Fuzzy support vector machine with graph for classifying imbalanced datasets

Since support vector machine (SVM) considers all the training samples equally, it suffers from the problems of noise/outliers and class imbalance. Although many fuzzy support vector machines (FSVMs) have been proposed to suppress the effect of noise/outliers and class imbalance, most of them ignore the impact of the curse of dimensionality on the discriminative performance of fuzzy membership function and do not give the fuzzy membership function corresponding to the kernel space, which seriously reduces the performance of FSVM. To solve these problems, we propose the fuzzy support vector machine with graph (GraphFSVM) in this paper. Specifically, we first design a graph-based fuzzy membership function to accurately assess the importance of samples in original feature space and prove that the function can mine discriminative information between samples in high-dimensional data. Additionally, since the data distribution in kernel space is different from those in the original feature space, a method is provided to calculate the fuzzy membership function in the kernel space. Finally, the GraphFSVM model analyzes samples of each class independently, this suppresses the effect of class imbalance. Following the above principles, we design the graph-based fuzzy support vector machine and propose a detailed optimization method. Experimental results on UCI, gene expression, and image datasets show that the GraphFSVM has better generalization and robustness than other state-of-the-art methods.(c) 2022 Elsevier B.V. All rights reserved.