Statistics on graphs and networks (II) | Vidéo | Carmin.tv

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Statistics on graphs and networks (II)

By Ulrike von Luxburg

Appears in collection : Meeting in mathematical statistics: new procedures for new data / Rencontre de statistiques mathématiques : nouvelles procédures pour de nouvelles données

Consider a sample of points drawn from some unknown density on $R^d$. Assume the only information we have about the sample are the $k$-nearest neighbor relationships: we know who is among the $k$-nearest neighors of whom, but we do not know any distances between points, nor the point coordinates themselves. We prove that as the sample size goes to infinty, it is possible to reconstruct the underlying density p and the distances of the points (up to a multiplicative constant).

$k$-nearest neighbor graph - random geometric graph - ordinal embedding

Information about the video

Date of recording 16/12/2014
Date of publication 08/01/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18659103
Cite this video von Luxburg, Ulrike (16/12/2014). Statistics on graphs and networks (II). CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18659103
URL https://dx.doi.org/10.24350/CIRM.V.18659103

Domain(s)

Bibliography

Terada, Y., & von Luxburg, U. (2014). Local ordinal embedding. In T. Jebara & E.P. Xing (Eds.) Proceedings of the 31st International Conference on Machine Learning (ICML-14). JMLR Workshop and Conference Proceedings, 32, p. 847-855 - http://jmlr.org/proceedings/papers/v32/terada14.pdf
von Luxburg, U., & Alamgir, M. (2013). Density estimation from unweighted $k$-NN graphs: a roadmap. In C.J.C. Burges, L. Bottou, M. Welling, Z. Ghahramani, & K.Q. Weinberger (Eds.), Advances in Neural Information Processing Systems 26 (pp. 225-233). New-York: Curran Associates - http://papers.nips.cc/paper/5112-density-estimation-from-unweighted-k-nearest-neighbor-graphs-a-roadmap.pdf

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