From 8d06fbeae596a0372bf9a921de7d04cc734eaa3b Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 30 Mar 2020 08:14:46 +0200 Subject: Biblio --- biblio/bibliography.bib | 15 +++++++++++++++ 1 file changed, 15 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 3bbe7960..f9d43638 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1192,3 +1192,18 @@ numpages = {11}, location = {Montr\'{e}al, Canada}, series = {NIPS’18} } +@Article{dtm, +author={Chazal, Fr{\'e}d{\'e}ric +and Cohen-Steiner, David +and M{\'e}rigot, Quentin}, +title={Geometric Inference for Probability Measures}, +journal={Foundations of Computational Mathematics}, +year={2011}, +volume={11}, +number={6}, +pages={733-751}, +abstract={Data often comes in the form of a point cloud sampled from an unknown compact subset of Euclidean space. The general goal of geometric inference is then to recover geometric and topological features (e.g., Betti numbers, normals) of this subset from the approximating point cloud data. It appears that the study of distance functions allows one to address many of these questions successfully. However, one of the main limitations of this framework is that it does not cope well with outliers or with background noise. In this paper, we show how to extend the framework of distance functions to overcome this problem. Replacing compact subsets by measures, we introduce a notion of distance function to a probability distribution in Rd. These functions share many properties with classical distance functions, which make them suitable for inference purposes. In particular, by considering appropriate level sets of these distance functions, we show that it is possible to reconstruct offsets of sampled shapes with topological guarantees even in the presence of outliers. Moreover, in settings where empirical measures are considered, these functions can be easily evaluated, making them of particular practical interest.}, +issn={1615-3383}, +doi={10.1007/s10208-011-9098-0}, +url={https://doi.org/10.1007/s10208-011-9098-0} +} -- cgit v1.2.3 From 0a404547afec2e43dd5edf9410ff079d156d691a Mon Sep 17 00:00:00 2001 From: Marc Glisse Date: Mon, 30 Mar 2020 08:18:38 +0200 Subject: One more ref, to be cited later --- biblio/bibliography.bib | 12 ++++++++++++ 1 file changed, 12 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index f9d43638..056ccd72 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1207,3 +1207,15 @@ issn={1615-3383}, doi={10.1007/s10208-011-9098-0}, url={https://doi.org/10.1007/s10208-011-9098-0} } +@article{dtmdensity, +author = "Biau, Gérard and Chazal, Frédéric and Cohen-Steiner, David and Devroye, Luc and Rodríguez, Carlos", +doi = "10.1214/11-EJS606", +fjournal = "Electronic Journal of Statistics", +journal = "Electron. J. Statist.", +pages = "204--237", +publisher = "The Institute of Mathematical Statistics and the Bernoulli Society", +title = "A weighted k-nearest neighbor density estimate for geometric inference", +url = "https://doi.org/10.1214/11-EJS606", +volume = "5", +year = "2011" +} -- cgit v1.2.3 From 889d7c92e9cdbab28eba53a9de38a7a0fb27688d Mon Sep 17 00:00:00 2001 From: tlacombe Date: Tue, 31 Mar 2020 11:20:49 +0200 Subject: added Turner 2014 Frechet in the bibliography --- biblio/bibliography.bib | 11 +++++++++++ 1 file changed, 11 insertions(+) (limited to 'biblio') diff --git a/biblio/bibliography.bib b/biblio/bibliography.bib index 3bbe7960..ca958e80 100644 --- a/biblio/bibliography.bib +++ b/biblio/bibliography.bib @@ -1192,3 +1192,14 @@ numpages = {11}, location = {Montr\'{e}al, Canada}, series = {NIPS’18} } + +@article{turner2014frechet, + title={Fr{\'e}chet means for distributions of persistence diagrams}, + author={Turner, Katharine and Mileyko, Yuriy and Mukherjee, Sayan and Harer, John}, + journal={Discrete \& Computational Geometry}, + volume={52}, + number={1}, + pages={44--70}, + year={2014}, + publisher={Springer} +} -- cgit v1.2.3