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تسجيل مستخدم جديدTropical Coordinates on the Space of Persistence Barcodes
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Sara Kalisnik Verovsek
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The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation of classical homology, which assigns a barcode, i.e. a collection of intervals, to a finite metric space. Because of the nature of the invariant, barcodes are not well-adapted for use by practitioners in machine learning tasks. We can circumvent this problem by assigning numerical quantities to barcodes and these outputs can then be used as input to standard algorithms. It is the purpose of this paper to identify tropical coordinates on the space of barcodes and prove that they are stable with respect to the bottleneck distance and Wasserstein distances.
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Multiparameter persistence is a natural extension of the well-known persistent homology, which has attracted a lot of interest. However, there are major theoretical obstacles preventing the full development of this promising theory. In this paper w
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