Bernoulli

  • Bernoulli
  • Volume 23, Number 3 (2017), 1663-1693.

Some theory for ordinal embedding

Ery Arias-Castro

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Abstract

Motivated by recent work on ordinal embedding (In Proceedings of the 27th Conference on Learning Theory (2014) 40–67), we derive large sample consistency results and rates of convergence for the problem of embedding points based on triple or quadruple distance comparisons. We also consider a variant of this problem where only local comparisons are provided. Finally, inspired by (In Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on (2011) 1077–1084 IEEE), we bound the number of such comparisons needed to achieve consistency.

Article information

Source
Bernoulli, Volume 23, Number 3 (2017), 1663-1693.

Dates
Received: January 2015
Revised: July 2015
First available in Project Euclid: 17 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1489737621

Digital Object Identifier
doi:10.3150/15-BEJ792

Mathematical Reviews number (MathSciNet)
MR3624874

Zentralblatt MATH identifier
06714315

Keywords
dissimilarity comparisons landmark multidimensional scaling non-metric multidimensional scaling (MDS) ordinal embedding

Citation

Arias-Castro, Ery. Some theory for ordinal embedding. Bernoulli 23 (2017), no. 3, 1663--1693. doi:10.3150/15-BEJ792. https://projecteuclid.org/euclid.bj/1489737621


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