Robust Topological Inference in the Presence of Outliers

  title={Robust Topological Inference in the Presence of Outliers},
  author={Siddharth Vishwanath and Bharath K. Sriperumbudur and Kenji Fukumizu and Satoshi Kuriki},
The distance function to a compact set plays a crucial role in the paradigm of topological data analysis. In particular,the sublevel sets of the distance function are used in the computation of persistent homology— a backbone of the topological data analysis pipeline. Despite its stability to perturbations in the Hausdorff distance, persistent homology is highly sensitive to outliers. In this work, we develop a framework of statistical inference for persistent homology in the presence of… 

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