Geodesic distance function learning via heat flow on vector fields

Binbin Lin, Ji Yangt, Xiaofei He, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm.

Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages1346-1354
Number of pages9
ISBN (Electronic)9781634393973
StatePublished - Jan 1 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: Jun 21 2014Jun 26 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume2

Other

Other31st International Conference on Machine Learning, ICML 2014
CountryChina
CityBeijing
Period6/21/146/26/14

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ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

Cite this

Lin, B., Yangt, J., He, X., & Ye, J. (2014). Geodesic distance function learning via heat flow on vector fields. In 31st International Conference on Machine Learning, ICML 2014 (pp. 1346-1354). (31st International Conference on Machine Learning, ICML 2014; Vol. 2). International Machine Learning Society (IMLS).