Abstract
In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth K in a metric space, but it got corrupted with noise so that some of the data points lie far away from K creating outliers also termed as ambient noise. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of K. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases. Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms are effective in practice.
Original language | English |
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Title of host publication | 33rd International Symposium on Computational Geometry, SoCG 2017 |
Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Pages | 231-2316 |
Number of pages | 2086 |
Volume | 77 |
ISBN (Electronic) | 9783959770385 |
DOIs | |
Publication status | Published - 1 Jun 2017 |
Externally published | Yes |
Event | 33rd International Symposium on Computational Geometry: SoCG 2017 - The University of Queensland, St Lucia, Brisbane, Australia Duration: 4 Jul 2017 → 7 Jul 2017 http://socg2017.smp.uq.edu.au/ |
Conference
Conference | 33rd International Symposium on Computational Geometry |
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Abbreviated title | SoCG |
Country/Territory | Australia |
City | Brisbane |
Period | 4/07/17 → 7/07/17 |
Internet address |
Keywords
- Compact sets
- Denoising
- K-distance
- Parameter free
ASJC Scopus subject areas
- Software