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- W4310632760 abstract "Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with fewer degrees of freedom, on the dataset. We introduce the frameworks of semiclassical and microlocal analysis to data analysis and develop a novel, yet natural uncertainty principle for extracting fine-scale features of this geometric structure in data, crucially dependent on data-driven approximations to quantum mechanical processes underlying geometric optics. This leads to the first tractable algorithm for approximation of wave dynamics and geodesics on data manifolds with rigorous probabilistic convergence rates under the manifold hypothesis. We demonstrate our algorithm on real-world datasets, including an analysis of population mobility information during the COVID-19 pandemic to achieve four-fold improvement in dimensionality reduction over existing state-of-the-art and reveal anomalous behavior exhibited by less than 1.2% of the entire dataset. Our work initiates the study of data-driven quantum dynamics for analyzing datasets, and we outline several future directions for research." @default.
- W4310632760 created "2022-12-13" @default.
- W4310632760 creator A5051203367 @default.
- W4310632760 creator A5070527083 @default.
- W4310632760 date "2022-12-01" @default.
- W4310632760 modified "2023-09-23" @default.
- W4310632760 title "Shining light on data: Geometric data analysis through quantum dynamics" @default.
- W4310632760 doi "https://doi.org/10.48550/arxiv.2212.00682" @default.
- W4310632760 hasPublicationYear "2022" @default.
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