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Revision as of 16:59, 2 March 2020
The homology of Data
Nina Otter (UCLA)
14.04. - 17.04.2020
Physikalisches Institut, INF 226
part of the Heidelberg Physics Graduate Days
Abstract Techniques and ideas from topology - the mathematical area that studies shapes - are being applied to the study of data with increasing frequency and success.
In this lecture series we will explore how we can use homology, a technique in topology that gives a measure of the number of holes of a space, to study data. The most well-known method of this type is persistent homology, in which one associates a one-parameter family of spaces to a data set and studies how the holes evolve across the parameter space. A more recent and less well-known technique is magnitude homology, which one can think of as giving a measure of the "effective number of points" of a metric space. In this course we will introduce the theoretical background for persistent and magnitude homology, and then dive into applications using software implementations and statistical analysis tools on real-world data sets.