Integrating global and local structures: A least squares framework for dimensionality reduction

Jianhui Chen, Jieping Ye, Qi Li

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

57 Scopus citations

Abstract

Linear Discriminant Analysis (LDA) is a popular statistical approach for dimensionality reduction. LDA captures the global geometric structure of the data by simultaneously maximizing the between-class distance and minimizing the within-class distance. However, local geometric structure has recently been shown to be effective for dimensionality reduction. In this paper, a novel dimensionality reduction algorithm is proposed, which integrates both global and local structures. The main contributions of this paper include: (1) We present a least squares formulation for dimensionality reduction, which facilities the integration of global and local structures; (2) We design an efficient model selection scheme for the optimal integration, which balances the tradeoff between the global and local structures; and (3) We present a detailed theoretical analysis on the intrinsic relationship between the proposed framework and LDA. Our extensive experimental studies on benchmark data sets show that the proposed integration framework is competitive with traditional dimensionality reduction algorithms, which use global or local structure only.

Original languageEnglish (US)
Title of host publication2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
DOIs
StatePublished - Oct 12 2007
Event2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07 - Minneapolis, MN, United States
Duration: Jun 17 2007Jun 22 2007

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISSN (Print)1063-6919

Other

Other2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07
CountryUnited States
CityMinneapolis, MN
Period6/17/076/22/07

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ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

Cite this

Chen, J., Ye, J., & Li, Q. (2007). Integrating global and local structures: A least squares framework for dimensionality reduction. In 2007 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR'07 [4270065] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition). https://doi.org/10.1109/CVPR.2007.383040