Statistical Topological Data Analysis - A Kernel Perspective

  title={Statistical Topological Data Analysis - A Kernel Perspective},
  author={Roland Kwitt and Stefan M Huber and Marc Niethammer and Weili Lin and Ulrich Bauer},
We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In… CONTINUE READING
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