A novel fuzzy twin support vector machine based on centered kernel alignment

Abstract

Twin Support Vector Machine (TSVM) transforms a single large quadratic programming problem (QPP) in support vector machine (SVM) into two smaller QPPs by finding two non-parallel classification hyperplanes, so that its computational time is reduced to a quarter of what the traditional SVM takes. However, TSVM ignores the data distribution of class, which makes TSVM sensitive to noise. In this paper, a fuzzy twin support vector machine based on centered kernel alignment (FTSVM-CKA) is proposed to solve the problem that TSVM is sensitive to noise. Firstly, a feature-weighted kernel function is constructed by using the information gain, and it is applied to the calculation of the centered kernel alignment (CKA). This assigns greater weight to strongly correlated features, emphasizing their classification importance over weakly correlated features. Secondly, the CKA method is utilized to derive a heuristic function for calculating the dependency between samples and their corresponding labels, which assigns fuzzy membership to different samples. Based on this, a fuzzy membership assignment strategy is proposed that can effectively address the sensitivity of TSVM to noise. Thirdly, this strategy is combined with TSVM to propose the FTSVM-CKA model. Moreover, this study employs a coordinate descent strategy with shrinking by active set to tackle the computational complexity arising from high-dimensional inputs. This can effectively accelerate the training speed of the model while ensuring classification performance. In order to evaluate the performance of FTSVM-CKA, this study conducts experiments designed on artificial and UCI datasets. The results demonstrate that FTSVM-CKA can efficiently and quickly solve binary classification problems with noise.