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Manifold Learning on Fibre Bundles

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时间:2017-12-05  来源:数学机械化重点实验室

题目:           Manifold Learning on Fibre Bundles 

报告人:      高挺然  (芝加哥大学

时间地点:   2017.12.6  15:00pm  N205

摘要:           We develop a geometric framework, based on the classical theory of fibre bundles, to characterize the cohomological nature of a large class of synchronization-type problems in the context of graph inference and combinatorial optimization. In this type of problems, the pairwise interaction between adjacent vertices in the graph is of a "non-scalar" nature, typically taking values in a group or groupoid; the "consistency" among these non-scalar pairwise interactions provide information for the dataset from which the graph is constructed. We model these data as a fibre bundle equipped with a connection, and consider a horizontal diffusion process on the fibre bundle driven by a standard diffusion process on the base manifold of the fibre bundle; the spectral information of the horizontal diffusion decouples the base manifold structure from the observed non-scalar pairwise interactions. We demonstrate an application of this framework on evolutionary anthropology.

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