Weighted relaxed support vector machines

Classification of imbalanced data is challenging when outliers exist. In this paper, we propose a supervised learning method to simultaneously classify imbalanced data and reduce the influence of outliers. The proposed method is a cost-sensitive extension of the relaxed support vector machines (RSVM), where the restricted penalty free-slack is split independently between the two classes in proportion to the number samples in each class with different weights, hence given the name weighted relaxed support vector machines (WRSVM). We compare classification results of WRSVM with SVM, WSVM and RSVM on public benchmark datasets with imbalanced classes and outlier noise, and show that WRSVM produces more accurate and robust classification results.