Neural FIM for learning Fisher Information Metrics from point cloud data

TL;DR

Neural FIM introduces a neural network-based approach to compute Fisher Information Metrics from point cloud data, enabling continuous manifold modeling and improved analysis of data geometry for visualization and biological datasets.

Contribution

It presents a novel neural method to derive Fisher Information Metrics from discrete point clouds, facilitating continuous geometric analysis of data manifolds.

Findings

Effective in selecting parameters for PHATE visualization

Able to identify local volume features like branching points and cluster centers

Demonstrated utility on toy and biological datasets

Abstract

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).