Multiple Kernel Spectral Regression for Dimensionality Reduction
Traditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR) solves the problem of learning an embedding function by estab...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/427462 |
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| author | Bing Liu Shixiong Xia Yong Zhou |
| author_facet | Bing Liu Shixiong Xia Yong Zhou |
| author_sort | Bing Liu |
| collection | DOAJ |
| description | Traditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR) solves the problem of learning an embedding function by establishing a regression framework, which can avoid eigen-decomposition of dense matrices. Motivated by the effectiveness of SR, we incorporate multiple kernel learning (MKL) into SR for dimensionality reduction. The proposed approach (termed MKL-SR) seeks an embedding function in the Reproducing Kernel Hilbert Space (RKHS) induced by the multiple base kernels. An MKL-SR algorithm is proposed to improve the performance of kernel-based SR (KSR) further. Furthermore, the proposed MKL-SR algorithm can be performed in the supervised, unsupervised, and semi-supervised situation. Experimental results on supervised classification and semi-supervised classification demonstrate the effectiveness and efficiency of our algorithm. |
| format | Article |
| id | doaj-art-5b59f1c30b5c4c8ea6345171b0c18ec9 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5b59f1c30b5c4c8ea6345171b0c18ec92025-02-03T01:25:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/427462427462Multiple Kernel Spectral Regression for Dimensionality ReductionBing Liu0Shixiong Xia1Yong Zhou2School of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaSchool of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaSchool of Computer Science and Technology, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaTraditional manifold learning algorithms, such as locally linear embedding, Isomap, and Laplacian eigenmap, only provide the embedding results of the training samples. To solve the out-of-sample extension problem, spectral regression (SR) solves the problem of learning an embedding function by establishing a regression framework, which can avoid eigen-decomposition of dense matrices. Motivated by the effectiveness of SR, we incorporate multiple kernel learning (MKL) into SR for dimensionality reduction. The proposed approach (termed MKL-SR) seeks an embedding function in the Reproducing Kernel Hilbert Space (RKHS) induced by the multiple base kernels. An MKL-SR algorithm is proposed to improve the performance of kernel-based SR (KSR) further. Furthermore, the proposed MKL-SR algorithm can be performed in the supervised, unsupervised, and semi-supervised situation. Experimental results on supervised classification and semi-supervised classification demonstrate the effectiveness and efficiency of our algorithm.http://dx.doi.org/10.1155/2013/427462 |
| spellingShingle | Bing Liu Shixiong Xia Yong Zhou Multiple Kernel Spectral Regression for Dimensionality Reduction Journal of Applied Mathematics |
| title | Multiple Kernel Spectral Regression for Dimensionality Reduction |
| title_full | Multiple Kernel Spectral Regression for Dimensionality Reduction |
| title_fullStr | Multiple Kernel Spectral Regression for Dimensionality Reduction |
| title_full_unstemmed | Multiple Kernel Spectral Regression for Dimensionality Reduction |
| title_short | Multiple Kernel Spectral Regression for Dimensionality Reduction |
| title_sort | multiple kernel spectral regression for dimensionality reduction |
| url | http://dx.doi.org/10.1155/2013/427462 |
| work_keys_str_mv | AT bingliu multiplekernelspectralregressionfordimensionalityreduction AT shixiongxia multiplekernelspectralregressionfordimensionalityreduction AT yongzhou multiplekernelspectralregressionfordimensionalityreduction |