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Algorithms for Metric Learning via Contrastive Embeddings

Authors Diego Ihara, Neshat Mohammadi, Anastasios Sidiropoulos



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Diego Ihara
  • University of Illinois at Chicago, USA
Neshat Mohammadi
  • University of Illinois at Chicago, USA
Anastasios Sidiropoulos
  • University of Illinois at Chicago, USA

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Diego Ihara, Neshat Mohammadi, and Anastasios Sidiropoulos. Algorithms for Metric Learning via Contrastive Embeddings. In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, pp. 45:1-45:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.SoCG.2019.45

Abstract

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe X and sets S, D subset binom{X}{2} of similar and dissimilar pairs, we seek to find a mapping f:X -> Y, into some target metric space M=(Y,rho), such that similar objects are mapped to points at distance at most u, and dissimilar objects are mapped to points at distance at least l. More generally, the goal is to find a mapping of maximum accuracy (that is, fraction of correctly classified pairs). We propose approximation algorithms for various versions of this problem, for the cases of Euclidean and tree metric spaces. For both of these target spaces, we obtain fully polynomial-time approximation schemes (FPTAS) for the case of perfect information. In the presence of imperfect information we present approximation algorithms that run in quasi-polynomial time (QPTAS). We also present an exact algorithm for learning line metric spaces with perfect information in polynomial time. Our algorithms use a combination of tools from metric embeddings and graph partitioning, that could be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • metric learning
  • contrastive distortion
  • embeddings
  • algorithms

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