An efficient weighted Lagrangian twin support vector machine for imbalanced data classification

• We propose an efficient WLTSVM for imbalanced data classification.
• A graph based under-sampling strategy is introduced, which is robustness to outliers.
• The weight biases are embedded in our WLTSVM formulations.
• One Lagrangian training algorithm is presented and its convergence is proven.
• Experimental results show its feasibility and efficiency.

In this paper, we propose an efficient weighted Lagrangian twin support vector machine (WLTSVM) for the imbalanced data classification based on using different training points for constructing the two proximal hyperplanes. The main contributions of our WLTSVM are: (1) a graph based under-sampling strategy is introduced to keep the proximity information, which is robustness to outliers, (2) the weight biases are embedded in the Lagrangian TWSVM formulations, which overcomes the bias phenomenon in the original TWSVM for the imbalanced data classification, (3) the convergence of the training procedure of Lagrangian functions is proven and (4) it is tested and compared with some other TWSVMs on synthetic and real datasets to show its feasibility and efficiency for the imbalanced data classification.