Analysis and convergence of weighted dimensionality reduction methods
We propose to use a Fisher type discriminant objective function addressed to weighted principal component analysis (WPCA) and weighted regularized discriminant analysis (WRDA) for dimensionality reduction. Additionally, two different proofs for the convergence of the method are obtained. First one...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Universidad de Antioquia
2013-02-01
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| Series: | Revista Facultad de Ingeniería Universidad de Antioquia |
| Subjects: | |
| Online Access: | https://revistas.udea.edu.co/index.php/ingenieria/article/view/14674 |
| _version_ | 1797861599054135296 |
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| author | Juan Carlos Riaño Rojas Flavio Augusto Prieto Ortiz Edgar Nelson Sánchez Camperos Carlos Daniel Acosta Medina Germán Augusto Castellanos Domínguez |
| author_facet | Juan Carlos Riaño Rojas Flavio Augusto Prieto Ortiz Edgar Nelson Sánchez Camperos Carlos Daniel Acosta Medina Germán Augusto Castellanos Domínguez |
| author_sort | Juan Carlos Riaño Rojas |
| collection | DOAJ |
| description |
We propose to use a Fisher type discriminant objective function addressed to weighted principal component analysis (WPCA) and weighted regularized discriminant analysis (WRDA) for dimensionality reduction. Additionally, two different proofs for the convergence of the method are obtained. First one analytically, by using the completeness theorem, and second one algebraically, employing spectral decomposition. The objective function depends on two parameters U matrix being the rotation and D diagonal matrix weight of relevant features, respectively. These parameters are computed iteratively, in order to maximize the reduction. Relevant features were obtained by determining the eigenvector associated to the most weighted eigenvalue onthe maximum value in U. Performance evaluation of the reduction methods was carried out on 70 benchmark databases. Results showed that weighted reduction methods presented the best behavior, PCA and PPCA lower than 17% while WPCA and WRDA higher than 45%. Particularly, WRDA method had the best performance in the 75% of the cases compared with the others studied here.
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| first_indexed | 2024-04-09T22:06:49Z |
| format | Article |
| id | doaj.art-0add45ce1ecb4f0c8d18906755d2e26b |
| institution | Directory Open Access Journal |
| issn | 0120-6230 2422-2844 |
| language | English |
| last_indexed | 2024-04-09T22:06:49Z |
| publishDate | 2013-02-01 |
| publisher | Universidad de Antioquia |
| record_format | Article |
| series | Revista Facultad de Ingeniería Universidad de Antioquia |
| spelling | doaj.art-0add45ce1ecb4f0c8d18906755d2e26b2023-03-23T12:35:55ZengUniversidad de AntioquiaRevista Facultad de Ingeniería Universidad de Antioquia0120-62302422-28442013-02-015610.17533/udea.redin.14674Analysis and convergence of weighted dimensionality reduction methodsJuan Carlos Riaño Rojas0Flavio Augusto Prieto Ortiz1Edgar Nelson Sánchez Camperos2Carlos Daniel Acosta Medina3Germán Augusto Castellanos Domínguez4National University of ColombiaNational University of ColombiaNational Polytechnic InstituteNational University of ColombiaNational University of Colombia We propose to use a Fisher type discriminant objective function addressed to weighted principal component analysis (WPCA) and weighted regularized discriminant analysis (WRDA) for dimensionality reduction. Additionally, two different proofs for the convergence of the method are obtained. First one analytically, by using the completeness theorem, and second one algebraically, employing spectral decomposition. The objective function depends on two parameters U matrix being the rotation and D diagonal matrix weight of relevant features, respectively. These parameters are computed iteratively, in order to maximize the reduction. Relevant features were obtained by determining the eigenvector associated to the most weighted eigenvalue onthe maximum value in U. Performance evaluation of the reduction methods was carried out on 70 benchmark databases. Results showed that weighted reduction methods presented the best behavior, PCA and PPCA lower than 17% while WPCA and WRDA higher than 45%. Particularly, WRDA method had the best performance in the 75% of the cases compared with the others studied here. https://revistas.udea.edu.co/index.php/ingenieria/article/view/14674PCAPPCAWPCAWRDAdimensionality reduction |
| spellingShingle | Juan Carlos Riaño Rojas Flavio Augusto Prieto Ortiz Edgar Nelson Sánchez Camperos Carlos Daniel Acosta Medina Germán Augusto Castellanos Domínguez Analysis and convergence of weighted dimensionality reduction methods Revista Facultad de Ingeniería Universidad de Antioquia PCA PPCA WPCA WRDA dimensionality reduction |
| title | Analysis and convergence of weighted dimensionality reduction methods |
| title_full | Analysis and convergence of weighted dimensionality reduction methods |
| title_fullStr | Analysis and convergence of weighted dimensionality reduction methods |
| title_full_unstemmed | Analysis and convergence of weighted dimensionality reduction methods |
| title_short | Analysis and convergence of weighted dimensionality reduction methods |
| title_sort | analysis and convergence of weighted dimensionality reduction methods |
| topic | PCA PPCA WPCA WRDA dimensionality reduction |
| url | https://revistas.udea.edu.co/index.php/ingenieria/article/view/14674 |
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