- Volume 23, Number 3 (2017), 1663-1693.
Some theory for ordinal embedding
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.
Bernoulli, Volume 23, Number 3 (2017), 1663-1693.
Received: January 2015
Revised: July 2015
First available in Project Euclid: 17 March 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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