Linear Twin Quadratic Surface Support Vector Regression

Abstract

Twin support vector regression (TSVR) generates two nonparallel hyperplanes by solving a pair of smaller-sized problems instead of a single larger-sized problem in the standard SVR. Due to its efficiency, TSVR is frequently applied in various areas. In this paper, we propose a totally new version of TSVR named Linear Twin Quadratic Surface Support Vector Regression (LTQSSVR), which directly uses two quadratic surfaces in the original space for regression. It is worth noting that our new approach not only avoids the notoriously difficult and time-consuming task for searching a suitable kernel function and its corresponding parameters in the traditional SVR-based method but also achieves a better generalization performance. Besides, in order to make further improvement on the efficiency and robustness of the model, we introduce the 1-norm to measure the error. The linear programming structure of the new model skips the matrix inverse operation and makes it solvable for those huge-sized problems. As we know, the capability of handling large-sized problem is very important in this big data era. In addition, to verify the effectiveness and efficiency of our model, we compare it with some well-known methods. The numerical experiments on 2 artificial data sets and 12 benchmark data sets demonstrate the validity and applicability of our proposed method.

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

“…When the optimal solution u * is obtained by the above two updated iteration Formulas (34) and (35), the optimal solution w * of the optimization problem ( 28) is w * = w 0 + Fu * . Then, we summarize the process of finding the optimal solution A * , b * , c * of the optimization problem (18) in Algorithm 1.…”

“…After that, Bai et al [28] proposed the quadratic kernel-free least-squares support vector machine for target diseases' classification. Following these leading works, some scholars performed further studies, e.g., see [29][30][31][32][33][34] for the classification problem, [35] for the regression problem, and [36] for the cluster problem. The good performance of these methods demonstrates that the quadratic hypersurface is an effective method to flexibly capture the nonlinear structure of data.…”

Kernel-Free Quadratic Surface Support Vector Regression with Non-Negative Constraints

“…For the regression problem, Ye et al [26,27] proposed two kernel-free nonlinear regression models, quadratic surface kernel-free least squares SVR (QLSSVR) and -kernel-free soft QSSVR ( -SQSSVR), respectively. Zhai et al [28] proposed a linear twin quadratic surface support vector regression. Zheng et al [29] developed a hybrid QSSVR and applied it to stock indices and price forecasting.…”