PFW: Polygonal fuzzy weighted—an SVM kernel for the classification of overlapping data groups

Abstract

Support vector machines are supervised learning models which are capable of classifying data and measuring regression by means of a learning algorithm. If data are linearly separable, a conventional linear kernel is used to classify them. Otherwise, the data are normally first transformed from input space to feature space, and then they are classified. However, carrying out this transformation is not always practical, and the process itself increases the cost of training and prediction. To address these problems, this paper puts forward an SVM kernel, called polygonal fuzzy weighted or PFW, which effectively classifies data without space transformation, even if the groups in question are not linearly separable and have overlapping areas. This kernel is based on Gaussian data distribution, standard deviation, the three-sigma rule and a polygonal fuzzy membership function. A comparison of our PFW, radial basis function (RBF) and conventional linear kernels in identical experimental conditions shows that PFW produces a minimum of 26% higher classification accuracy compared with the linear kernel, and it outperforms the RBF kernel in two-thirds of class labels, by a minimum of 3%. Moreover, Since PFW runs within the original feature space, it involves no additional computational cost.