Diffusion curvature is a pointwise extension of Ollivier-Ricci curvature, designed specifically for the often messy world of pointcloud data. Its advantages include: 1. Unaffected by density fluctuations in data: it inherits the diffusion operator’s denoising properties. 2. Fast, and scalable to millions of points: it depends only on matrix powering - no optimal transport required.

It’s not yet available via PyPI. In the meantime, you can run:

pip install git+git://github.com/professorwug/diffusion_curvature@master

To compute diffusion curvature, first create a graphtools graph with your data. Graphtools offers extensive support for different kernel types (if creating from a pointcloud), and can also work with graphs in the PyGSP format. We recommend using anistropy=1, and verifying that the supplied knn value encompasses a reasonable portion of the graph.

from diffusion_curvature.datasets import torus
import graphtools
X_torus, torus_gaussian_curvature = torus(n=5000)
G_torus = graphtools.Graph(X_torus, anisotropy=1, knn=30)

Next, instantiate a DiffusionCurvature operator.

from diffusion_curvature.graphtools import DiffusionCurvature
DC = DiffusionCurvature(t=12)

 DiffusionCurvature (t:int, distance_type='PHATE', use_entropy:bool=False,
                     **kwargs)

Initialize self. See help(type(self)) for accurate signature.

And, finally, pass your graph through it. The DiffusionCurvature operator will store everything it computes – the powered diffusion matrix, the estimated manifold distances, and the curvatures – as attributes of your graph. To get the curvatures, you can run G.ks.

G_torus = DC.curvature(G_torus, dimension=2)

plot_3d(X_torus, G_torus.ks, colorbar=True, title="Diffusion Curvature on the torus")