From Cyborg-Insect to Human Motion: Topological Data Analysis Applied to Time Series

Edgar Lobaton (May 23, 2018)

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Abstract

Topological Data Analysis has been applied to a number of problems in order to study the geometric and topological structure of point cloud data. In this talk, we discuss their application to the analysis of time series from cyborg-insect to human motion. These tools allow us to identify different type of motion behaviors from the agents, and help us discover the geometric structure of their surroundings. The mathematical framework developed allows us to derive bounds on the sampling of the data space in order to ensure recovery of the correct topological information, and also provide guarantees on the robustness of these quantities to perturbations on the data.