A fuzzy twin support vector machine based on information entropy for class imbalance learning

Gupta, Deepak; Richhariya, Bharat; Borah, Parashjyoti

doi:10.1007/s00521-018-3551-9

Cited by 61 publications

(27 citation statements)

References 25 publications

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“…It can be seen that the left and right derivatives of the pinball loss function at zero are not equal, that is, the function is not differentiable at zero. To this end, a smooth function ϕ τ (u, ε) is used to approximate it by using (16) and (17), where ε is a sufficiently small parameter, and the function ϕ τ (u, ε) is shown in (18):…”

Section: Pinball Loss and Its Smooth Approximation Functionmentioning

confidence: 99%

“…According to (17), we also obtain another approximation smooth function of the pinball loss function as follows:…”

Section: Appendixmentioning

confidence: 99%

“…It further improves the generalization performance of the TWSVM. In addition, researchers have proposed different twin support vector machines by exploring the structures of datasets and the different roles of samples [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

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Smooth twin bounded support vector machine with pinball loss

2021

Appl Intell

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The twin support vector machine improves the classification performance of the support vector machine by solving two small quadratic programming problems. However, this method has the following defects: (1) For the twin support vector machine and some of its variants, the constructed models use a hinge loss function, which is sensitive to noise and unstable in resampling. (2) The models need to be converted from the original space to the dual space, and their time complexity is high. To further enhance the performance of the twin support vector machine, the pinball loss function is introduced into the twin bounded support vector machine, and the problem of the pinball loss function not being differentiable at zero is solved by constructing a smooth approximation function. Based on this, a smooth twin bounded support vector machine model with pinball loss is obtained. The model is solved iteratively in the original space using the Newton-Armijo method. A smooth twin bounded support vector machine algorithm with pinball loss is proposed, and theoretically the convergence of the iterative algorithm is proven. In the experiments, the proposed algorithm is validated on the UCI datasets and the artificial datasets. Furthermore, the performance of the presented algorithm is compared with those of other representative algorithms, thereby demonstrating the effectiveness of the proposed algorithm.

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Section: Pinball Loss and Its Smooth Approximation Functionmentioning

confidence: 99%

“…According to (17), we also obtain another approximation smooth function of the pinball loss function as follows:…”

Section: Appendixmentioning

confidence: 99%

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Smooth twin bounded support vector machine with pinball loss

2021

Appl Intell

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“…Motivated by entropy-based fuzzy support vector machine (EFSVM) [53], Gupta et al [54] proposed an entropy-based fuzzy twin support vector machine for imbalanced datasets (EFTWSVM-CIL). In EFTWSVM-CIL, in order to enhance the participation of the minority class in decision classifier, the samples of majority class with lower entropy get larger fuzzy membership values.…”

Section: Eftwsvm-cilmentioning

confidence: 99%

“…Recently, Fan et al [53] proposed an entropy-based fuzzy SVM (EFSVM) for class imbalance problem in which fuzzy membership is computed based on class certainty of samples. Following EFSVM, Gupta et al [54] proposed a fuzzy twin support vector machine based on information entropy which is termed as EFTWSVM-CIL. At the same time, Gupta et al [55] proposed a new fuzzy least squares twin support vector machine (EFLSTWSVM-CIL) for class imbalance learning.…”

Section: Introductionmentioning

confidence: 99%

Entropy-Based Fuzzy Twin Bounded Support Vector Machine for Binary Classification

et al. 2019

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Twin support vector machine (TWSVM) is a new machine learning method, as opposed to solving a single quadratic programming problem in support vector machine (SVM), which generates two nonparallel hyperplanes by solving two smaller size quadratic programming problems. However, the TWSVM obtains the final classifier by giving the same importance to all training samples which may be important for classification performance. In order to address this problem, in this paper, we propose a novel entropy-based fuzzy twin bounded support vector machine (EFTBSVM) for binary classification problems. By considering the fuzzy membership value for each sample and assigning it based on the entropy value, the samples with higher class certainty are assigned to relatively larger fuzzy membership. In addition, the proposed EFTBSVM not only maintains the superior characteristics of the TWSVM but also exploits the structural risk minimization principle by introducing a regularization term. The experimental results achieved on synthetic datasets and benchmark datasets illustrate the effectiveness of the proposed method.

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Inequality distance hyperplane multiclass support vector machines

Ren

et al. 2021

Int J of Intelligent Sys

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In this study, inequality distance hyperplane multiclass support vector machines (IDH-MSVM) algorithm is proposed on the basis of multiclassification support vector machine (MSVM) which was proposed by J. Weston and C. Watkins in 1999. It only needs to solve a single objective optimization problem to deal with multiclassification problems. For original MSVM, the hyperplane distance refers to the classification interval between classical margin and hyperplane, which is equality. However, the IDH-MSVM introduces parameters to adjust distance between every classification hyperplane and classical margin, which makes the hyperplane distance inequality. The effectiveness of the proposed method is experimented on UCI standard data sets and compared with several multiclassification algorithms. Experimental results show that this method has a better classification effect on multiclassification data.

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A fuzzy twin support vector machine based on information entropy for class imbalance learning

Cited by 61 publications

References 25 publications

Smooth twin bounded support vector machine with pinball loss

Smooth twin bounded support vector machine with pinball loss

Entropy-Based Fuzzy Twin Bounded Support Vector Machine for Binary Classification

Inequality distance hyperplane multiclass support vector machines

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