Smooth twin support vector machines via unconstrained convex minimization

Abstract

Twin support vector machine (TWSVM) exhibits fast training speed with better classification abilities compared with standard SVM. However, it suffers the following drawbacks: (i) the objective functions of TWSVM are comprised of empirical risk and thus may suffer from overfitting and suboptimal solution in some cases. (ii) a convex quadratic programming problems (QPPs) need to be solve, which is relatively complex to implement. To address these problems, we proposed two smoothing approaches for an implicit Lagrangian TWSVM classifiers by formulating a pair of unconstrained minimization problems in dual variables whose solutions will be obtained by solving two systems of linear equations rather than solving two QPPs in TWSVM. Our proposed formulation introduces regularization terms to each objective function with the idea of maximizing the margin. In addition, our proposed formulation becomes well-posed model due to this term, which introduces invertibility in the dual formulation. Moreover, the structural risk minimization principle is implemented in our formulation which embodies the essence of statistical learning theory. The experimental results on several benchmark datasets show better performance of the proposed approach over existing approaches in terms of estimation accuracy with less training time.

A method of dimensionality reduction by selection of components in principal component analysis for text classification

“…Support Vector Machine (SVM) is chosen as the classifier for the experiments. SVM obtains the minimum structural risk to improve the ability of model learning and generalization by searching for the maximum margin hyperplane (see, e.g., Vapnik, 2006;Tsochantaridis, 2005;Joachims, 2006Joachims, , 2009Chapelle, 2012;Swaminathan, 2015;Tanveer, 2017). Performance evaluation of the classifier on the dataset includes the precision, recall, and F-measure using the confusion matrix given in Table 1.…”

Comprehensive Review On Twin Support Vector Machines

“…Tanveer [175] also proposed an implicit Lagrangian TSVM which is solved by using finite Newton method. Tanveer and Shubham [190] in 2017 proposed smooth TSVM via UMP which increases the generalization ability and training speed of TSVM.…”

A novel method for the classification of Alzheimer's disease from normal controls using magnetic resonance imaging

“…Recently, Tanveer, Sharma, and Suganthan (2019) proposed a novel general TSVM with pinball loss (Pin-GTSVM) that is insensitive to noise and performs better for noise corrupted datasets. To retain the sparsity in the Pin-GTSVM, Tanveer, Tiwari, Choudhary, and Jalan (2019) proposed a novel sparse pinball twin SVM (SPTSVM) that is insensitive to outliers and retail sparsity. Richhariya and Tanveer (2020) used universum learning for the first time to solve the class imbalance problem in which reduced kernel was incorporated for reducing storage and computation cost.…”

“…In recent years, concepts based on constructing a different variation of non‐parallel hyperplanes as in Tanveer (2015c), Tanveer and Shubham (2017), and Tanveer (2015a)) have emerged. TSVM is an efficient classification method, and, as mentioned in Jayadeva et al (2007), the two non‐parallel proximal hyperplanes are designed in such a way that each hyperplane is as close as possible to one class and as far as possible from the other class.…”