Laplacian Lp norm least squares twin support vector machine

Xie, Xijiong; Sun, Feixiang; Qian, Jing; Guo, Lanwei; Zhang, Rong; Ye, Xulun; Wang, Zhijin

doi:10.1016/j.patcog.2022.109192

Cited by 18 publications

(8 citation statements)

References 27 publications

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“…Unlike SVM, TSVM aims to generate two non-parallel planes such that each plane is closer to one of the two classes and as far away from the other as possible (Rezvani and Wang, 2021). Furthermore, the single large quadratic programming problem in SVM is transformed into two smaller quadratic programming problems, so that the computational time of TSVM is reduced to a quarter of that of traditional SVM (Rezvani and Wang, 2022;Xie et al, 2023). The speed advantage of TSVM partially compensates the shortcomings of existing SVMs when solving large-scale classification problems.…”

Section: Introductionmentioning

confidence: 99%

A robust twin support vector machine based on fuzzy systems

Qiu,

Xie,

Zhang

et al. 2023

IJICC

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PurposeTwin support vector machine (TSVM) is an effective machine learning technique. However, the TSVM model does not consider the influence of different data samples on the optimal hyperplane, which results in its sensitivity to noise. To solve this problem, this study proposes a twin support vector machine model based on fuzzy systems (FSTSVM).Design/methodology/approachThis study designs an effective fuzzy membership assignment strategy based on fuzzy systems. It describes the relationship between the three inputs and the fuzzy membership of the sample by defining fuzzy inference rules and then exports the fuzzy membership of the sample. Combining this strategy with TSVM, the FSTSVM is proposed. Moreover, to speed up the model training, this study employs a coordinate descent strategy with shrinking by active set. To evaluate the performance of FSTSVM, this study conducts experiments designed on artificial data sets and UCI data sets.FindingsThe experimental results affirm the effectiveness of FSTSVM in addressing binary classification problems with noise, demonstrating its superior robustness and generalization performance compared to existing learning models. This can be attributed to the proposed fuzzy membership assignment strategy based on fuzzy systems, which effectively mitigates the adverse effects of noise.Originality/valueThis study designs a fuzzy membership assignment strategy based on fuzzy systems that effectively reduces the negative impact caused by noise and then proposes the noise-robust FSTSVM model. Moreover, the model employs a coordinate descent strategy with shrinking by active set to accelerate the training speed of the model.

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Section: Introductionmentioning

confidence: 99%

A robust twin support vector machine based on fuzzy systems

Qiu,

Xie,

Zhang

et al. 2023

IJICC

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“…Chen et al [23] introduced the Laplacian least squares TSVM (Lap-LSTSVM), which solves the two linear equation systems, reducing the computational cost. In recently, in stead of using the L1 or L2 norm, Xie et al [24] improve the Lap-LSTSVM to Laplacian Lp norm least squares TSVM (Lap-LpLSTSVM). From the perspective of noise sensitivity and unstable for resampling in the Lap-TSVM , many techniques have been proposed to tackle these problems, such as IFLap-TSVM [25], SIFTSVM [26].…”

Section: Introductionmentioning

confidence: 99%

Laplacian Twin Support Vector Machine With Pinball Loss for Semi-Supervised Classification

2023

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Semi-supervised learning utilizes labeled data and the geometric information in the unlabeled data to construct a model whereas supervised learning makes use of the only label data. So, semi-supervised learning establishes a more reasonable classifier. In recent years, the Laplacian support vector machine (Lap-SVM) has received a lot of interest in the framework of semi-supervised classification. To develop the performance of Lap-SVM, Laplacian twin support vector machine (Lap-TSVM) has shown exceptional performance as an addition to improve the computational complexity. However, dealing with noise sensitivity and instability for resampling due to its hinge loss function is still a challenge. In this paper, we provide a novel Laplacian twin support vector machine by combining pinball loss function, termed as Lap-PTSVM, to effectively handle the aforementioned problems. As a result, it improves a better generalization ability of the classifier. Several experiments have been performed on artificial and UCI datasets. The results show that the proposed model has noise insensitivity comparable to the Lap-TSVM and has a great generalization performance. Furthermore, non-parametric statistical test are also conducted to justify the competitive performance of Lap-PTSVM.INDEX TERMS Laplacian twin support vector machine, Pinball loss function, Semi-supervised classification.

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“…Wang proposes to use an upper bound L1 parametrization, 11 setting an upper limit of loss

\varepsilon

, where the loss does not exceed

\varepsilon

regardless of the misclassify‐cation level of the sample, to limit the value of the loss function to

\varepsilon

ensure better robustness. Xie introduces the Lp‐norm regularization term, 12 to effectively exploit the geometric information embedded in the data, avoiding overfitting while improving the generalization ability of the algorithm. Liang modeled each uncertain sample as a random vector with a Gaussian distribution of the proposed model 13 .…”

Section: Introductionmentioning

confidence: 99%

“…the loss function to 𝜀 ensure better robustness. Xie introduces the Lp-norm regularization term, 12 to effectively exploit the geometric information embedded in the data, avoiding overfitting while improving the generalization ability of the algorithm. Liang modeled each uncertain sample as a random vector with a Gaussian distribution of the proposed model.…”

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confidence: 99%

Adaptive kernel density estimation weighted twin support vector machine and its sample screening method

Lv,

Zhang,

Qiu

et al. 2023

Concurrency and Computation

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SummaryIn twin support vector machines (TSVM), noise blurs the boundary between positive and negative samples, increasing the probability of classification errors. In this article, we propose an adaptive kernel density estimation weighted twin support vector machine(AKWTSVM). AKWTSVM uses KDE based on K‐nearest neighbor estimation to calculate the probability density of samples. It automatically selects the optimal bandwidth based on the local density of the samples to improve the robustness of the algorithm. However, TSVM has high time complexity, to reduce the time costs, a sample screening method is proposed for AKWTSVM, named AKWTSVM‐SSM, which is based on the overall distance and local density, and reduces the time costs of the algorithm by reducing the sample size while ensuring the accuracy of the algorithm. The experiment with differently scaled noise environments of 0%, 5%, 10%, 15%, and 20% on 12 UCI datasets validate the accuracy and running time of AKWTSVM and AKWTSVM‐SSM. Experimental results prove the effectiveness and robustness of AKWTSVM, the robustness of AKWTSVM‐SSM, and its applicability to large‐scale datasets.

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Laplacian Lp norm least squares twin support vector machine

Cited by 18 publications

References 27 publications

A robust twin support vector machine based on fuzzy systems

A robust twin support vector machine based on fuzzy systems

Laplacian Twin Support Vector Machine With Pinball Loss for Semi-Supervised Classification

Adaptive kernel density estimation weighted twin support vector machine and its sample screening method

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