An improved regularization based Lagrangian asymmetric ν-twin support vector regression using pinball loss function

In twin support vector regression (TSVR), one can notice that the samples are having the same importance even they are laying above the up-bound and below the down-bound on the estimation function for regression problem. Instead of giving the same emphasis to the samples, a novel approach Asymmetric nu-twin support vector regression (Asy-nu-TSVR) is suggested in this context where samples are having different influences with the estimation function based on samples distribution. Inspired by this concept, in this paper, we propose a new approach as improved regularization based Lagrangian asymmetric nu-twin support vector regression using pinball loss function (LAsy-nu-TSVR) which is more effective and efficient to deal with the outliers and noise. The solution is obtained by solving the simple linearly convergent approach which reduces the computational complexity of the proposed LAsy-nu-TSVR. Also, the structural risk minimization principle is implemented to make the problem strongly convex and more stable by adding the regularization term in their objective functions. The superiority of proposed LAsy-nu-TSVR is justified by performing the various numerical experiments on artificial generated datasets with symmetric and heteroscedastic structure noise as well as standard real-world datasets. The results of LAsy-nu-TSVR compares with support vector regression (SVR), TSVR, TSVR with Huber loss (HN-TSVR) and Asy-nu-TSVR, regularization on Lagrangian TSVR (RLTSVR) for the linear and Gaussian kernel which clearly demonstrates the efficacy and efficiency of the proposed algorithm LAsy-nu-TSVR.