A geometric take on metric learning

Søren Hauberg, Oren Freifeld, Michael J. Black

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

32 Scopus citations


Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Number of pages9
StatePublished - 1 Dec 2012
Externally publishedYes
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: 3 Dec 20126 Dec 2012

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Country/TerritoryUnited States
CityLake Tahoe, NV

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing


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