L1-norm loss-based projection twin support vector machine for binary classification

Hua, Xiaopeng; Xu, Sen; Gao, Jun; Ding, Shifei

doi:10.1007/s00500-019-04002-6

Cited by 13 publications

(3 citation statements)

References 30 publications

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“…With eight methods and 12 data sets, F F is distributed according to the F distribution with (7, 77) degrees of freedom. According to (26), (27), and Table 5, we can obtain χ 2 F � 14.8364 and F F � 2.3593. e critical value of F (7, 77) for α � 0.05 is 2.131 and similarly is 1.796 for α � 0.1, so we reject both levels of the null hypothesis. We can identify that there is a significantly different between the eight methods.…”

Section: Benchmark Data Setsmentioning

confidence: 95%

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Linear Twin Quadratic Surface Support Vector Regression

Zhai

Tian

Zhou

2020

Mathematical Problems in Engineering

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Twin support vector regression (TSVR) generates two nonparallel hyperplanes by solving a pair of smaller-sized problems instead of a single larger-sized problem in the standard SVR. Due to its efficiency, TSVR is frequently applied in various areas. In this paper, we propose a totally new version of TSVR named Linear Twin Quadratic Surface Support Vector Regression (LTQSSVR), which directly uses two quadratic surfaces in the original space for regression. It is worth noting that our new approach not only avoids the notoriously difficult and time-consuming task for searching a suitable kernel function and its corresponding parameters in the traditional SVR-based method but also achieves a better generalization performance. Besides, in order to make further improvement on the efficiency and robustness of the model, we introduce the 1-norm to measure the error. The linear programming structure of the new model skips the matrix inverse operation and makes it solvable for those huge-sized problems. As we know, the capability of handling large-sized problem is very important in this big data era. In addition, to verify the effectiveness and efficiency of our model, we compare it with some well-known methods. The numerical experiments on 2 artificial data sets and 12 benchmark data sets demonstrate the validity and applicability of our proposed method.

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Section: Benchmark Data Setsmentioning

confidence: 95%

“…It is noting that 2-norm is sensitive to those points which are far away from the regressor and may amplify the influence of those error points, especially in the case with outliers or mislabeled information. Compared with 2-norm, 1-norm is more robust and insensitive to the errors [26,27].…”

Section: Linear Twin Quadratic Surface Support Vector Regressionmentioning

confidence: 99%

Linear Twin Quadratic Surface Support Vector Regression

Zhai

Tian

Zhou

2020

Mathematical Problems in Engineering

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show abstract

“…However, it is worth noting that 2-norm is sensitive to the point which is far away from other points, and may amplify the influence of this error, especially in the case of outliers or mislabeled information. Compared with 2-norm, 1-norm is more robust and insensitive to errors [9]. In this paper, to increase the robustness, we apply the 1-norm d(x i , x j ) = |x i − x j | to define the distance.…”

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confidence: 99%

A SMOTE-based quadratic surface support vector machine for imbalanced classification with mislabeled information

Zhai

Tian

Zhou

2023

JIMO

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<p style='text-indent:20px;'>Recently, Synthetic Minority Over-Sampling Technique (SMOTE) has been widely used to handle the imbalanced classification. To address the issues of existing benchmark methods, we propose a novel scheme of SMOTE based on the K-means and Intuitionistic Fuzzy Set theory to assign proper weights to the existing points and generate new synthetic points from them. Besides, we introduce the state-of-the-art kernel-free fuzzy quadratic surface support vector machine (QSSVM) to do the classification. Finally, the numerical experiments on various artificial and real data sets strongly demonstrate the validity and applicability of our proposed method, especially in the presence of mislabeled information.</p>

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Fast clustering-based weighted twin support vector regression

Fang

Pan

et al. 2020

Soft Comput

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L1-norm loss-based projection twin support vector machine for binary classification

Cited by 13 publications

References 30 publications

Linear Twin Quadratic Surface Support Vector Regression

Linear Twin Quadratic Surface Support Vector Regression

A SMOTE-based quadratic surface support vector machine for imbalanced classification with mislabeled information

Fast clustering-based weighted twin support vector regression

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