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Persistent homology for multivariate data visualization
Intervenant(s) : Bastian Rieck (IWR, Ruprecht-Karls-Universität Heidelberg) Multivariate, unstructured data sets are increasingly common in the application domains. Their built-in complexity necessitates the use of novel data analysis methods. The ultimate goal is to obtain visualizations that lead users such as domain scientists to an improved understanding of processes and properties inherent to their data. Recently, methods that focus on topological properties such as the connectivity of a data set have proven to be very effective in summarizing complex behaviour in data. This talk focuses on persistent homology, one of the techniques from computational topology. I will first briefly outline the required framework from algebraic topology that is necessary to understand persistent homology. Next, I will give an overview of the intuition that underlies persistent homology, demonstrating its computation on simple examples. Last, I will present examples from my own research that demonstrate how to use persistent homology in the context of data analysis and visualization. The focus here lies on visualizing both qualitative and quantitative aspects of data.
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