Abstract
In general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.
Highlights
Support vector machine (SVM) was proposed in details by Vapnik et al [1]
Intuitionistic fuzzy twin support vector machine (IFTSVM) [24] has been proposed which assigns a pair of membership and nonmembership functions to every training sample
We introduce the ideas of fuzzy membership functions and the Lap-TSVM
Summary
Support vector machine (SVM) was proposed in details by Vapnik et al [1]. The goal of SVM was to find an optimal hyperplane to separate the labeled data points into two classes. Intuitionistic fuzzy twin support vector machine (IFTSVM) [24] has been proposed which assigns a pair of membership and nonmembership functions to every training sample. These two functions help the IFTSVM to reduce the influence of noises and identify support vectors from noises. We proposed a novel intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) for a semi-supervised classification problem. (2) Intuitionistic fuzzy number can reduce the influence of noises and outliers in labeled samples, and the semi-supervised framework of manifold regularization was introduced to deal with labeled and unlabeled samples in the primal space and the feature space.
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