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Robust Persistence Diagrams using Reproducing Kernels
Siddharth Vishwanath · Kenji Fukumizu · Satoshi Kuriki · Bharath Sriperumbudur

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1437

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams are very sensitive to perturbations in the input space. In this work, we develop a framework for constructing robust persistence diagrams from superlevel filtrations of robust density estimators constructed using reproducing kernels. Using an analogue of the influence function on the space of persistence diagrams, we establish the proposed framework to be less sensitive to outliers. The robust persistence diagrams are shown to be consistent estimators in the bottleneck distance, with the convergence rate controlled by the smoothness of the kernel — this, in turn, allows us to construct uniform confidence bands in the space of persistence diagrams. Finally, we demonstrate the superiority of the proposed approach on benchmark datasets.

Author Information

Siddharth Vishwanath (The Pennsylvania State University)
Kenji Fukumizu (Institute of Statistical Mathematics / Preferred Networks / RIKEN AIP)
Satoshi Kuriki (Institute of Statistical Mathematics)
Bharath Sriperumbudur (Penn State University)

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