---
_id: '48857'
abstract:
- lang: eng
  text: 'While finding minimum-cost spanning trees (MST) in undirected graphs is solvable
    in polynomial time, the multi-criteria minimum spanning tree problem (mcMST) is
    NP-hard. Interestingly, the mcMST problem has not been in focus of evolutionary
    computation research for a long period of time, although, its relevance for real
    world problems is easy to see. The available and most notable approaches by Zhou
    and Gen as well as by Knowles and Corne concentrate on solution encoding and on
    fairly dated selection mechanisms. In this work, we revisit the mcMST and focus
    on the mutation operators as exploratory components of evolutionary algorithms
    neglected so far. We investigate optimal solution characteristics to discuss current
    mutation strategies, identify shortcomings of these operators, and propose a sub-tree
    based operator which offers what we term Pareto-beneficial behavior: ensuring
    convergence and diversity at the same time. The operator is empirically evaluated
    inside modern standard evolutionary meta-heuristics for multi-criteria optimization
    and compared to hitherto applied mutation operators in the context of mcMST.'
author:
- first_name: Jakob
  full_name: Bossek, Jakob
  id: '102979'
  last_name: Bossek
  orcid: 0000-0002-4121-4668
- first_name: Christian
  full_name: Grimme, Christian
  last_name: Grimme
citation:
  ama: 'Bossek J, Grimme C. A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria
    Minimum Spanning Tree Problem. In: <i>2017 IEEE Symposium Series on Computational
    Intelligence (SSCI)</i>. ; 2017:1–8. doi:<a href="https://doi.org/10.1109/SSCI.2017.8285183">10.1109/SSCI.2017.8285183</a>'
  apa: Bossek, J., &#38; Grimme, C. (2017). A Pareto-Beneficial Sub-Tree Mutation
    for the Multi-Criteria Minimum Spanning Tree Problem. <i>2017 IEEE Symposium Series
    on Computational Intelligence (SSCI)</i>, 1–8. <a href="https://doi.org/10.1109/SSCI.2017.8285183">https://doi.org/10.1109/SSCI.2017.8285183</a>
  bibtex: '@inproceedings{Bossek_Grimme_2017, title={A Pareto-Beneficial Sub-Tree
    Mutation for the Multi-Criteria Minimum Spanning Tree Problem}, DOI={<a href="https://doi.org/10.1109/SSCI.2017.8285183">10.1109/SSCI.2017.8285183</a>},
    booktitle={2017 IEEE Symposium Series on Computational Intelligence (SSCI)}, author={Bossek,
    Jakob and Grimme, Christian}, year={2017}, pages={1–8} }'
  chicago: Bossek, Jakob, and Christian Grimme. “A Pareto-Beneficial Sub-Tree Mutation
    for the Multi-Criteria Minimum Spanning Tree Problem.” In <i>2017 IEEE Symposium
    Series on Computational Intelligence (SSCI)</i>, 1–8, 2017. <a href="https://doi.org/10.1109/SSCI.2017.8285183">https://doi.org/10.1109/SSCI.2017.8285183</a>.
  ieee: 'J. Bossek and C. Grimme, “A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria
    Minimum Spanning Tree Problem,” in <i>2017 IEEE Symposium Series on Computational
    Intelligence (SSCI)</i>, 2017, pp. 1–8, doi: <a href="https://doi.org/10.1109/SSCI.2017.8285183">10.1109/SSCI.2017.8285183</a>.'
  mla: Bossek, Jakob, and Christian Grimme. “A Pareto-Beneficial Sub-Tree Mutation
    for the Multi-Criteria Minimum Spanning Tree Problem.” <i>2017 IEEE Symposium
    Series on Computational Intelligence (SSCI)</i>, 2017, pp. 1–8, doi:<a href="https://doi.org/10.1109/SSCI.2017.8285183">10.1109/SSCI.2017.8285183</a>.
  short: 'J. Bossek, C. Grimme, in: 2017 IEEE Symposium Series on Computational Intelligence
    (SSCI), 2017, pp. 1–8.'
date_created: 2023-11-14T15:58:54Z
date_updated: 2023-12-13T10:44:28Z
department:
- _id: '819'
doi: 10.1109/SSCI.2017.8285183
extern: '1'
keyword:
- Convergence
- Encoding
- Euclidean distance
- Evolutionary computation
- Heating systems
- Optimization
- Standards
language:
- iso: eng
page: 1–8
publication: 2017 IEEE Symposium Series on Computational Intelligence (SSCI)
publication_status: published
status: public
title: A Pareto-Beneficial Sub-Tree Mutation for the Multi-Criteria Minimum Spanning
  Tree Problem
type: conference
user_id: '102979'
year: '2017'
...
---
_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'
...