Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD
Multivariate binary data are increasingly frequent in practice. Although some adaptations of principal component analysis are used to reduce dimensionality for this kind of data, none of them provide a simultaneous representation of rows and columns (biplot). Recently, a technique named logistic bip...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/2015 |
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| author | Jose Giovany Babativa-Márquez José Luis Vicente-Villardón |
| author_facet | Jose Giovany Babativa-Márquez José Luis Vicente-Villardón |
| author_sort | Jose Giovany Babativa-Márquez |
| collection | DOAJ |
| description | Multivariate binary data are increasingly frequent in practice. Although some adaptations of principal component analysis are used to reduce dimensionality for this kind of data, none of them provide a simultaneous representation of rows and columns (biplot). Recently, a technique named logistic biplot (LB) has been developed to represent the rows and columns of a binary data matrix simultaneously, even though the algorithm used to fit the parameters is too computationally demanding to be useful in the presence of sparsity or when the matrix is large. We propose the fitting of an LB model using nonlinear conjugate gradient (CG) or majorization–minimization (MM) algorithms, and a cross-validation procedure is introduced to select the hyperparameter that represents the number of dimensions in the model. A Monte Carlo study that considers scenarios with several sparsity levels and different dimensions of the binary data set shows that the procedure based on cross-validation is successful in the selection of the model for all algorithms studied. The comparison of the running times shows that the CG algorithm is more efficient in the presence of sparsity and when the matrix is not very large, while the performance of the MM algorithm is better when the binary matrix is balanced or large. As a complement to the proposed methods and to give practical support, a package has been written in the R language called BiplotML. To complete the study, real binary data on gene expression methylation are used to illustrate the proposed methods. |
| first_indexed | 2024-03-10T08:37:22Z |
| format | Article |
| id | doaj.art-b3463de636b54733b2f4c2503ab776d9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T08:37:22Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b3463de636b54733b2f4c2503ab776d92023-11-22T08:35:16ZengMDPI AGMathematics2227-73902021-08-01916201510.3390/math9162015Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVDJose Giovany Babativa-Márquez0José Luis Vicente-Villardón1Department of Statistics, University of Salamanca, 37008 Salamanca, SpainDepartment of Statistics, University of Salamanca, 37008 Salamanca, SpainMultivariate binary data are increasingly frequent in practice. Although some adaptations of principal component analysis are used to reduce dimensionality for this kind of data, none of them provide a simultaneous representation of rows and columns (biplot). Recently, a technique named logistic biplot (LB) has been developed to represent the rows and columns of a binary data matrix simultaneously, even though the algorithm used to fit the parameters is too computationally demanding to be useful in the presence of sparsity or when the matrix is large. We propose the fitting of an LB model using nonlinear conjugate gradient (CG) or majorization–minimization (MM) algorithms, and a cross-validation procedure is introduced to select the hyperparameter that represents the number of dimensions in the model. A Monte Carlo study that considers scenarios with several sparsity levels and different dimensions of the binary data set shows that the procedure based on cross-validation is successful in the selection of the model for all algorithms studied. The comparison of the running times shows that the CG algorithm is more efficient in the presence of sparsity and when the matrix is not very large, while the performance of the MM algorithm is better when the binary matrix is balanced or large. As a complement to the proposed methods and to give practical support, a package has been written in the R language called BiplotML. To complete the study, real binary data on gene expression methylation are used to illustrate the proposed methods.https://www.mdpi.com/2227-7390/9/16/2015binary datalogistic biplotoptimization methodsconjugate gradient algorithmcoordinate descent algorithmMM algorithm |
| spellingShingle | Jose Giovany Babativa-Márquez José Luis Vicente-Villardón Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD Mathematics binary data logistic biplot optimization methods conjugate gradient algorithm coordinate descent algorithm MM algorithm |
| title | Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD |
| title_full | Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD |
| title_fullStr | Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD |
| title_full_unstemmed | Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD |
| title_short | Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD |
| title_sort | logistic biplot by conjugate gradient algorithms and iterated svd |
| topic | binary data logistic biplot optimization methods conjugate gradient algorithm coordinate descent algorithm MM algorithm |
| url | https://www.mdpi.com/2227-7390/9/16/2015 |
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