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Title: Robust Persistence Diagrams using Reproducing Kernels
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.  more » « less
Award ID(s):
1945396
NSF-PAR ID:
10420402
Author(s) / Creator(s):
; ;
Editor(s):
Larochelle, H.; Ranzato, M.; Hadsell, R.; Balcan, M.F.; and Lin, H.
Date Published:
Journal Name:
Advances in neural information processing systems
Volume:
33
ISSN:
1049-5258
Page Range / eLocation ID:
21900--21911
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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