Twin minimax probability machine for pattern classification

Yang, Liming; Wen, Yakun; Zhang, Min; Wang, Xue

doi:10.1016/j.neunet.2020.07.030

Cited by 7 publications

(5 citation statements)

References 22 publications

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“…For smooth convex-concave minimax problems when K is not bilinear, many numerical algorithms are proposed such as the projection method [19], extragradient method [10], Tseng's accelerated proximal gradient algorithm [21], catalyst algorithm framework [24]. Recently, Mokhtari et al [12] proposed algorithms admitting a unified analysis as approximations of the classical proximal point method for solving saddle point problems.…”

Section: Problem Settingmentioning

confidence: 99%

Semi-Proximal Point Method for Nonsmooth Convex-Concave Minimax Optimization

Dai¹,

Zhang²

2024

JCM

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Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas. While there have been many numerical algorithms for solving smooth convex-concave minimax problems, numerical algorithms for nonsmooth convex-concave minimax problems are rare. This paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem. A semi-proximal point method (SPP) is proposed, in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each subproblem. This construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly chosen. We prove the global convergence of our algorithm under mild assumptions, without requiring strong convexity-concavity condition. Under the locally metrical subregularity of the solution mapping, we prove that our algorithm has the linear rate of convergence. Preliminary numerical results are reported to verify the efficiency of our algorithm.

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Section: Problem Settingmentioning

confidence: 99%

Semi-Proximal Point Method for Nonsmooth Convex-Concave Minimax Optimization

Dai¹,

Zhang²

2024

JCM

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“…The minimax probability machine (MPM) was introduced in [85,86] as an excellent discriminant classifier based on prior knowledge. Yang et al [87] combined an MPM with TWSVM to obtain a twin MPM, which they named TWMPM. The authors developed a simple and effective algorithm that transforms the problem into concave fractional programming by applying multivariate Chebyshev inequality.…”

Section: Probability Machine Combined With Twsvmmentioning

confidence: 99%

An Overview on the Advancements of Support Vector Machine Models in Healthcare Applications: A Review

Guido,

Ferrisi,

Lofaro

et al. 2024

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Support vector machines (SVMs) are well-known machine learning algorithms for classification and regression applications. In the healthcare domain, they have been used for a variety of tasks including diagnosis, prognosis, and prediction of disease outcomes. This review is an extensive survey on the current state-of-the-art of SVMs developed and applied in the medical field over the years. Many variants of SVM-based approaches have been developed to enhance their generalisation capabilities. We illustrate the most interesting SVM-based models that have been developed and applied in healthcare to improve performance metrics on benchmark datasets, including hybrid classification methods that combine, for instance, optimization algorithms with SVMs. We even report interesting results found in medical applications related to real-world data. Several issues around SVMs, such as selection of hyperparameters and learning from data of questionable quality, are discussed as well. The several variants developed and introduced over the years could be useful in designing new methods to improve performance in critical fields such as healthcare, where accuracy, specificity, and other metrics are crucial. Finally, current research trends and future directions are underlined.

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“…Following the transformation (19), the training set (1) in the d-dimensional space correspondingly becomes:…”

Section: Optimization Problemmentioning

confidence: 99%

“…In addition, we give the computational complexity of the MPM and the SVM. Their complexity is O(d 3 + Nd 2 ) [9] and O(N 3 ) [19], respectively. Then, by referencing the computational complexity of SVM, we obtain that the computational complexity of the QSSVM is O(N 3 + Nd 2 ).…”

Section: Computational Complexitymentioning

confidence: 99%

“…Therefore, it has been widely used in computer vision [10], engineering technology [11,12], agriculture [13], and novelty detection [14]. Moreover, many researchers have proposed a variety of improved versions of the MPM from different perspectives [14][15][16][17][18][19][20][21][22][23][24][25]. The representative works can be briefly reviewed as follows.…”

Section: Introductionmentioning

confidence: 99%

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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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Twin minimax probability machine for pattern classification

Cited by 7 publications

References 22 publications

Semi-Proximal Point Method for Nonsmooth Convex-Concave Minimax Optimization

Semi-Proximal Point Method for Nonsmooth Convex-Concave Minimax Optimization

An Overview on the Advancements of Support Vector Machine Models in Healthcare Applications: A Review

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

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