Training primal twin support vector regression via unconstrained convex minimization

Twin Least Square Support Vector Regression Model Based on Gauss-Laplace Mixed Noise Feature with Its Application in Wind Speed Prediction

In this article, it was observed that the noise in some real-world applications, such as wind power forecasting and direction of the arrival estimation problem, does not satisfy the single noise distribution, including Gaussian distribution and Laplace distribution, but the mixed distribution. Therefore, combining the twin hyperplanes with the fast speed of Least Squares Support Vector Regression (LS-SVR), and then introducing the Gauss-Laplace mixed noise feature, a new regressor, called Gauss-Laplace Twin Least Squares Support Vector Regression (GL-TLSSVR), for the complex noise. Subsequently, we apply the augmented Lagrangian multiplier method to solve the proposed model. Finally, we apply the short-term wind speed data-set to the proposed model. The results of this experiment confirm the effectiveness of our proposed model.

Projection wavelet weighted twin support vector regression for OFDM system channel estimation

In this paper, an efficient projection wavelet weighted twin support vector regression (PWWTSVR) based orthogonal frequency division multiplexing system (OFDM) system channel estimation algorithm is proposed. Most Channel estimation algorithms for OFDM systems are based on the linear assumption of channel model. In the proposed algorithm, the OFDM system channel is consumed to be nonlinear and fading in both time and frequency domains. The PWWTSVR utilizes pilot signals to estimate response of nonlinear wireless channel, which is the main work area of SVR. Projection axis in optimal objective function of PWWRSVR is sought to minimize the variance of the projected points due to the utilization of a priori information of training data. Different from traditional support vector regression algorithm, training samples in different positions in the proposed PWWTSVR model are given different penalty weights determined by the wavelet transform. The weights are applied to both the quadratic empirical risk term and the first-degree empirical risk term to reduce the influence of outliers. The final regressor can avoid the overfitting problem to a certain extent and yield great generalization ability for channel estimation. The results of numerical experiments show that the propose algorithm has better performance compared to the conventional pilot-aided channel estimation methods.

Nonparallel support vector regression model and its SMO-type solver

Although the twin support vector regression (TSVR) method has been widely studied and various variants are successfully developed, the structural risk minimization (SRM) principle and model's sparseness are not given sufficient consideration. In this paper, a novel nonparallel support vector regression (NPSVR) is proposed in spirit of nonparallel support vector machine (NPSVM), which outperforms existing twin support vector regression (TSVR) methods in the following terms: (1) For each primal problem, a regularized term is added by rigidly following the SRM principle so that the kernel trick can be applied directly to the dual problems for the nonlinear case without considering an extra kernel-generated surface; (2) An ε-insensitive loss function is adopted to remain inherent sparseness as the standard support vector regression (SVR); (3) The dual problems have the same formulation with that of the standard SVR, so computing inverse matrix is well avoided and a sequential minimization optimization (SMO)-type solver is exclusively designed to accelerate the training for large-scale datasets; (4) The primal problems can approximately degenerate to those of the existing TSVRs if corresponding parameters are appropriately chosen. Numerical experiments on diverse datasets have verified the effectiveness of our proposed NPSVR in sparseness, generalization ability and scalability.