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There is a great deal of recent excitement around the idea of finding shape in data. The relatively young field of topological data analysis (TDA) provides tools which can quantify, investigate, and utilize shape in data to understand something about the domain from which the data was obtained. These methods have been successfully used in many fields, including atmospheric science, time series analysis, and genetics to provide deep insights. However, what does it really mean for data to have shape? In this talk, we will look at some common tools used in TDA such as persistence diagrams, Reeb graphs, and mapper, and ideas for how different kinds of data can fit into the TDA pipeline.
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