Abstract
Given a real-valued function f defined over a manifold M embedded in Rd, we are interested in recovering structural information about f from the sole information of its values on a finite sample P. Existing methods provide approximation to the persistence diagram of f when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field.
Original language | English |
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Title of host publication | 31st International Symposium on Computational Geometry, SoCG 2015 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Pages | 827-841 |
Number of pages | 15 |
Volume | 34 |
ISBN (Electronic) | 9783939897835 |
DOIs | |
Publication status | Published - 1 Jun 2015 |
Externally published | Yes |
Event | 31st International Symposium on Computational Geometry, SoCG 2015: SoCG 2015 - Eindhoven, Netherlands Duration: 22 Jun 2015 → 25 Jun 2015 |
Conference
Conference | 31st International Symposium on Computational Geometry, SoCG 2015 |
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Abbreviated title | SoCG 2015 |
Country/Territory | Netherlands |
City | Eindhoven |
Period | 22/06/15 → 25/06/15 |
Keywords
- Distance to a Measure
- Nested Rips Filtration
- Persistent Homology
- Scalar Field Analysis
- Topological Data Analysis
ASJC Scopus subject areas
- Software