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Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, May 11, 2020 - 12:00 to 12:50

Location:

Zoom

Local Speaker:

Abstract:

Mapper is a tool designed by Singh, Mémoli, and Carlsson for Topological Data Analysis (TDA) that constructs a simplicial complex from a finite subset of a metric space. Due to the varying input parameters of Mapper and the potential Mapper has shown in TDA, questioning its stability is natural. In this talk, we begin by defining a machine learning technique known as clustering and then provide a definition of the Mapper algorithm. Following this, we outline a measure of instability of the Mapper algorithm proposed by Belchí, Brodzki, Burfitt, and Niranjan. This instability measure is based on the work of Ben-David and von Luxburg on clustering instability. Finally, we present a theorem by Belchí et. al. that provides a bound on the proposed instability measure. This bound can be used to describe conditions under which the instability measure converges to zero for large enough sample sizes. This talk assumes only a basic understanding of TDA and all are encouraged to attend.