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Twin support vector machine (TSVM) is a practical machine learning algorithm, whereas traditional TSVM can be limited for data with outliers or noises. To address this problem, we propose a novel TSVM with the symmetric LINEX loss function (SLTSVM) for robust classification. There are several advantages of our method: (1) The performance of the proposed SLTSVM for data with outliers or noise can be improved by using the symmetric LINEX loss function. (2) The introduction of regularization term can effectively improve the generalization ability of our model. (3) An efficient iterative algorithm is developed to solve the optimization problems of our SLTSVM. (4) The convergence and time complexity of the iterative algorithm are analyzed in detail. Furthermore, our model does not involve loss function parameter, which makes our method more competitive. Experimental results on synthetic, benchmark and image datasets with label noises and feature noises demonstrate that our proposed method slightly outperforms other state-of-the-art methods on most datasets. • This paper proposes SLTSVM by introducing symmetric LIENX loss function. • An interpretable method is proposed for selecting the loss parameter. • The convergence of the designed solution algorithm are further analyzed. • Experiments show that our method is efficient for data with outliers or noises. [ABSTRACT FROM AUTHOR]

Among the extensions of twin support vector machine (TSVM), some scholars have utilized K-nearest neighbor (KNN) graph to enhance TSVM's classification accuracy. However, these KNN-based TSVM classifiers have two major issues such as high computational cost and overfitting. In order to address these issues, this paper presents an enhanced regularized K-nearest neighbor-based twin support vector machine (RKNN-TSVM). It has three additional advantages: (1) Weight is given to each sample by considering the distance from its nearest neighbors. This further reduces the effect of noise and outliers on the output model. (2) An extra stabilizer term was added to each objective function. As a result, the learning rules of the proposed method are stable. (3) To reduce the computational cost of finding KNNs for all the samples, location difference of multiple distances-based K-nearest neighbors algorithm (LDMDBA) was embedded into the learning process of the proposed method. The extensive experimental results on several synthetic and benchmark datasets show the effectiveness of our proposed RKNN-TSVM in both classification accuracy and computational time. Moreover, the largest speedup in the proposed method reaches to 14 times. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TWSVM) has gained increasing interest from various research fields recently. In this paper, we aim to report the current state of the theoretical research and practical advances on TWSVM. We first give the basic thought and theory of TWSVM, including the theory of proximal support vector machine, generalized eigenvalue proximal support vector machine, and TWSVM. Then, we focus on the various improvements made to TWSVM, mainly including least squares twin support vector machine, smooth twin support vector machine, regularized twin support vector machine, projection twin support vector machine, and modified TWSVM on the model selection problem. These newly emerging algorithms greatly expand the applications of TWSVM. In recent years, there is a lot of research on application of TWSVM. Next, we list some research on application of TWSVM in detail. Finally, we try to provide a comprehensive view of these advances in TWSVM and discuss the direction of future research. [ABSTRACT FROM AUTHOR]

Abstract: It has been shown that the structural information of data may contain useful prior domain knowledge for training a classifier. How to apply the structural information of data to build a good classifier is a new research focus recently. As we all know, the all existing structural large margin methods are the common in considering all structural information within classes into one model. In fact, these methods do not balance all structural information’s relationships both infra-class and inter-class, which directly results in these prior information not being exploited sufficiently. In this paper, we design a new Structural Twin Support Vector Machine (called -TWSVM). Unlike existing methods based on structural information, -TWSVM uses two hyperplanes to decide the category of new data, of which each model only considers one class’s structural information and closer to the class at the same time far away from the other class. This makes -TWSVM fully exploit these prior knowledge to directly improve the algorithm’s the capacity of generalization. All experiments show that our proposed method is rigidly superior to the state-of-the-art algorithms based on structural information of data in both computation time and classification accuracy. [Copyright &y& Elsevier]

Twin support vector machine (TSVM) is a new machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems (QPPs) rather than a single large one. However, when constructing the classification plane for one class, a large number of samples of this class are considered in the objective function, but only fewer samples in the other class are considered, which easily results in over-fitting problem. In addition, the same penalties are given to each misclassified samples in the TSVM. In fact, the misclassified samples have different effects on the decision of the hyper-plane. In order to overcome these two disadvantages, by introducing the rough set theory into ν-TSVM, we propose a rough margin-based ν-TSVM in this paper. In the proposed algorithm, the different points in the different positions are proposed to have different effects on the separating hyper-plane. We firstly construct rough lower margin, rough upper margin, and rough boundary in the ν-TSVM and then give the different penalties to the different misclassified samples according to their positions. The new classifier can avoid the over-fitting problem to a certain extent. Numerical experiments on one artificial dataset and six benchmark datasets demonstrate the feasibility and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]