Optimal manifold representation of data: An information theoretic approach

Denis Chigirev, William Bialek

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

6 Scopus citations

Abstract

We introduce an information theoretic method for nonparametric, nonlinear dimensionality reduction, based on the infinite cluster limit of rate distortion theory.By constraining the information available to manifold coordinates, a natural probabilistic map emerges that assigns original data to corresponding points on a lower dimensional manifold. With only the information-distortion trade off as a parameter, our method determines the shape of the manifold, its dimensionality, the probabilistic map and the prior that provide optimal description of the data.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003
PublisherNeural information processing systems foundation
ISBN (Print)0262201526, 9780262201520
StatePublished - Jan 1 2004
Event17th Annual Conference on Neural Information Processing Systems, NIPS 2003 - Vancouver, BC, Canada
Duration: Dec 8 2003Dec 13 2003

Publication series

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

Other

Other17th Annual Conference on Neural Information Processing Systems, NIPS 2003
CountryCanada
CityVancouver, BC
Period12/8/0312/13/03

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

Cite this

Chigirev, D., & Bialek, W. (2004). Optimal manifold representation of data: An information theoretic approach. In Advances in Neural Information Processing Systems 16 - Proceedings of the 2003 Conference, NIPS 2003 (Advances in Neural Information Processing Systems). Neural information processing systems foundation.