Coordinate Descent Algorithm for Ramp Loss Linear Programming Support Vector Machines

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• 作者：Xiangming Xi ; Xiaolin Huang ; Johan A. K. Suykens ; Shuning Wang
• 刊名：Neural Processing Letters
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：43
• 期：3
• 页码：887-903
• 全文大小：482 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Complexity
  Artificial Intelligence and Robotics
  Electronic and Computer Engineering
  Operation Research and Decision Theory
  
• 出版者：Springer Netherlands
• ISSN：1573-773X
• 卷排序：43

文摘

In order to control the effects of outliers in training data and get sparse results, Huang et al. (J Mach Learn Res 15:2185–2211, 2014) proposed the ramp loss linear programming support vector machine. This combination of \(\mathrm {l}_1\) regularization and ramp loss does not only lead to the sparsity of parameters in decision functions, but also limits the effects of outliers with a maximal penalty. However, due to its non-convexity, the computational cost to achieve a satisfying solution is often expensive. In this paper, we propose a modified coordinate descent algorithm, which deals with a series of one-variable piecewise linear subproblems. Considering that the obtained subproblems are DC programming problems, we linearize the concave part of the objective functions and solve the obtained convex problems. To test the performances of the proposed algorithm, numerical experiments have been carried out and analysed on benchmark data sets. To enhance the sparsity and robustness, the experiments are initialized from C-SVM solutions. The results confirm its excellent performances in classification accuracy, robustness and efficiency in computation.KeywordsSupport vector machinesRamp lossl\(_1\) RegularizationCoordinate descent algorithm