Uncertainty-aware twin support vector machines. (September 2022) - Liang, Zhizheng; Zhang, Lei
Highlights: This paper proposes uncertainty-aware twin support vector machines. We derive a theorem which helps us simplify the models. The proposed decision rule allows us to classify uncertain samples with Gaussian distributions. The experiments have been conducted to demonstrate the effectiveness of the proposed models in handling uncertain data. Abstract: There exist uncertain data in the real world due to some factors such as imprecise measurements and noise. Unlike deterministic data, the features of samples in uncertain data are often described by interval numbers or random vectors with probability density functions. In this paper we propose novel twin support vector machines (TSVMs) to handle uncertain data. In the proposed models which are referred to as uncertainty-aware TSVMs, each uncertain sample is modeled as a random vector with Gaussian distributions. To deal with the multi-dimensional integrals in the original models, we derive an interesting and important theorem which helps us transform the original models into the model involving one-dimensional integrals. The simplification of models makes the optimization problem tractable and the simplified models are solved by using the quasi-Newton optimization algorithm. The proposed decision rule allows us to classify uncertain samples with means and covariance matrices. In addition, we extend the proposed models to their kernel versions to capture the nonlinear structure of uncertain data. Experiments on a series of data sets have been performed to demonstrate that the proposed models gain better classification performance than some existing algorithms, especially for representing uncertain cross-plane problems.