Neural FIM for learning Fisher Information Metrics from point cloud data
This work addresses the problem of modeling continuous geometry from discrete data for researchers in unsupervised learning and data visualization, though it appears incremental as it builds on existing diffusion embedding techniques.
The authors tackled the limitation of discrete diffusion embeddings by proposing Neural FIM, a method to compute the Fisher information metric from point cloud data, enabling a continuous manifold model; they demonstrated its utility in parameter selection for PHATE visualization and in analyzing local volume for branching points and cluster centers in toy and single-cell datasets.
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).