An Unconstrained Primal Based Twin Parametric Insensitive Support Vector Regression

In this paper, we propose an efficient regression algorithm based on primal formulation of twin support vector machine. This is an efficient approach to solve the optimization problem leading to reduced computation time. The proposed method is termed as twin parametric insensitive support vector regression (UPTPISVR). The optimization problems of the proposed (UPTPISVR) are a pair of unconstrained convex minimization problems. Moreover, the objective functions of UPTPISVR are strongly convex, differentiable and piecewise quadratic. Therefore, an approximate solution is obtained in primal variables instead of solving the dual formulation. Further, an absolute value equation problem is solved by using a functional iterative algorithm for UPTPISVR, termed as FUPTPISVR. The objective function of the proposed formulation involves the plus function which is non-smooth and therefore, smooth approximation functions are used to replace the plus function, termed as SUPTPISVR. The Newton-Armijo algorithm is then used to iteratively obtain the solutions, thus eliminates the requirement of any optimization toolbox. Various numerical experiments on synthetic and benchmark real-world datasets are presented for justifying the applicability and effectiveness of the proposed UPTPISVR. The results clearly indicate that the proposed algorithms outperform the existing algorithms in terms of root mean square error (RMSE) on most datasets.