Functional form estimation using oblique projection matrices for ls-SVM regression models
Kernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called 'black box' models, indicating that the relation between the input variables and the output, depending on the kernel se...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2019
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/22835
- Acceso en línea:
- https://doi.org/10.1371/journal.pone.0217967
https://repository.urosario.edu.co/handle/10336/22835
- Palabra clave:
- Analysis of variance
Article
Decomposition
Human
Least square analysis
Support vector machine
Algorithm
Artificial intelligence
Least square analysis
Machine learning
Statistical model
Support vector machine
Algorithms
Artificial intelligence
Least-squares analysis
Machine learning
Support vector machine
Statistical
Models
- Rights
- License
- Abierto (Texto Completo)
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1413951260026c827fb-524d-4c98-829a-5c9a9c9c6127373c77e3-5093-43fd-831b-0db88cefa50da03a974e-aaea-4359-86ad-ead6f862a0912020-05-25T23:58:17Z2020-05-25T23:58:17Z2019Kernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called 'black box' models, indicating that the relation between the input variables and the output, depending on the kernel selection, is unknown. In this paper we propose a new methodology to retrieve the relation between each input regressor variable and the output in a least squares support vector machine (LS-SVM) regression model. The method is based on oblique subspace projectors (ObSP), which allows to decouple the influence of input regressors on the output by including the undesired variables in the null space of the projection matrix. Such functional relations are represented by the nonlinear transformation of the input regressors, and their subspaces are estimated using appropriate kernel evaluations. We exploit the properties of ObSP in order to decompose the output of the obtained regression model as a sum of the partial nonlinear contributions and interaction effects of the input variables, we called this methodology Nonlinear ObSP (NObSP). We compare the performance of the proposed algorithm with the component selection and smooth operator (COSSO) for smoothing spline ANOVA models. We use as benchmark 2 toy examples and a real life regression model using the concrete strength dataset from the UCI machine learning repository. We showed that NObSP is able to outperform COSSO, producing stable estimations of the functional relations between the input regressors and the output, without the use of prior-knowledge. This methodology can be used in order to understand the functional relations between the inputs and the output in a regression model, retrieving the physical interpretation of the regression models. © 2019 Caicedo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.application/pdfhttps://doi.org/10.1371/journal.pone.02179671932-6203https://repository.urosario.edu.co/handle/10336/22835engPublic Library of ScienceNo. 6PLoS ONEVol. 14PLoS ONE, ISSN:19326203, Vol.14, No.6 (2019)https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067381270&doi=10.1371%2fjournal.pone.0217967&partnerID=40&md5=a0bbb2bd48d46bdbdc95d15b265f2fedAbierto (Texto Completo)http://purl.org/coar/access_right/c_abf2instname:Universidad del Rosarioreponame:Repositorio Institucional EdocURAnalysis of varianceArticleDecompositionHumanLeast square analysisSupport vector machineAlgorithmArtificial intelligenceLeast square analysisMachine learningStatistical modelSupport vector machineAlgorithmsArtificial intelligenceLeast-squares analysisMachine learningSupport vector machineStatisticalModelsFunctional form estimation using oblique projection matrices for ls-SVM regression modelsarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Caicedo Dorado, AlexanderVaron, CarolinaVan Huffel, SabineSuykens, Johan A. K.ORIGINALjournal-pone-0217967.pdfapplication/pdf4001819https://repository.urosario.edu.co/bitstreams/98643c4a-507c-42c3-b755-10d42f47fca8/download063fa3dbabbca42e4768b7c1d6f6180dMD51TEXTjournal-pone-0217967.pdf.txtjournal-pone-0217967.pdf.txtExtracted texttext/plain67690https://repository.urosario.edu.co/bitstreams/1e86e5c0-e454-4c95-8de9-91026f2e6ecd/downloadf027f9c47159cbf229f986ed89fc21eaMD52THUMBNAILjournal-pone-0217967.pdf.jpgjournal-pone-0217967.pdf.jpgGenerated Thumbnailimage/jpeg4341https://repository.urosario.edu.co/bitstreams/b0d8407f-01aa-49ec-9b46-f71c9dff1acb/downloade5287c5644508082f383abb51b9acfcfMD5310336/22835oai:repository.urosario.edu.co:10336/228352022-08-27 13:02:10.055https://repository.urosario.edu.coRepositorio institucional EdocURedocur@urosario.edu.co |
dc.title.spa.fl_str_mv |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
title |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
spellingShingle |
