Neural FIM for learning Fisher information metrics from point cloud data
Oluwadamilola Fasina,u00a0Guillaume Huguet,u00a0Alexander Tong,u00a0Yanlei Zhang,u00a0Guy Wolf,u00a0Maximilian Nickel,u00a0Ian Adelstein,u00a0Smita Krishnaswamy
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 FIMu2019s 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).
