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Abstract:
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Topology studies the structure of shapes. Topological data analysis (TDA) is the study of the shape of (often large high-dimensional, and noisy) data. Often, in TDA, the data set is transformed into a concise descriptor, such as a persistence diagram or a dendogram, which can then be used to (indirectly) compare or classify data sets. In this talk, we will define a persistence diagram and confidence sets for persistence diagrams. Then, we will discuss how we can use these confidence sets to perform statistical hypothesis testing, and we will share some resent results in applying these methods to data sets from the Sloan Digital Sky Survey.
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