Polynomial Smooth Twin Support Vector Machines

Abstract

Smoothing functions can transform the unsmooth twin support vector machines (TWSVM) into smooth ones, and thus better classification results can be obtained. It has been one of the key problems to seek a better smoothing function in this field for a long time. In this paper, a novel version for smooth TWSVM, termed polynomial smooth twin support vector machines (PSTWSVM), is proposed. In PSTWSVM, using the series expansion, a new class of polynomial smoothing is proposed, and then their important properties are discussed. It is shown that the approximation accuracy and smoothness rank of polynomial functions can be as high as required. Subsequently, the polynomial functions are adopted to convert the original constrained quadratic programming problems of TWSVM into unconstrained minimization problems, and then are solved by the well-known Newton-Armijo algorithm. The effectiveness of the proposed method is demonstrated via experiments on synthetic and real-word benchmark datasets.

Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application

“…Unwrapping experiments using real data from the Jining area in China show that our proposed algorithm achieves more precise results than the least squares unwrapping algorithms. Quantitative indexes include differences in RMSE between rewrapped results and the original wrapped phase, computation time, and̃values [26][27][28]. The sequential quadratic programming method achieves better results with respect to three indices.…”

Tikhonov Regularized Variable Projection Algorithms for Separable Nonlinear Least Squares Problems

“…Moreover, when the original problem is ill posed, the degree of ill-posedness can be reduced [2][3][4][5]. As research has progressed, the mathematical models of many problems in actual engineering can be expressed as separable nonlinear least squares, for instance, in inverse problems and problems in signal processing, medical and biological imaging, neural networks, communication, electrical and electronic engineering, and di erential equation dynamic systems [6][7][8][9][10][11][12][13][14][15].…”