Towards topological machine learning

I am incredibly grateful about how my academic year started so far: four preprints were at least conditionally accepted for publication in a forthcoming book on topological methods in data visualization, while another publication of my new lab was accepted as a poster for ICLR 2019. The underlying theme of all these publications is to shift the focus of machine learning towards topological methods, i.e. methods that focus on connectivity properties of input data. I am convinced that thinking about these types of properties is worthwhile, as the resulting shift in perspective often leads to novel insights. This spring of papers follows two themes: in the first, topology is used directly to drive algorithms, for example to classify data, or to elucidate its properties. In the second theme, topology is used indirectly to learn something about the behaviour of other algorithms. In Persistent Intersection Homology for the Analysis of Discrete Data, Markus Banagl, Filip Sadlo, Heike Leitte, and I describe how to use persistent intersection homology, an extension of persistent homology in order to describe spaces that do not consist of a single manifold, but of multiple ones.