Twin support-vector machine (TSVM), which generates two nonparallel hyperplanes by solving a pair of smaller-sized quadratic programming problems (QPPs) instead of a single larger-sized QPP, works faster than the standard SVM, especially for the large-scale data sets. However, the traditional TSVM adopts hinge loss which easily leads to its sensitivity of the noise and instability for resampling. To enhance the performance of the TSVM, we present a novel TSVM with the pinball loss (Pin-TSVM) which deals with the quantile distance and is less sensitive to noise points. We further investigate its properties, including the noise insensitivity, between-class distance maximization, and within-class scatter minimization. In addition, we compare our Pin-TSVM with the twin parametric-margin SVM and the SVM with the pinball loss in theory. Numerical experiments on a synthetic data set and 14 benchmark data sets with different noises demonstrate the feasibility and validity of our proposed method.
The least square twin support vector machine (LS-TSVM) obtains two non-parallel hyperplanes by directly solving two systems of linear equations instead of two quadratic programming problems (QPPs) as in the conventional twin support vector machine (TSVM), which makes the computational speed of LS-TSVM faster than that of the TSVM. However, LS-TSVM ignores the structural information of data which may contain some vital prior domain knowledge for training a classifier. In this paper, we apply the prior structural information of data into the LS-TSVM to build a better classifier, called the structural least square twin support vector machine (S-LSTSVM). Since it incorporates the data distribution information into the model, S-LSTSVM has good generalization performance. Furthermore, S-LSTSVM costs less time by solving two systems of linear equations compared with other existing methods based on structural information. Experimental results on twelve benchmark datasets demonstrate that our S-LSTSVM performs well. Finally, we apply it into Alzheimer's disease diagnosis to further demonstrate the advantage of our algorithm.
The twin support vector machine (TSVM) is widely used in classification problems, but it is not efficient enough for large-scale data sets. Furthermore, to get the optimal parameter, the exhaustive grid search method is applied to TSVM. It is very time-consuming, especially for multiparameter models. Although many techniques have been presented to solve these problems, all of them always affect the performance of TSVM to some extent. In this paper, we propose a safe screening rule (SSR) for linear-TSVM, and give a modified SSR (MSSR) for nonlinear TSVM, which contains multiple parameters. The SSR and MSSR can delete most training samples and reduce the scale of TSVM before solving it. Sequential versions of SSR and MSSR are further introduced to substantially accelerate the whole parameter tuning process. One important advantage of SSR and MSSR is that they are safe, i.e., we can obtain the same solution as the original problem by utilizing them. Experiments on eight real-world data sets and an imbalanced data set with different imbalanced ratios demonstrate the efficiency and safety of SSR and MSSR.
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