Cost sensitive ν-support vector machine with LINEX loss

摘要

Support vector machine (SVM) is a fundamental machine learning algorithm, while the traditional SVMs have limitations for massive and ubiquitous class-imbalanced data in practice. To address this issue, we propose a novel cost sensitive learning model called ν-CSSVM for imbalanced classification, which simultaneously inherits the advantages of ν-SVM and the asymmetric LINEX loss function. On one hand, the introduction of the LINEX loss function allocates different costs to each instance, demonstrating the high efficiency of realizing cost sensitive learning at the instance level. On the other hand, ν in the objective function is used to constrain the model sparsity. Compared with other studies lacking theoretical analysis, we provide detailed proof of ν-CSSVM generalization error bound through Rademacher complexity. Taking into full consideration of the intrinsic and potential properties including the smoothness, convexity and differentiability of ν-CSSVM, the alternating direction method of multipliers (ADMM) and gradient descent (GD) approach are designed. Considerable experiments validate that ν-CSSVM is more competitive than the benchmarks in class imbalance learning. The statistical test further confirms this conclusion.