Polynomial Smooth Twin Support Vector Machines Based on Invasive Weed Optimization Algorithm

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 used 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. Meanwhile, in order to find the suitable parameters of PSTWSVM, Invasive Weed Optimization (IWO) algorithm is used to optimize the proposed algorithm. Then we propose an algorithm called polynomial smooth twin support vector machines based on invasive weed optimization algorithm (PSTWSVM-IWO). Finally, the effectiveness of the proposed method is demonstrated via experiments on synthetic and UCI benchmark datasets.