Training robust support vector machine with smooth Ramp loss in the primal space

Wang, Lei; Jia, H. Y.; Li, Jie

doi:10.1016/j.neucom.2007.12.032

Cited by 60 publications

(29 citation statements)

References 4 publications

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“…하지만 일반적으로 SVM은 이상점(outlier)들에 민감하 다 [2]. SVM이 초평면(hyperplane)을 결정할 때 이상점들은 최대 margin 손실을 갖기 때문에 초평면은 이상점들의 영 향을 많이 받게 되고 그 결과 SVM의 성능이 하락한다.…”

Section: 서 론unclassified

“…SVM이 초평면(hyperplane)을 결정할 때 이상점들은 최대 margin 손실을 갖기 때문에 초평면은 이상점들의 영 향을 많이 받게 되고 그 결과 SVM의 성능이 하락한다. 따 라서 이상점들에 강인한 SVM들이 많이 개발되고 있다 [2,3] procedure GA t=0; initialize P(t); evaluate P(t); while termination condition not satisfied do t=t+1; select P(t) from P(t-1); recombine and mutate P(t); evaluate P(t); end end 초기 염색체들의 집단인 P(0)를 생성한다. 초기 집단은 해 공간 내에서 무작위로 분포되도록 선택되거나 경험적인 방법으로 선택된다.…”

Section: 서 론unclassified

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Design of Robust Support Vector Machine Using Genetic Algorithm

Lee¹,

Hong²,

Lee³

et al. 2010

Journal of Korean Institute of Intelligent Systems

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The support vector machine (SVM) has been widely used in variety pattern recognition problems applicable to recommendation systems due to its strong theoretical foundation and excellent empirical successes. However, SVM is sensitive to the presence of outliers since outlier points can have the largest margin loss and play a critical role in determining the decision hyperplane. For robust SVM, we limit the maximum value of margin loss which includes the non-convex optimization problem. Therefore, we proposed the design method of robust SVM using genetic algorithm (GA) which can solve the non-convex optimization problem. To demonstrate the performance of the proposed method, we perform experiments on various databases selected in UCI repository.

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Section: 서 론unclassified

Design of Robust Support Vector Machine Using Genetic Algorithm

Lee¹,

Hong²,

Lee³

et al. 2010

Journal of Korean Institute of Intelligent Systems

View full text Add to dashboard Cite

show abstract

“…However, SVM also has the drawback of sensitivity to outliers and its performance can be degraded by their presence. Even though slack variables are introduced to suppress outliers [8,9], outliers continue to influence the determination of the decision hyperplane because they have a relatively high margin loss compared to those of the other data points [10]. Further, when quadratic margin loss is employed, the influence of outliers increases [11].…”

Section: Introductionmentioning

confidence: 99%

“…Further, when quadratic margin loss is employed, the influence of outliers increases [11]. Previous research has considered this problem [8][9][10][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Genetic Outlier Detection for a Robust Support Vector Machine

Lee

Kim

2015

Int. J. Fuzzy Log. Intell. Syst.

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Support vector machine (SVM) has a strong theoretical foundation and also achieved excellent empirical success. It has been widely used in a variety of pattern recognition applications. Unfortunately, SVM also has the drawback that it is sensitive to outliers and its performance is degraded by their presence. In this paper, a new outlier detection method based on genetic algorithm (GA) is proposed for a robust SVM. The proposed method parallels the GA-based feature selection method and removes the outliers that would be considered as support vectors by the previous soft margin SVM. The proposed algorithm is applied to various data sets in the UCI repository to demonstrate its performance.

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“…Another method proposed by Collobert et al in [9] is based on transforming the non-convex ramp loss SVM into a series of convex problems which can be solved by concave-convex procedure. Similar technique is utilized in [32] on the smooth ramp loss SVMs. In addition, Huang et al [15] propose the ramp loss linear programming support vector machine (ramp-LPSVM).…”

Section: Introductionmentioning

confidence: 99%

Coordinate Descent Algorithm for Ramp Loss Linear Programming Support Vector Machines

Huang

Suykens

et al. 2015

Neural Process Lett

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In order to control the effects of outliers in training data and get sparse results, Huang et al. [15] proposed the ramp loss linear programming support vector machine (ramp-LPSVM). This combination of 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.

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Training robust support vector machine with smooth Ramp loss in the primal space

Cited by 60 publications

References 4 publications

Design of Robust Support Vector Machine Using Genetic Algorithm

Design of Robust Support Vector Machine Using Genetic Algorithm

Genetic Outlier Detection for a Robust Support Vector Machine

Coordinate Descent Algorithm for Ramp Loss Linear Programming Support Vector Machines

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