diffusion-curvature 0.0.1

Fast, pointwise graph curvature

Diffusion Curvature

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.

Install

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

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

Usage

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)

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source

DiffusionCurvature

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

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

	Type	Default	Details
t	int		Number of diffusion steps to use when measuring curvature. TODO: Heuristics
distance_type	str	PHATE
use_entropy	bool	False	If true, uses KL Divergence instead of Wasserstein Distances. Faster, seems empirically as good, but less proven.
kwargs

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")