Using Topology to Measure Shape in Data
Lori Ziegelmeier, Ph.D.
Macalester College
Data of various kinds is being collected at an enormous rate, and in many different forms. Often, the data are equipped with a notion of distance that reflects similarity in some sense. Using this distance measure, certain topological features–e.g. the number of connected components, loops, and trapped volumes–can be ascertained and can provide insight into the structure of these complex data sets. In this talk, I will introduce topology and a fundamental tool of topological data analysis, persistent homology. Then, we will consider examples of using this tool in two research projects by Macalester undergraduate students (1) exploring the relationship between country development and geography and (2) analyzing the collective behavior of pea aphids.
Lori Ziegelmeier was a graduate student at Colorado State University, completing her doctoral dissertation in 2013. She started at Macalester College in St. Paul, MN as a Visiting Assistant Professor that year, transitioned to tenure track in 2015, and is now an Associate Professor there. Ziegelmeier works in the field of geometric and topological data analysis, an area of mathematics at the intersection of many mathematical fields: geometry, topology, linear algebra, optimization, computing, and machine learning. She is particularly interested in developing and applying tools from computational geometry and topology to a wide variety of data sets from biological aggregations to networks of scientific concepts.
