unnormalized_histogram2 / unnormalized_histogram2.sum()

emd_distance = pyemd.emd(histogram1, histogram2, distance_matrix=D)

print(emd_distance)