caa a22 4500 445331542 CHVBK 20180317142739.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s10208-011-9103-7 doi (NATIONALLICENCE)springer-10.1007/s10208-011-9103-7 Model Selection for Simplicial Approximation [Elektronische Daten] [Claire Caillerie, Bertrand Michel] 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. SFoCM, 2011 Computational geometry nationallicence Geometric inference nationallicence Simplicial complexes nationallicence Model selection nationallicence Penalization nationallicence Slope heuristics nationallicence Spectral clustering nationallicence Caillerie Claire INRIA Saclay, Parc Club Orsay Université, 2-4 rue Jacques Monod, 91893, Orsay Cedex, France aut Michel Bertrand LSTA UPMC, 4 place Jussieu, 75252, Paris cedex 05, France aut Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 707-731 1615-3375 11:6<707 2011 11 10208 https://doi.org/10.1007/s10208-011-9103-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10208-011-9103-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Caillerie Claire INRIA Saclay, Parc Club Orsay Université, 2-4 rue Jacques Monod, 91893, Orsay Cedex, France aut NATIONALLICENCE 700 1- Michel Bertrand LSTA UPMC, 4 place Jussieu, 75252, Paris cedex 05, France aut NATIONALLICENCE 773 0- Foundations of Computational Mathematics Springer-Verlag 11/6(2011-12-01), 707-731 1615-3375 11:6<707 2011 11 10208 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer