Efficient and Robust TWSVM Classification via a Minimum L1-Norm Distance Metric Criterion

Abstract

A twin support vector machine (TWSVM) is a classic distance metric learning method for classification problems. The TWSVM criterion is formulated based on the squared L2-norm distance, making it prone to being influenced by the presence of outliers. In this paper, to develop a robust distance metric learning method, we propose a new objective function, called L1-TWSVM, for the TWSVM classifier using the robust L1-norm distance metric. The optimization strategy is to maximize the ratio of the inter-class distance dispersion to the intra-class distance dispersion by using the robust L1-norm distance rather than the traditional L2-norm distance. The resulting objective function is much more challenging to optimize because it involves a non-smooth L1-norm term. As an important contribution of this paper, we design a simple but valid iterative algorithm for solving L1-norm optimal problems. This algorithm is easy to implement, and its convergence to an optimum is theoretically guaranteed. The efficiency and robustness of L1-TWSVM have been validated by extensive experiments on both UCI datasets as well as synthetic datasets. The promising experimental results indicate that our proposal approaches outperform relevant state-of-the-art methods in all kinds of experimental settings.