Intuitionistic fuzzy proximal support vector machine for multicategory classification problems

Fuzzy support vector machine and their variants are prominent classification techniques that reduce the adverse effects of noises and outliers as compare to classical support vector machine. However, in these methods, only the distance between the training pattern and the class center is considered, and hence, the edge support vectors cannot be distinguished from noises and outliers properly. These limitations are overcome by intuitionistic fuzzy-based support vector machine which allocate two parameters (membership and non-membership degrees) to each pattern of a dataset and hence define score number based on the importance of a pattern. In this paper, an intuitionistic fuzzy proximal support vector machine for multi-category classification problems is proposed. The method significantly reduces the impacts of noises and outliers present in the dataset by assigning the intuitionistic fuzzy score function to each training point based on its location and surroundings. Moreover, the method is computationally efficient as the robust classifiers are obtained by solving the system of linear equations instead of large size quadratic programming problems. In the proposed method, using polynomial and Gaussian kernels, the hyperplanes are also developed in the feature space. The geometrical advantages of the suggested method over the existing techniques are ascertained using the simulated two-dimensional artificial dataset having three target classes. Further, extensive experimental studies on ten UCI benchmark datasets have been performed which demonstrate that the proposed algorithm predicts more precisely about future data as comparison to some well-established algorithms. Figures are also illustrated by varying different parameters involved in the model which confirms the performance of the method over the existing algorithms. Moreover, the analysis of the predictive behavior of the proposed approach is done using the Friedman test, a nonparametric alternative to the analysis of variance test at 5%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5\%$$\end{document} significance level. Further, the proposed method has also been applied to image classification and gesture-phase segmentation problems which confirms the efficiency and handling capabilities of the proposed algorithm in practical applications.