Adaptively weighted learning for twin support vector machines via Bregman divergences

Some versions of weighted (twin) support vector machines have been developed to handle the contaminated data. However, the weights of samples are generally obtained from the prior knowledge of data in advance. This article develops an adaptively weighted twin support vector machine via Bregman divergences. To better handle the contaminated data, we employ an insensitive loss function to control the fitting error of the samples in one class and introduce the weight (fuzzy membership) of each sample into the proposed model. The alternating optimization technique is utilized to solve the proposed model due to the characteristics of the model. The accelerated version of first-order methods is used to solve a quadratic programming problem, and the fuzzy membership of each sample is achieved analytically in the case of Bregman divergences. Experiments on some data sets have been conducted to show that our method gains better classification performance than previous methods, especially for the open set experiment.