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Cross kernel distance minimization for designing support vector machines

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Abstract

Cross distance minimization algorithm (CDMA) is an iterative method for designing a hard margin linear SVM based on the nearest point pair between the convex hulls of two linearly separable data sets. In this paper, we propose a new version of CDMA with clear explanation of its linear time complexity. Using kernel function and quadratic cost, we extend the new CDMA to its kernel version, namely, the cross kernel distance minimization algorithm (CKDMA), which has the requirement of linear memory storage and the advantages over the CDMA including: (1) it is applicable in the non-linear case; (2) it allows violations to classify non-separable data sets. In terms of testing accuracy, training time, and number of support vectors, experimental results show that the CKDMA is very competitive with some well-known and powerful SVM methods such as nearest point algorithm (NPA), kernel Schlesinger-Kozinec (KSK) algorithm and sequential minimal optimization (SMO) algorithm implemented in LIBSVM2.9.

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Acknowledgments

This work was supported in part by the National Science Foundation of China under Grant 61175004, the Beijing Natural Science Foundation under Grant 4112009, the Program of Science Development of Beijing Municipal Education Commission under Program KM201010005012, and the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20121103110029.

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Authors and Affiliations

  1. College of Computer Science, Beijing University of Technology, Beijing, 100124, China

    Yujian Li, Qiangkui Leng & Yaozong Fu

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  1. Yujian Li
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  2. Qiangkui Leng
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  3. Yaozong Fu
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Correspondence to Yujian Li.

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Li, Y., Leng, Q. & Fu, Y. Cross kernel distance minimization for designing support vector machines. Int. J. Mach. Learn. & Cyber. 8, 1585–1593 (2017). https://doi.org/10.1007/s13042-016-0529-8

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  • DOI: https://doi.org/10.1007/s13042-016-0529-8

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