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The Reeb graph interleaving distance

Elizabeth Munch, U Albany

  • Computer Science Seminar
  • Geometry/ Topology Seminar
When Wed, Oct 12, 2016
from 03:10 PM to 04:00 PM
Where 115 Ritter Hall
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In order to understand the properties of a real-valued function on a topological space, we can study the Reeb graph of that function.  Since it is efficient to compute and is a useful descriptor for the function, it has found its place in many applications. However, as with many other constructions in computational topology, we are interested in how to deal with this construction in the context of noise.  In this talk, we will define the interleaving distance for Reeb graphs, discuss computational complexity issues arising from this definition and potential directions for approximation.  The interleaving distance also provides other insights such as convergence and approximation results for Mapper, a commonly used tool in TDA, as well as an understanding of these structures in higher dimensional settings.

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