Kernel Geometric Mean Metric Learning
Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. Howe...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/13/21/12047 |
| _version_ | 1797632122022789120 |
|---|---|
| author | Zixin Feng Teligeng Yun Yu Zhou Ruirui Zheng Jianjun He |
| author_facet | Zixin Feng Teligeng Yun Yu Zhou Ruirui Zheng Jianjun He |
| author_sort | Zixin Feng |
| collection | DOAJ |
| description | Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space through nonlinear transformation, and use the integral representation of the weighted geometric mean and the Woodbury matrix identity in new feature space to generalize the analytical solution obtained in the GMML algorithm as a form represented by a kernel matrix, and then the KGMML algorithm is obtained through operations. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms. |
| first_indexed | 2024-03-11T11:32:24Z |
| format | Article |
| id | doaj.art-2bf2bff07c7b469faedb8f60f51e4d3a |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T11:32:24Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2bf2bff07c7b469faedb8f60f51e4d3a2023-11-10T14:59:46ZengMDPI AGApplied Sciences2076-34172023-11-0113211204710.3390/app132112047Kernel Geometric Mean Metric LearningZixin Feng0Teligeng Yun1Yu Zhou2Ruirui Zheng3Jianjun He4School of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, ChinaSchool of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, ChinaSchool of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, ChinaSchool of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, ChinaSchool of Information and Communication Engineering, Dalian Minzu University, Dalian 116600, ChinaGeometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space through nonlinear transformation, and use the integral representation of the weighted geometric mean and the Woodbury matrix identity in new feature space to generalize the analytical solution obtained in the GMML algorithm as a form represented by a kernel matrix, and then the KGMML algorithm is obtained through operations. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.https://www.mdpi.com/2076-3417/13/21/12047metric learningkernel methodsweighted geometric mean |
| spellingShingle | Zixin Feng Teligeng Yun Yu Zhou Ruirui Zheng Jianjun He Kernel Geometric Mean Metric Learning Applied Sciences metric learning kernel methods weighted geometric mean |
| title | Kernel Geometric Mean Metric Learning |
| title_full | Kernel Geometric Mean Metric Learning |
| title_fullStr | Kernel Geometric Mean Metric Learning |
| title_full_unstemmed | Kernel Geometric Mean Metric Learning |
| title_short | Kernel Geometric Mean Metric Learning |
| title_sort | kernel geometric mean metric learning |
| topic | metric learning kernel methods weighted geometric mean |
| url | https://www.mdpi.com/2076-3417/13/21/12047 |
| work_keys_str_mv | AT zixinfeng kernelgeometricmeanmetriclearning AT teligengyun kernelgeometricmeanmetriclearning AT yuzhou kernelgeometricmeanmetriclearning AT ruiruizheng kernelgeometricmeanmetriclearning AT jianjunhe kernelgeometricmeanmetriclearning |