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).

提出一种名为神经FIM的新方法，可以从离散点云数据中计算Fisher信息度量，并创建一个可扩展的度量空间，以建立连续流形模型来生成嵌入数据，以量化该流形的各种特征，证明了神经FIM在选择PHATE可视化方法的参数方面的实用性以及在IPSC重编程和PBMCs（免疫细胞）等单细胞数据集的分支点和聚类中心嵌入的局部体积方面获取的信息。

神经 FIM：从点云数据中学习 Fisher 信息度量