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Ramp loss KNN-weighted multi-class twin support vector machine

  • Optimization
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Abstract

The K-nearest neighbor-weighted multi-class twin support vector machine (KWMTSVM) is an effective multi-classification algorithm which utilizes the local information of all training samples. However, it is easily affected by the noises and outliers owing to the use of the hinge loss function. That is because the outlier will obtain a huge loss and become the support vector, which will shift the separating hyperplane inappropriately. To reduce the negative influence of outliers, we use the ramp loss function to replace the hinge loss function in KWMTSVM and propose a novel sparse and robust multi-classification algorithm named ramp loss K-nearest neighbor-weighted multi-class twin support vector machine (RKWMTSVM) in this paper. Firstly, the proposed RKWMTSVM restricts the loss of outlier to a fixed value, thus the negative influence on the construction of hyperplane is suppressed and the classification performance is further improved. Secondly, since outliers will not become support vectors, the RKWMTSVM is a sparser algorithm, especially compared with KWMTSVM. Thirdly, because RKWMTSVM is a non-differentiable non-convex optimization problem, we use the concave–convex procedure (CCCP) to solve it. In each iteration of CCCP, the proposed RKWMTSVM solves a series of KWMTSVM-like problems. That also means RKWMTSVM inherits the merits of KWMTSVM, namely, it can exploit the local information of intra-class to improve the generalization ability and use inter-class information to remove the redundant constraints and accelerate the solution process. In the end, the clipping dual coordinate descent (clipDCD) algorithm is employed into our RKWMTSVM to further speed up the computational speed. We do numerical experiments on twenty-four benchmark datasets. The experimental results verify the validity and effectiveness of our algorithm.

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Data availability

Enquiries about data availability should be directed to the authors.

Notes

  1. http://archive.ics.uci.edu/ml/datasets.html

  2. https://www.csie.ntu.edu.tw/~cjlin/libsvm

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Acknowledgements

The authors gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

Funding

This work was supported in part by the Fundamental Research Funds for the Central Universities (No. 2021ZY92, BLX201928), National Natural Science Foundation of China (No.11671010) and Beijing Natural Science Foundation (No. 4172035).

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Authors and Affiliations

  1. College of Science, Beijing Forestry University, No.35 Qinghua East Road, Haidian, 100083, Beijing, China

    Huiru Wang

  2. College of Science, China Agricultural University, No.17 Qinghua East Road, Haidian, 100083, Beijing, China

    Yitian Xu & Zhijian Zhou

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  1. Huiru Wang
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Correspondence to Zhijian Zhou.

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Wang, H., Xu, Y. & Zhou, Z. Ramp loss KNN-weighted multi-class twin support vector machine. Soft Comput 26, 6591–6618 (2022). https://doi.org/10.1007/s00500-022-07040-9

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