Functional form estimation using oblique projection matrices for ls-SVM regression models Analysis of variance Article Decomposition Human Least square analysis Support vector machine Algorithm Artificial intelligence Least square analysis Machine learning Statistical model Support vector machine Algorithms Artificial intelligence Least-squares analysis Machine learning Support vector machine Statistical Models |
title_short |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
title_full |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
title_fullStr |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
title_full_unstemmed |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
title_sort |
Functional form estimation using oblique projection matrices for ls-SVM regression models |
dc.subject.keyword.spa.fl_str_mv |
Analysis of variance Article Decomposition Human Least square analysis Support vector machine Algorithm Artificial intelligence Least square analysis Machine learning Statistical model Support vector machine Algorithms Artificial intelligence Least-squares analysis Machine learning Support vector machine |
topic |
Analysis of variance Article Decomposition Human Least square analysis Support vector machine Algorithm Artificial intelligence Least square analysis Machine learning Statistical model Support vector machine Algorithms Artificial intelligence Least-squares analysis Machine learning Support vector machine Statistical Models |
dc.subject.keyword.eng.fl_str_mv |
Statistical Models |
description |
Kernel regression models have been used as non-parametric methods for fitting experimental data. However, due to their non-parametric nature, they belong to the so-called 'black box' models, indicating that the relation between the input variables and the output, depending on the kernel selection, is unknown. In this paper we propose a new methodology to retrieve the relation between each input regressor variable and the output in a least squares support vector machine (LS-SVM) regression model. The method is based on oblique subspace projectors (ObSP), which allows to decouple the influence of input regressors on the output by including the undesired variables in the null space of the projection matrix. Such functional relations are represented by the nonlinear transformation of the input regressors, and their subspaces are estimated using appropriate kernel evaluations. We exploit the properties of ObSP in order to decompose the output of the obtained regression model as a sum of the partial nonlinear contributions and interaction effects of the input variables, we called this methodology Nonlinear ObSP (NObSP). We compare the performance of the proposed algorithm with the component selection and smooth operator (COSSO) for smoothing spline ANOVA models. We use as benchmark 2 toy examples and a real life regression model using the concrete strength dataset from the UCI machine learning repository. We showed that NObSP is able to outperform COSSO, producing stable estimations of the functional relations between the input regressors and the output, without the use of prior-knowledge. This methodology can be used in order to understand the functional relations between the inputs and the output in a regression model, retrieving the physical interpretation of the regression models. © 2019 Caicedo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
publishDate |
2019 |
dc.date.created.spa.fl_str_mv |
2019 |
dc.date.accessioned.none.fl_str_mv |
2020-05-25T23:58:17Z |
dc.date.available.none.fl_str_mv |
2020-05-25T23:58:17Z |
dc.type.eng.fl_str_mv |
article |
dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
dc.type.spa.spa.fl_str_mv |
Artículo |
dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.1371/journal.pone.0217967 |
dc.identifier.issn.none.fl_str_mv |
1932-6203 |
dc.identifier.uri.none.fl_str_mv |
https://repository.urosario.edu.co/handle/10336/22835 |
url |
https://doi.org/10.1371/journal.pone.0217967 https://repository.urosario.edu.co/handle/10336/22835 |
identifier_str_mv |
1932-6203 |
dc.language.iso.spa.fl_str_mv |
eng |
language |
eng |
dc.relation.citationIssue.none.fl_str_mv |
No. 6 |
dc.relation.citationTitle.none.fl_str_mv |
PLoS ONE |
dc.relation.citationVolume.none.fl_str_mv |
Vol. 14 |
dc.relation.ispartof.spa.fl_str_mv |
PLoS ONE, ISSN:19326203, Vol.14, No.6 (2019) |
dc.relation.uri.spa.fl_str_mv |
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85067381270&doi=10.1371%2fjournal.pone.0217967&partnerID=40&md5=a0bbb2bd48d46bdbdc95d15b265f2fed |
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http://purl.org/coar/access_right/c_abf2 |
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Abierto (Texto Completo) http://purl.org/coar/access_right/c_abf2 |
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Universidad del Rosario |
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