Date
Fri, 02 Mar 2018
Time
12:00 - 13:00
Location
N3.12
Speaker
Sara Kalisnik
Organisation
MPI Leipzig

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. I will explain how we can use tropical-like functions to coordinatize the space of persistence barcodes. These coordinates are stable with respect to the bottleneck and Wasserstein distances. I will also show how they can be used in practice.

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