Abstract:
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Topological Data Analysis generally refers to utilizing topological features from data. One of the main areas in topological data analysis is persistent homology, which observes data in different resolutions and summarizes topological features that persistently appear. However, directly applying persistent homology to statistical or machine learning frameworks is difficult due to its complex structure. To facilitate further application, the persistent homology is often featurized in Euclidean space or functional space. In this talk, I will explore how persistent homology can be featurized to be further applied in statistical or machine learning frameworks. Among featurizations for persistent homology, I will take a look at persistence landscape and circular coordinates. First, I will introduce persistence landscape and how it can be used to featurize time series data and build a topological layer. Then, I will introduce circular coordinates and how they can be used for visualization and dimension reduction.
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