Department of Mathematics Calendar
Yu-Min Chung, UNC Greensboro, Summaries of persistence diagrams and their applications to data science
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Topological Data Analysis (TDA) is a relatively young field in both algebraic topology and machine learning. Tools from TDA, in particular persistent homology, have proven successful in many scientific disciplines. Persistence diagrams, a typical way to study persistent homology, contain fruitful information about the underlying objects. However, performing statistical methods directly on the space of persistence diagrams is challenging due to its complicated structure. Extracting features from persistence diagrams is one of the major research areas in TDA. In this talk, we will demonstrate two methods we propose to summarize persistence diagrams, and discuss their stability. Applications to various datasets from cell biology, physiology, and climatology, will be presented to illustrate the proposed methods.