  Although data diffusion embeddings are ubiquitous in unsupervised learning
and have proven to be a viable technique for uncovering the underlying
intrinsic geometry of data, diffusion embeddings are inherently limited due to
their discrete nature. To this end, we propose neural FIM, a method for
computing the Fisher information metric (FIM) from point cloud data - allowing
for a continuous manifold model for the data. Neural FIM creates an extensible
metric space from discrete point cloud data such that information from the
metric can inform us of manifold characteristics such as volume and geodesics.
We demonstrate Neural FIM's utility in selecting parameters for the PHATE
visualization method as well as its ability to obtain information pertaining to
local volume illuminating branching points and cluster centers embeddings of a
toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs
(immune cells).
