Support vector machines with the ε-insensitive pinball loss function for uncertain data classification

Due to the use of the quantile function, support vector machines with the pinball loss (PinSVMs) have good properties such as noise insensitivity and stability of re-sampling. In this paper we propose a novel model with the e-insensitive pinball loss function for uncertain data classification. The original model we propose involves the high-dimensional integral problem. In order to make the optimization model become tractable, we transform the original model into the simplified one by using some techniques. We theoretically analyze some properties of the proposed optimization model including noise insensitivity and scatter minimization. Based on the probability of uncertain samples in the halfspaces, we make a rule to classify uncertain samples. In the proposed model a probabilistic degree of the uncertain sample that belongs to the positive or negative class can be given. In addition, we use the kernel trick to extend the proposed model to deal with nonlinear problems. The experiments on artificial data and real-world data sets are carried out to confirm the effectiveness of the proposed model in handling uncertain data. (C) 2021 Elsevier B.V. All rights reserved.