Neural FIM for learning Fisher Information Metrics from point cloud data
Neural FIM for learning Fisher Information Metrics from point cloud data
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DOI：
10.48550/arxiv.2306.06062
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
O. Fasina;Guilluame Huguet;Alexander Tong;Yanlei Zhang;Guy Wolf;Maximilian Nickel;Ian M. Adelstein;Smita Krishnaswamy
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文献类型：
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作者：
O. Fasina;Guilluame Huguet;Alexander Tong;Yanlei Zhang;Guy Wolf;Maximilian Nickel;Ian M. Adelstein;Smita Krishnaswamy
虽然数据扩散嵌入在无监督学习中无处不在，并且已被证明是一种可行的技术，用于揭示数据的潜在内在几何结构，但由于其离散性，扩散嵌入固有地受到限制。为此，我们提出了神经网络，一种从点云数据中计算Fisher信息度量（Fisher information metric）的方法-允许数据的连续流形模型。神经网络从离散点云数据中创建了一个可扩展的度量空间，这样来自度量的信息就可以告诉我们诸如体积和测地线之类的流形特征。我们证明了神经元的实用程序在选择参数的PHATE可视化方法，以及它的能力，以获得有关的信息，局部体积照明分支点和集群中心嵌入的玩具数据集和两个单细胞数据集的IPSC重编程和PBMC（免疫细胞）。
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).