RSVM: Reduced Support Vector Machines. An algorithm is proposed which generates a nonlinear kernel-based separating surface that requires as little as 1% of a large dataset for its explicit evaluation. To generate this nonlinear surface, the entire dataset is used as a constraint in an optimization problem with very few variables corresponding to the 1% of the data kept. The remainder of the data can be thrown away after solving the optimization problem. This is achieved by making use of a rectangular m × kernel K(A, Ā′) that greatly reduces the size of the quadratic program to be solved and simplifies the characterization of the nonlinear separating surface. Here, the m rows of A represent the original m data points while the rows of Ā represent a greatly reduced data points. Computational results indicate that test set correctness for the reduced support vector machine (RSVM), with a nonlinear separating surface that depends on a small randomly selected portion of the dataset, is better than that of a conventional support vector machine (SVM) with a nonlinear surface that explicitly depends on the entire dataset, and much better than a conventional SVM using a small random sample of the data. Computational times, as well as memory usage, are much smaller for RSVM than that of a conventional SVM using the entire dataset.

References in zbMATH (referenced in 37 articles )

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  1. Manh Cuong, Nguyen; Van Thien, Nguyen: A method for reducing the number of support vectors in fuzzy support vector machine (2016)
  2. Zhao, Yong-Ping; Wang, Kang-Kang; Li, Fu: A pruning method of refining recursive reduced least squares support vector regression (2015)
  3. Bai, Yan-Qin; Shen, Yan-Jun; Shen, Kai-Ji: Consensus proximal support vector machine for classification problems with sparse solutions (2014)
  4. Couellan, Nicolas; Jan, Sophie: Incremental accelerated gradient methods for SVM classification: study of the constrained approach (2014)
  5. Shao, Yuan-Hai; Chen, Wei-Jie; Deng, Nai-Yang: Nonparallel hyperplane support vector machine for binary classification problems (2014)
  6. Chang, Lo-Bin; Bai, Zhidong; Huang, Su-Yun; Hwang, Chii-Ruey: Asymptotic error bounds for kernel-based Nyström low-rank approximation matrices (2013)
  7. Ma, Jiayi; Zhao, Ji; Tian, Jinwen; Bai, Xiang; Tu, Zhuowen: Regularized vector field learning with sparse approximation for mismatch removal (2013)
  8. Wang, Zhen; Shao, Yuan-Hai; Wu, Tie-Ru: A GA-based model selection for smooth twin parametric-margin support vector machine (2013)
  9. Xia, Xiao-Lei; Qian, Suxiang; Liu, Xueqin; Xing, Huanlai: Efficient model selection for sparse least-square SVMs (2013)
  10. Zhou, Shuisheng; Cui, Jiangtao; Ye, Feng; Liu, Hongwei; Zhu, Qiang: New smoothing SVM algorithm with tight error bound and efficient reduced techniques (2013)
  11. Chang, Chien-Chung; Pao, Hsing-Kuo; Lee, Yuh-Jye: An RSVM based two-teachers-one-student semi-supervised learning algorithm (2012) ioport
  12. Huang, Chia-Hui: A reduced support vector machine approach for interval regression analysis (2012)
  13. Shao, Yuan-Hai; Deng, Nai-Yang: A coordinate descent margin based-twin support vector machine for classification (2012)
  14. Yu, Hwanjo; Kim, Jinha; Kim, Youngdae; Hwang, Seungwon; Lee, Young Ho: An efficient method for learning nonlinear ranking SVM functions (2012) ioport
  15. Zhao, Yong-Ping; Sun, Jian-Guo; Du, Zhong-Hua; Zhang, Zhi-An; Li, Ye-Bo: Online independent reduced least squares support vector regression (2012)
  16. Chang, Chih-Cheng; Chien, Li-Jen; Lee, Yuh-Jye: A novel framework for multi-class classification via ternary smooth support vector machine (2011)
  17. Peng, Xinjun: TPMSVM: A novel twin parametric-margin support vector machine for pattern recognition (2011)
  18. Pham, Huy Nguyen Anh; Triantaphyllou, Evangelos: A meta-heuristic approach for improving the accuracy in some classification algorithms (2011)
  19. Woodsend, Kristian; Gondzio, Jacek: Exploiting separability in large-scale linear support vector machine training (2011)
  20. Ghorai, Santanu; Hossain, Shaikh Jahangir; Mukherjee, Anirban; Dutta, Pranab K.: Newton’s method for nonparallel plane proximal classifier with unity norm hyperplanes (2010)

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