Model selection for simplicial approximation Caillerie, Claire; Michel, Bertrand

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Authors
Caillerie, Claire ; Michel, Bertrand
Appears In
Foundations of Computational Mathematics
Subjects
computational geometry; geometrical inference; slope heuristics
Audience
Academic
Summary
In the computational geometry field, simplicial complexes have been used to describe an underlying geometric shape knowing a point cloud sampled on it. In this article, an adequate statistical framework is first proposed for the choice of a simplicial complex among a parametrized family. A least-squares penalized criterion is introduced to choose a complex, and a model selection theorem states how to select the "best" model, from a statistical point of view. This result gives the shape of the penalty, and then the "slope heuristics method" is used to calibrate the penalty from the data. Some experimental studies on simulated and real datasets illustrate the method for the selection of graphs and simplicial complexes of dimension two. Keywords Computational geometry * Geometric inference * Simplicial complexes * Model selection * Penalization * Slope heuristics * Spectral clustering Mathematics Subject Classification (2000) 62H12 * 62H30 * 05E45 * 55U10
Bookmark
http://trove.nla.gov.au/work/196398
Work ID
196398

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