Weighted least squares twin support vector machine based on density peaks

Abstract

The least-squares twin support vector machine integrates all samples equally into the quadratic programming problem to calculate the optimal classification hyperplane, and does not distinguish the noise points in the samples, which causes the model to be sensitive to noise points and affected by the overlapping samples of positive and negative classes, and reduces the classification accuracy. To address the above problems, this paper proposes a weighted least squares twin support vector machine based on density peaks. Firstly, the algorithm combines the idea of density peaks to construct a new density weighting strategy, which gives a suitable weight value to this sample through the local density of the sample as well as the relative distance together to highlight the importance of the local center and reduce the influence of noise on the model; secondly, the separability between classes is defined according to the local density matrix, which reduces the influence of positive and negative class overlapping samples on the model and enhances the inter-class separability of the model; finally, an extensive weighting strategy is used in the model to assign weight values to both classes of samples to improve the robustness of the model to cross samples. The comparison experiments on the artificial dataset and the UCI dataset show that the algorithm in this paper can assign appropriate weights to different samples to improve the classification accuracy, while the experiments on the MNIST dataset demonstrate the effectiveness of the algorithm in this paper for real classification problems.