Comparing Distance Metrics on Vectorized Persistence Summaries
The persistence diagram (PD) is an important tool in topological data analysis for encoding an abstract representation of the homology of a shape at different scales. Different vectorizations of PD summary are commonly used in machine learning applications, however distances between vectorized persistence summaries may differ greatly from the distances between the original PDs. Surprisingly, no research has been carried out in this area before. In this work we compare distances between PDs and between different commonly used vectorizations. Our results give new insights into comparing vectorized persistence summaries and can be used to design better feature-based learning models based on PDs.
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