Keeping the TDA promise

Tuesday, February 18, 2014 - 1:30pm - 2:30pm
Lind 305
Jose Perea (Duke University)
Advocacy for the use of topological methods in the analysis of real-world
data often comes as a two-part promise:

1. Topological methods provide ways of identifying hidden structures in
data,which would otherwise be inaccessible. Moreover, finding such structures
is not only interesting but really useful.

2. Persistence diagrams and bar codes yield rich and succinct
of highly nontrivial objects. These representations, in turn, can be used
to successfully attack challenging problems.

In this talk I will present results geared toward keeping this two-part
I will show how having access to the Klein-bottle model for highly
image-patches can be used with high success in the problem of texture
and how understanding persistence diagrams from time-delay embeddings
yields good methods for quantifying periodicity and quasiperiodicity
in time-series data.