Identity and variation spaces: Revisiting the fisher linear discriminant

Sheng Zhang, Terence Sim, Mei Chen Yeh

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

1 Citation (Scopus)

Abstract

The Fisher Linear Discriminant (FLD) is commonly used in classification to find a subspace that maximally separates class patterns according to the Fisher Criterion. It was previously proven that a pre-whitening step can be used to truly optimize the Fisher Criterion. In this paper, we study the theoretical properties of the subspaces induced by this whitened FLD. Of the four subspaces induced, two are most important for classification and representation of patterns. We call these Identity Space and Variation Space. We show that only the between-class variation remains in Identity Space, and only the within-class variation remains in Variation Space. Both spaces can be used for decomposition and representation of class data. Moreover, we give sufficient conditions for these spaces to exist. Finally, we also run experiments to show how Identity and Variation Spaces may be used for classification and image synthesis.

Original languageEnglish
Title of host publication2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009
Pages123-130
Number of pages8
DOIs
Publication statusPublished - 2009 Dec 1
Event2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009 - Kyoto, Japan
Duration: 2009 Sep 272009 Oct 4

Publication series

Name2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009

Other

Other2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009
CountryJapan
CityKyoto
Period09/9/2709/10/4

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ASJC Scopus subject areas

  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

Cite this

Zhang, S., Sim, T., & Yeh, M. C. (2009). Identity and variation spaces: Revisiting the fisher linear discriminant. In 2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009 (pp. 123-130). [5457708] (2009 IEEE 12th International Conference on Computer Vision Workshops, ICCV Workshops 2009). https://doi.org/10.1109/ICCVW.2009.5457708