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A novel robust generalized eigenvalue proximal support vector machine for pattern classification

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Abstract

By minimizing the p-order of \(L_{2}\)-norm distance of the objection function of the improved generalized eigenvalue proximal support vector machine (IGEPSVM), the \(L_{2,p}\)-LIGEPSVM is proposed in this paper. Firstly, the solution of the \(L_{2,p}\)-LIGEPSVM is demonstrated to be related to the minimum eigenvalue of the correlation matrix, and an improved inverse power method is devised to solve the \(L_{2,p}\)-LIGEPSVM. Compared with IGEPSVM, \(L_{2,p}\)-LIGEPSVM not only retains the advantages of linear IGEPSVM, but also overcomes the shortcomings of exaggeration of outliers based on squared Frobenius-norm distance metrics. Furthermore, the main improvements of \(L_{2,p}\)-LIGEPSVM over IGEPSVM are the robustness and learning efficiency in solving outlier problems. Finally, in order to illustrate the effectiveness and accuracy of the proposed algorithms, five other relevant algorithms are tested on the artificial and the UCI datasets. The classification accuracy of the two algorithms of \(L_{2,p}\)-LIGEPSVM on the Artificial, Australian, Cancer and Sonar datasets are (83%, 84.2%), (98.70%, 99.25%), (98.84%, 98.77%) and (95.65%, 95.70%), respectitvely, and they are all higher than other related 5 algorithms. Experimental results show that \(L_{2,p}\)-LIGEPSVM has some obvious advantages, such as not sensitive to outliers, resistant to noise, high computational efficiency and effective to classification. It is worth mentioning that we introduce the application of the proposed method and elaborate on its economic value.

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Acknowledgements

This work was supported in part by the Fundamental Research Funds for the Central Universities (No. 2023ZRLG01, No. 2021KYQD23), in part by the Key Research and Development Program of Ningxia (Introduction of Talents Project), China (No. 2022BSB03046), in part by the 2023 doctoral innovation project of North Minzu University (No. YCX23225), in part by the Natural Science Foundation of Ningxia Provincial, China(No. 2023AAC02053), in part by the National Natural Science Foundation of China (No. 62366001, No. 12361062), in part by the Science and Technology Foundation of Guizhou Province of China (ZK[2022]557).

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Authors and Affiliations

  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, People’s Republic of China

    Weizhi Xiong, Guolin Yu, Jun Ma & Sheng Liu

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  1. Weizhi Xiong
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  2. Guolin Yu
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Contributions

Weizhi Xiong: Writing-original draft, Supervision, Validation, Project administration, Funding acquisition. Guolin Yu: Writing-original draft, Supervision, Validation, Project administration, Funding acquisition. Jun Ma: Writing-original draft, Conceptualization, Writing-reviewing & editing, Software, Data curation.

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Correspondence to Guolin Yu.

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Xiong, W., Yu, G., Ma, J. et al. A novel robust generalized eigenvalue proximal support vector machine for pattern classification. Pattern Anal Applic 27, 140 (2024). https://doi.org/10.1007/s10044-024-01355-z

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