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In this paper, a simple and linearly convergent Lagrangian support vector machine algorithm for the dual of the twin support vector regression (TSVR) is proposed. Though at the outset the algorithm requires inverse of matrices, it has been shown that they would be obtained by performing matrix subtraction of the identity matrix by a scalar multiple of inverse of a positive semi-definite matrix that arises in the original formulation of TSVR. The algorithm can be easily implemented and does not need any optimization packages. To demonstrate its effectiveness, experiments were performed on well-known synthetic and real-world datasets. Similar or better generalization performance of the proposed method in less training time in comparison with the standard and twin support vector regression methods clearly exhibits its suitability and applicability. [ABSTRACT FROM AUTHOR]

In this paper, extreme learning machine (ELM) for ε-insensitive error loss function-based regression problem formulated in 2-norm as an unconstrained optimization problem in primal variables is proposed. Since the objective function of this unconstrained optimization problem is not twice differentiable, the popular generalized Hessian matrix and smoothing approaches are considered which lead to optimization problems whose solutions are determined using fast Newton-Armijo algorithm. The main advantage of the algorithm is that at each iteration, a system of linear equations is solved. By performing numerical experiments on a number of interesting synthetic and real-world datasets, the results of the proposed method are compared with that of ELM using additive and radial basis function hidden nodes and of support vector regression (SVR) using Gaussian kernel. Similar or better generalization performance of the proposed method on the test data in comparable computational time over ELM and SVR clearly illustrates its efficiency and applicability. [ABSTRACT FROM AUTHOR]

Twin support vector regression (TSVR) was proposed recently as a novel regressor that tries to find a pair of nonparallel planes, i.e., ε-insensitive up- and down-bounds, by solving two related SVM-type problems. However, it may incur suboptimal solution since its objective function is positive semi-definite and the lack of complexity control. In order to address this shortcoming, we develop a novel SVR algorithm termed as smooth twin SVR (STSVR). The idea is to reformulate TSVR as a strongly convex problem, which results in unique global optimal solution for each subproblem. To solve the proposed optimization problem, we first adopt a smoothing technique to convert the original constrained quadratic programming problems into unconstrained minimization problems, and then use the well-known Newton-Armijo algorithm to solve the smooth TSVR. The effectiveness of the proposed method is demonstrated via experiments on synthetic and real-world benchmark datasets. [ABSTRACT FROM AUTHOR]