**UM Math Graduate Students Seminar**

Dr. Anton Dochtermann

* University of Miami *

**will present**

**Topological data analysis **

Friday, October 25, 2013, 4:00pm

Ungar Building Room 402

**Abstract:** These days everyone is talking about 'Big Data' (a Google search gives more than 30 million hits, and it even has its own Wiki page). Mathematically speaking we can think of Big Data as simply a large (but finite) collection of vectors in some high dimensional space. The assumption is that this data cloud is not just random, but in fact has some underlying (and 'hidden') structure. Perhaps the data is clumped into several components, or has high dimensional 'holes', or perhaps it even lies on some submanifold.

Topological data analysis, developed by Carlsson and collaborators, is a simple but powerful way to dynamically access this structure. The basic idea is to associate a one parameter family of topological spaces to the data cloud, and to record the Betti numbers (the 'holes') as we vary the parameter. The resulting 'bar code' tells us which features of the data 'persist', an insight into the 'shape' of the data. I will describe the basics of topological data analysis and sketch an application to the 'space of natural images'.

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