Intuitionistic proximity-consensus fuzzy geometric twin support vector machine with best subset selection

The intuitionistic fuzzy twin support vector machine (IFTSVM) utilizes the intuitionistic fuzzy set (IFS) to enhance the robustness of twin support vector machine (TSVM). While IFTSVM has successfully mitigated the impact of noise and outliers, significant room for improvement remains: (1) IFS cannot reduce resampling noise deviation; (2) TSVM is sensitive to noise features. To address these problems, we propose a novel intuitionistic proximity-consensus fuzzy (IPCF) geometric TSVM with l₀-norm-based best subset selection to reduce the influence of outliers, resampling noise and noise features, simultaneously. The proposed IPCF is induced by the distance to the hyperplane obtained from the least squares one-class support vector machine, rather than considering the distance to the class center as in IFS. This strategy can effectively alleviate the effects of both outliers and resampling noise. Moreover, by incorporating the l₀-norm penalty, we can achieve significant feature selection and noise feature reduction at the same time. Due to the non-convexity, non-smoothness and non-continuity of l₀-norm penalty, it is difficult to solve the optimization problem. Inspired by the recently proposed variable sorted active set algorithm, we design an intuitionistic proximity-consensus fuzzy-optimized variable sorted active set algorithm (IPCF-VSAS) for optimizing the problem. On both simulating datasets and UCI datasets, it is the experimental results that validate the advantages of the proposed method. Specifically, compared with other state-of-the-art support vector classifiers, ours typically performs optimally on the datasets with redundant features and noise.