Preserving, Tracking and Exploiting Topological Features

Friday, May 2, 2014 - 10:15am - 11:05am
Keller 3-180
Harish Chintakunta (North Carolina State University), Hamid Krim (North Carolina State University)
The persistent/zig-zag persistent intervals provide a
meaningful topological summary of a given filtration/sequence of
spaces. However, there often arises the need to compute sparse
generators for these intervals which serve to track the features
corresponding to the intervals. We will address this problem on two
aspects: 1) simplification of the data in order to reduce the
computational complexity while preserving the desired topological
features , and 2) computing a specific summand decomposition of the
given persistent/zig-zag module where the summands result in the
desired generators. Further, given a choice of a set of filtrations, we
will present meaningful ways to choose the right filtration where the
resulting bar-code reflects some underlying geometric features.
MSC Code: