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LPDA: A new classification method based on linear programming
The search of separation hyperplanes is an efficient way to find rules with classification purposes. This paper presents an alternative mathematical programming formulation to existing methods to find a discriminant hyperplane. The hyperplane H is found by minimizing the sum of all the distances to...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9262202/ https://www.ncbi.nlm.nih.gov/pubmed/35797275 http://dx.doi.org/10.1371/journal.pone.0270403 |
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author | Nueda, María J. Gandía, Carmen Molina, Mariola D. |
author_facet | Nueda, María J. Gandía, Carmen Molina, Mariola D. |
author_sort | Nueda, María J. |
collection | PubMed |
description | The search of separation hyperplanes is an efficient way to find rules with classification purposes. This paper presents an alternative mathematical programming formulation to existing methods to find a discriminant hyperplane. The hyperplane H is found by minimizing the sum of all the distances to the area assigned to the group each individual belongs to. It results in a convex optimization problem for which we find an equivalent linear programming problem. We demonstrate that H exists when the centroids of the two groups are not equal. The method is effective dealing with low and high dimensional data where reduction of the dimension is proposed to avoid overfitting problems. We show the performance of this approach with different data sets and comparisons with other classifications methods. The method is called LPDA and it is implemented in a R package available in https://github.com/mjnueda/lpda. |
format | Online Article Text |
id | pubmed-9262202 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-92622022022-07-08 LPDA: A new classification method based on linear programming Nueda, María J. Gandía, Carmen Molina, Mariola D. PLoS One Research Article The search of separation hyperplanes is an efficient way to find rules with classification purposes. This paper presents an alternative mathematical programming formulation to existing methods to find a discriminant hyperplane. The hyperplane H is found by minimizing the sum of all the distances to the area assigned to the group each individual belongs to. It results in a convex optimization problem for which we find an equivalent linear programming problem. We demonstrate that H exists when the centroids of the two groups are not equal. The method is effective dealing with low and high dimensional data where reduction of the dimension is proposed to avoid overfitting problems. We show the performance of this approach with different data sets and comparisons with other classifications methods. The method is called LPDA and it is implemented in a R package available in https://github.com/mjnueda/lpda. Public Library of Science 2022-07-07 /pmc/articles/PMC9262202/ /pubmed/35797275 http://dx.doi.org/10.1371/journal.pone.0270403 Text en © 2022 Nueda et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Nueda, María J. Gandía, Carmen Molina, Mariola D. LPDA: A new classification method based on linear programming |
title | LPDA: A new classification method based on linear programming |
title_full | LPDA: A new classification method based on linear programming |
title_fullStr | LPDA: A new classification method based on linear programming |
title_full_unstemmed | LPDA: A new classification method based on linear programming |
title_short | LPDA: A new classification method based on linear programming |
title_sort | lpda: a new classification method based on linear programming |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9262202/ https://www.ncbi.nlm.nih.gov/pubmed/35797275 http://dx.doi.org/10.1371/journal.pone.0270403 |
work_keys_str_mv | AT nuedamariaj lpdaanewclassificationmethodbasedonlinearprogramming AT gandiacarmen lpdaanewclassificationmethodbasedonlinearprogramming AT molinamariolad lpdaanewclassificationmethodbasedonlinearprogramming |