Related papers: Newton Method for Soft Quadratic Surface Support V…

For the binary classification problem, a novel nonlinear kernel-free quadratic hyper-surface support vector machine with 0-1 loss function (QSSVM$_{0/1}$) is proposed. Specifically, the task of QSSVM$_{0/1}$ is to seek a quadratic…

Recent advance on linear support vector machine with the 0-1 soft margin loss ($L_{0/1}$-SVM) shows that the 0-1 loss problem can be solved directly. However, its theoretical and algorithmic requirements restrict us extending the linear…

Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…

Support vector machine (SVM) has proved to be a successful approach for machine learning. Two typical SVM models are the L1-loss model for support vector classification (SVC) and $\epsilon$-L1-loss model for support vector regression (SVR).…

It has been widely recognized that the 0/1 loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to…

Support Vector Machines (SVMs) are among the most popular and the best performing classification algorithms. Various approaches have been proposed to reduce the high computation and memory cost when training and predicting based on…

Support vector machine is an important and fundamental technique in machine learning. In this paper, we apply a semismooth Newton method to solve two typical SVM models: the L2-loss SVC model and the \epsilon-L2-loss SVR model. The…

Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…

In binary classification, kernel-free linear or quadratic support vector machines are proposed to avoid dealing with difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data…

Twin support vector machine (TSVM) is a very classical and practical classifier for pattern classification. However, the traditional TSVM has two limitations. Firstly, it uses the L_2-norm distance metric that leads to its sensitivity to…

We propose $\ell_1$ norm regularized quadratic surface support vector machine models for binary classification in supervised learning. We establish their desired theoretical properties, including the existence and uniqueness of the optimal…

Kernel-free quadratic surface support vector machines (QSVM) have recently gained traction due to their flexibility in modeling nonlinear decision boundaries without relying on kernel functions. However, the introduction of a full quadratic…

In this paper we present GSSN, a globalized SCD semismooth* Newton method for solving nonsmooth nonconvex optimization problems. The global convergence properties of the method are ensured by the proximal gradient method, whereas locally…

We present two new remarkably simple stochastic second-order methods for minimizing the average of a very large number of sufficiently smooth and strongly convex functions. The first is a stochastic variant of Newton's method (SN), and the…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…

Support vector machines (SVMs) are successful modeling and prediction tools with a variety of applications. Previous work has demonstrated the superiority of the SVMs in dealing with the high dimensional, low sample size problems. However,…

The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…

The previous support vector machine(SVM) including $0/1$ loss SVM, hinge loss SVM, ramp loss SVM, truncated pinball loss SVM, and others, overlooked the degree of penalty for the correctly classified samples within the margin. This…

Support vector classification (SVC) with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with…

Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…