C-parameter version of robust bounded one-class support vector classification

Junyou Ye

doi:10.1038/s41598-025-85151-7

C-parameter version of robust bounded one-class support vector classification

2025-01-06

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DOI：10.1038/s41598-025-85151-7

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}-one-class support vector classification (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}-OCSVC) has garnered significant attention for its remarkable performance in handling single-class classification and anomaly detection. Nonetheless, the model does not yield a unique decision boundary, and potentially compromises learning performance when the training data is contaminated by some outliers or mislabeled observations. This paper presents a novel C-parameter version of bounded one-class support vector classification (C-BOCSVC) to determine a unique decision boundary. The distance from the origin to decision boundary is the geometrical margin in the space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\mathcal {H}}$$\end{document} (higher 1-dimension than feature space), and its maximization corresponds to the structural risk minimization (SRM) principle inscribed by an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}-norm regularization term both on the normal direction and bias of the decision boundary. To enhance the anti-noise and anti-outlier abilities of C-BOCSVC, the alternative robust version (C-RBOCSVC) is also developed, which incorporates the k-nearest neighbor relative density to assign varying weights to observations and mitigate the negative impact of outliers on the optimal decision boundary. The theoretical properties of the proposed method are successively derived, including the relationship between the solutions to the primal and dual problems, the connections between our C-BOCSVC and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}-OCSVC and the computational complexity. Experimental results over massive datasets demonstrate the feasibility and reliability of our C-BOCSVC, and highlight the superior performance of C-RBOCSVC compared to other state-of-the-art one-class classifiers when data is contaminated. The demo code of this work is publicly available at https://github.com/Zhangmath1122/C-RBOCSVC.

Keywords:

C-Bounded one-class support vector classification

Maximal geometrical margin

Robust

k-Nearest neighbor relative density

C-parameter version of robust bounded one-class support vector classification

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