Ramp loss for twin multi-class support vector classification

Wang, Huiru; Lu, Sijie; Zhou, Zhijian

doi:10.1080/00207721.2020.1765047

Cited by 10 publications

(3 citation statements)

References 35 publications

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“…For any sample x, we can get the category to which it belongs by the following discriminant function (29):…”

Section: Algorithmmentioning

confidence: 99%

Twin Bounded Support Vector Machine with Capped Pinball Loss

Wang,

Hong,

Zhang

2023

Preprint

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In this paper, we propose a novel classifier termed as twin bounded support vector machine with capped pinball loss (CPin-TBSVM), which has the excellent properties of being insensitive to noise. Given that the proposed model is non-convex, we use the convex-concave procedure algorithm (CCCP) to solve a series of two smaller-sized quadratic programming problems to find the optimal solution. In the process of solving the iterative sub-problem, the dual coordinate descent method (DCDM) is used for speeding up solving optimization problems. Moreover, we analyze its theoretical properties, including that the capped pinball loss satisfies Bayes’ rule and CPin-TBSVM has certain noise insensitivity and sparsity. The properties are verified on an artificial dataset as well. The numerical experiment is conducted on 24 UCI datasets and the results are compared with four other models which include SVM, TSVM, Pin-GTSVM and TPin-TSVM. The results show that the proposed CPin-TBSVM has a better classification effect and noise insensitivity.

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“…For any sample x, we can get the category to which it belongs by the following discriminant function (29):…”

Section: Algorithmmentioning

confidence: 99%

Twin Bounded Support Vector Machine with Capped Pinball Loss

Wang,

Hong,

Zhang

2023

Preprint

Self Cite

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“…e authors in [16] propose a noise-resilient online classification algorithm, which is scalable and robust to noisy labels and applied it to peptide identification [17]. To reduce the negative influence of outliers, the authors in [18] propose a more robust algorithm termed as ramp loss for twin K-class support vector classification (Ramp-TKSVC) where the ramp loss function was used to substitute the Hinge loss function.…”

Section: Introductionmentioning

confidence: 99%

Perceptron Ranking Using Interval Labels with Ramp Loss for Online Ordinal Regression

Zhang

Liang

et al. 2020

Mathematical Problems in Engineering

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Due to its wide applications and learning efficiency, online ordinal regression using perceptron algorithms with interval labels (PRIL) has been increasingly applied to solve ordinal ranking problems. However, it is still a challenge for the PRIL method to handle noise labels, in which case the ranking results may change dramatically. To tackle this problem, in this paper, we propose noise-resilient online learning algorithms using ramp loss function, called PRIL-RAMP, and its nonlinear variant K-PRIL-RAMP, to improve the performance of PRIL method for noisy data streams. The proposed algorithms iteratively optimize the decision function under the framework of online gradient descent (OGD), and we justify the algorithms by showing the order preservation of thresholds. It is validated in the experiments that both approaches are more robust and efficient to noise labels than state-of-the-art online ordinal regression algorithms on real-world datasets.

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“…Since the KKT conditions provided effective characterization of optimal solution to L r -SVM (3), this class of approaches continued to be widely studied in theory as well as algorithms. For more details, see, e.g., [7,13,17,19] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Proximal Operator and Optimality Conditions for Ramp Loss SVM

Wang

Shao

Xiu

2020

Preprint

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Support vector machines with ramp loss (dubbed as L r -SVM) have attracted wide attention due to the boundedness of ramp loss. However, the corresponding optimization problem is non-convex and the given Karush-Kuhn-Tucker (KKT) conditions are only the necessary conditions. To enrich the optimality theory of L r -SVM and go deep into its statistical nature, we first introduce and analyze the proximal operator for ramp loss, and then establish a stronger optimality conditions: P-stationarity, which is proved to be the first-order necessary and sufficient conditions for local minimizer of L r -SVM. Finally, we define the L r support vectors based on the concept of P-stationary point, and show that all L r support vectors fall into the support hyperplanes, which possesses the same feature as the one of hard margin SVM.

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Ramp loss for twin multi-class support vector classification

Cited by 10 publications

References 35 publications

Twin Bounded Support Vector Machine with Capped Pinball Loss

Twin Bounded Support Vector Machine with Capped Pinball Loss

Perceptron Ranking Using Interval Labels with Ramp Loss for Online Ordinal Regression

Proximal Operator and Optimality Conditions for Ramp Loss SVM

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