A complexity-regularized quantization approach to nonlinear dimensionality reduction

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

Abstract

We consider the problem of nonlinear dimensionality reduction: given a training set of high-dimensional data whose "intrinsic" low dimension is assumed known, find a feature extraction map to low-dimensional space, a reconstruction map back to high-dimensional space, and a geometric description of the dimension-reduced data as a smooth manifold. We introduce a complexity-regularized quantization approach for fitting a Gaussian mixture model to the training set via a Lloyd algorithm. Complexity regularization controls the trade-off between adaptation to the local shape of the underlying manifold and global geometric consistency. The resulting mixture model is used to design the feature extraction and reconstruction maps and to define a Riemannian metric on the low-dimensional data. We also sketch a proof of consistency of our scheme for the purposes of estimating the unknown underlying pdf of high-dimensional data.

Original languageEnglish (US)
Title of host publicationProceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05
Pages352-356
Number of pages5
DOIs
StatePublished - Dec 1 2005
Event2005 IEEE International Symposium on Information Theory, ISIT 05 - Adelaide, Australia
Duration: Sep 4 2005Sep 9 2005

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2005
ISSN (Print)2157-8099

Other

Other2005 IEEE International Symposium on Information Theory, ISIT 05
CountryAustralia
CityAdelaide
Period9/4/059/9/05

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

    Raginsky, M. (2005). A complexity-regularized quantization approach to nonlinear dimensionality reduction. In Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05 (pp. 352-356). [1523353] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2005). https://doi.org/10.1109/ISIT.2005.1523353