---
_id: '11870'
abstract:
- lang: eng
  text: We derive a class of computationally inexpensive linear dimension reduction
    criteria by introducing a weighted variant of the well-known K-class Fisher criterion
    associated with linear discriminant analysis (LDA). It can be seen that LDA weights
    contributions of individual class pairs according to the Euclidean distance of
    the respective class means. We generalize upon LDA by introducing a different
    weighting function
author:
- first_name: M.
  full_name: Loog, M.
  last_name: Loog
- first_name: R.P.W.
  full_name: Duin, R.P.W.
  last_name: Duin
- first_name: Reinhold
  full_name: Haeb-Umbach, Reinhold
  id: '242'
  last_name: Haeb-Umbach
citation:
  ama: Loog M, Duin RPW, Haeb-Umbach R. Multiclass linear dimension reduction by weighted
    pairwise Fisher criteria. <i>IEEE Transactions on Pattern Analysis and Machine
    Intelligence</i>. 2001;23(7):762-766. doi:<a href="https://doi.org/10.1109/34.935849">10.1109/34.935849</a>
  apa: Loog, M., Duin, R. P. W., &#38; Haeb-Umbach, R. (2001). Multiclass linear dimension
    reduction by weighted pairwise Fisher criteria. <i>IEEE Transactions on Pattern
    Analysis and Machine Intelligence</i>, <i>23</i>(7), 762–766. <a href="https://doi.org/10.1109/34.935849">https://doi.org/10.1109/34.935849</a>
  bibtex: '@article{Loog_Duin_Haeb-Umbach_2001, title={Multiclass linear dimension
    reduction by weighted pairwise Fisher criteria}, volume={23}, DOI={<a href="https://doi.org/10.1109/34.935849">10.1109/34.935849</a>},
    number={7}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
    author={Loog, M. and Duin, R.P.W. and Haeb-Umbach, Reinhold}, year={2001}, pages={762–766}
    }'
  chicago: 'Loog, M., R.P.W. Duin, and Reinhold Haeb-Umbach. “Multiclass Linear Dimension
    Reduction by Weighted Pairwise Fisher Criteria.” <i>IEEE Transactions on Pattern
    Analysis and Machine Intelligence</i> 23, no. 7 (2001): 762–66. <a href="https://doi.org/10.1109/34.935849">https://doi.org/10.1109/34.935849</a>.'
  ieee: M. Loog, R. P. W. Duin, and R. Haeb-Umbach, “Multiclass linear dimension reduction
    by weighted pairwise Fisher criteria,” <i>IEEE Transactions on Pattern Analysis
    and Machine Intelligence</i>, vol. 23, no. 7, pp. 762–766, 2001.
  mla: Loog, M., et al. “Multiclass Linear Dimension Reduction by Weighted Pairwise
    Fisher Criteria.” <i>IEEE Transactions on Pattern Analysis and Machine Intelligence</i>,
    vol. 23, no. 7, 2001, pp. 762–66, doi:<a href="https://doi.org/10.1109/34.935849">10.1109/34.935849</a>.
  short: M. Loog, R.P.W. Duin, R. Haeb-Umbach, IEEE Transactions on Pattern Analysis
    and Machine Intelligence 23 (2001) 762–766.
date_created: 2019-07-12T05:29:51Z
date_updated: 2022-01-06T06:51:11Z
department:
- _id: '54'
doi: 10.1109/34.935849
intvolume: '        23'
issue: '7'
keyword:
- approximate pairwise accuracy
- Bayes error
- Bayes methods
- error statistics
- Euclidean distance
- Fisher criterion
- linear dimension reduction
- linear discriminant analysis
- pattern classification
- statistical analysis
- statistical pattern classification
- weighting function
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://groups.uni-paderborn.de/nt/pubs/2001/LoDuHa01.pdf
oa: '1'
page: 762-766
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
status: public
title: Multiclass linear dimension reduction by weighted pairwise Fisher criteria
type: journal_article
user_id: '44006'
volume: 23
year: '2001'
...