Math @ Duke

Publications [#329938] of Francis C. Motta
Papers Published
 Motta, FC, Topological Data Analysis: Developments and Applications,
in Advances in Nonlinear Geosciences, edited by Tsonis, A
(November, 2017),
pp. 369391, Springer, ISBN 3319588958
(last updated on 2018/01/23)
Abstract: Topological Data Analysis (TDA) and its mainstay computational device, persistent homology (PH), has established a strong track record of providing researchers across the datadriven sciences with new insights and methodologies by characterizing lowdimensional geometric structures in highdimensional data. When combined with machine learning (ML) methods, PH is valued as a discriminatingfeature extraction tool. This work highlights many of the recent successes at the intersection of TDA and ML, introduces some of the foundational mathematics underpinning TDA, and summarizes the efforts to strengthen the bridge between TDA and ML. Thus, this document is a launching point for experimentalists and theoreticians to consider what can be learned from the shape of their data.


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