Robust support vector machines and their sparse algorithms

被引：0
|
作者：
An Y. [1 ]
Zhou S. [1 ]
Chen L. [1 ]
Wang B. [1 ]
机构：
[1] School of Mathematics and Statistics, Xidian Univ., Xi'an
来源：
Xi'an Dianzi Keji Daxue Xuebao/Journal of Xidian University | 2019年 / 46卷 / 01期
关键词：
Low-rank approximation; Nonconvex and smooth loss; Robust support vector machines; Sparse solution;
D O I：
10.19665/j.issn1001-2400.2019.01.011
中图分类号：
学科分类号：
摘要：
Based on nonconvex and smooth loss, the robust support vector machine (RSVM) is insenstive to outliers for classification problems. However, the existing algorithms for RSVM are not suitable for dealing with large-scale problems, because they need to iteratively solve quadratic programmings, which leads to a large amount of calculation and slow convergence. To overcome this drawback, the method with a faster convergence rate is used to solve the RSVM. Then, by using the idea of least square, a generalized exponentially robust LSSVM (ER-LSSVM) model is proposed, which is solved by the algorithm with a faster convergence rate. Moreover, the robustness of the ER-LSSVM is interpreted theoretically. Finally, ultilizing low-rank approximation of the kernel matrix, the sparse RSVM algorithm (SR-SVM) and sparse ER-LSSVM algorithm (SER-LSSVM) are proposed for handing large-scale problems. Many experimental results illustrate that the proposed algorithm outperforms the related algorithms in terms of convergence speed, test accuracy and training time. © 2019, The Editorial Board of Journal of Xidian University. All right reserved.
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页码：64 / 72
页数：8
相关论文
共 20 条
  • [1] Vapnik V.N., The Nature of Statistical Learning Theory, Technometrics, 38, 4, (1996)
  • [2] Sun Y., Song C., Emotional Speech Feature Extraction and Optimization of Phase Space Reconstruction, Journal of Xidian University, 44, 6, pp. 162-168, (2017)
  • [3] Han B., Jia Z., Gao X., Improved PCANet for Aurora Images Classification, Journal of Xidian University, 44, 1, pp. 83-88, (2017)
  • [4] Li M., Hu Y., Zhou C., Et al., On the Short-term Regional Prediction of foF2 Based on the Support Vector Machine, Journal of Xidian University, 42, 5, pp. 147-153, (2015)
  • [5] Suykens J.A.K., Vandewalle J., Least Squares Support Vector Machine Classifiers, Neural Processing Letters, 9, 3, pp. 293-300, (1999)
  • [6] Gao Y.F., Shan X., Hu Z.X., Et al., Extended Compressed Tracking via Random Projection Based on MSERs and Online LS-SVM Learning, Pattern Recognition, 59, pp. 245-254, (2016)
  • [7] Rizvi S.Z., Velni J.M., Abbasi F., Et al., State-space LPV Model Identification Using Kernelized Machine Learning, Automatica, 88, pp. 38-47, (2018)
  • [8] Shen X.T., Tseng G.C., Zhang X.G., Et al., On ψ-Learning, Journal of the American Statistical Association, 98, 463, pp. 724-734, (2003)
  • [9] Wu Y.C., Liu Y.F., Robust Truncated Hinge Loss Support Vector Machines, Journal of the American Statistical Association, 102, pp. 974-983, (2007)
  • [10] Wang K.N., Zhong P., Robust Non-convex Least Squares Loss Function for Regression with Outliers, Knowledge-Based Systems, 71, pp. 290-302, (2014)
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