Clustering via fuzzy one-class quadratic surface support vector machine

Luo, Jian; Tian, Ye; Yan, Xin

doi:10.1007/s00500-016-2462-x

Cited by 10 publications

(14 citation statements)

References 20 publications

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“…It is important to choose a suitable fuzzy membership function, as different fuzzy membership functions may affect the classifier differently. The Euclidean distance between training points and their class centers is the most common membership function in FSVM models [11,19,20]. However, this method is not suitable for unsupervised classification.…”

Section: Fuzzy Membership Functionmentioning

confidence: 99%

“…The algorithm reduces reliance on dataset labels. The weight one-class SVM and fuzzy one-class SVM further improve the efficiency and accuracy of the OC-SVM [10,11]. However, OC-SVM-based methods rely heavily on the initial labeled data points.…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted, however, that all these methods solve the problem of noise points through binary classification problems. The fuzzy one-class quadratic surface support vector machine (FOC-QSSVM) considers minimizing the within-class scatter, which solves the noise problem of OC-SVM [11]. However, fuzzy membership equations do not address the negative impact of noise points and outliers on unsupervised learning decision planes.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Novel Fuzzy Unsupervised Quadratic Surface Support Vector Machine Based on DC Programming: An Application to Credit Risk Management

Yu,

Huang,

Tang

2023

Mathematics

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Unsupervised classification is used in credit risk assessment to reduce human resource costs and make informed decisions in the shortest possible time. Although several studies show that support vector machine-based methods have better performance in unlabeled datasets, several factors still negatively affect these models, such as unstable results due to random initialization, reduced effectiveness due to kernel dependencies, and noise points and outliers. This paper introduces an unsupervised classification method based on a fuzzy unsupervised quadratic surface support vector machine without a kernel to avoid selecting related kernel parameters for credit risk assessment. In addition, we propose an innovative fuzzy membership function for reducing noise points and outliers in line with the direction of sample density variation. Fuzzy Unsupervised QSSVM (FUS-QSSVM) outperforms well-known SVM-based methods based on numerical tests on public benchmark credit data. In some real-world applications, the proposed method has significant potential as well as being effective, efficient, and robust. The algorithm can therefore increase the number of potential customers of financial institutions as well as increase profitability.

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Section: Fuzzy Membership Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Novel Fuzzy Unsupervised Quadratic Surface Support Vector Machine Based on DC Programming: An Application to Credit Risk Management

Yu,

Huang,

Tang

2023

Mathematics

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“…Next, Gao et al [6,7] proposed two kernel-free quartic surface support vector classification (DWPSVC) for the binary and multi-class classification problems, which further improved the classification accuracy. In addition, some kernel-free classifiers are also applied to semi-supervised learning [18,23,24,30], credit scoring [12,20], universum data [13,25], and some other extended models [11,22]. Except to the above research achievements in the classification problem, kernel-free techniques have also been applied to the regression problem.…”

Section: Introductionmentioning

confidence: 99%

Kernel-free double well potential support vector regression

Wang

Yang

2023

Preprint

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In this paper, for the regression problem, a novel kernel-free support vector regression based on the double well potential function (DWPSVR) is proposed.In fact, our model applies a type of kernel-free technique, which directly find a double well potential function to fit data, so that the regression function has geometric diversity. The principle of maximizing G-margin is used to construct our optimization problem, where G-margin is independent of the data and is an approximation of the relative geometric margin. At the same time, the ε-insensitive loss function is introduced. In addition, the primal and dual problems of our model are convex quadratic programming problems, so they can be solved directly. The existence and uniqueness of the optimal solution to both primal and dual problems and some concepts of support vectors are also addressed in theoretical analysis. The 5 artificial and 10 benchmark datasets are utilized in numerical experiments. The experimental results validate that the regression function obtained by our method has geometric diversity and the comprehensive performance of our method outperforms the linear support vector regression model and two kernel-free quadratic regression models.

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“…After that, Bai et al [28] proposed the quadratic kernel-free least-squares support vector machine for target diseases' classification. Following these leading works, some scholars performed further studies, e.g., see [29][30][31][32][33][34] for the classification problem, [35] for the regression problem, and [36] for the cluster problem. The good performance of these methods demonstrates that the quadratic hypersurface is an effective method to flexibly capture the nonlinear structure of data.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Free Quadratic Surface Minimax Probability Machine for a Binary Classification Problem

Wang

Yang

2021

Symmetry

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In this paper, we propose a novel binary classification method called the kernel-free quadratic surface minimax probability machine (QSMPM), that makes use of the kernel-free techniques of the quadratic surface support vector machine (QSSVM) and inherits the advantage of the minimax probability machine (MPM) without any parameters. Specifically, it attempts to find a quadratic hypersurface that separates two classes of samples with maximum probability. However, the optimization problem derived directly was too difficult to solve. Therefore, a nonlinear transformation was introduced to change the quadratic function involved into a linear function. Through such processing, our optimization problem finally became a second-order cone programming problem, which was solved efficiently by an alternate iteration method. It should be pointed out that our method is both kernel-free and parameter-free, making it easy to use. In addition, the quadratic hypersurface obtained by our method was allowed to be any general form of quadratic hypersurface. It has better interpretability than the methods with the kernel function. Finally, in order to demonstrate the geometric interpretation of our QSMPM, five artificial datasets were implemented, including showing the ability to obtain a linear separating hyperplane. Furthermore, numerical experiments on benchmark datasets confirmed that the proposed method had better accuracy and less CPU time than corresponding methods.

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Clustering via fuzzy one-class quadratic surface support vector machine

Cited by 10 publications

References 20 publications

A Novel Fuzzy Unsupervised Quadratic Surface Support Vector Machine Based on DC Programming: An Application to Credit Risk Management

A Novel Fuzzy Unsupervised Quadratic Surface Support Vector Machine Based on DC Programming: An Application to Credit Risk Management

Kernel-free double well potential support vector regression

Kernel-Free Quadratic Surface Minimax Probability Machine for a Binary Classification Problem

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