Empirical probability mass functions and entropies of N-dimensional clouds of points, as seen in
Onesto, V., M. Romano, F. Gentile, and F. Amato. "Relating the small world coefficient to the entropy of 2D networks and applications in neuromorphic engineering." Journal of Physics Communications 3, no. 9 (2019): 095011.
Simply
pip install cloudtropy
Given an array X of M points in N dimensions (X.shape-> M,N)
get the N-dimensional grid object and the probability mass function on the elements of the grid
import cloudtropy as ctpy
grid,pmf = ctpy.pmf(X)
which you can then use in graphics, for example if N=2:
fig = plt.figure(figsize=(4,3))
ax = fig.add_subplot(1,1,1)
cs = ax.contourf(grid[0], grid[1], pmf, cmap='Purples_r')
ax.axis('equal')
cbar = fig.colorbar(cs)
plt.show()
or to compute its entropy:
ctpy.entropy(X)
>>> 8.4976
but, in order to compare entropies between clouds you should read the reference, or the code documentation.
This work has been partially funded by the French National Agency for Research under grant ANR-19-CE38-0006 "Geometry of Public Issues" (GOPI).