V-Shaped Ravine Loss for Twin Concentric Hyper-Spheres Maximum Margin Classifier for Robust Classification in Pattern Recognition

The Maximum Margin Twin Spheres Support Vector Machine (MTSVM) can effectively address the class imbalance problem by maximizing the margin between two concentric spheres. However, the underlying improvement method fails to simultaneously ensure sparsity and handle feature noise and label noise. To address this issue, we propose the V-Shaped Ravine Loss for Twin Concentric Hyper-Spheres Maximum Margin Classifier (V-CMMC), which is stable and simultaneously robust to feature noise and outliers. By penalizing far-margin outliers while preserving sensitivity to informative samples, V-CMMC yields a sparse, robust, and reliable decision hypersphere. The resulting non-differentiable non-convex optimization problem is efficiently solved using the Concave-Convex Procedure (CCCP). Theoretical analysis, including proofs of parameter properties and Bayes consistency, further establishes the method’s statistical reliability. Experiments on multiple imbalanced and image pattern recognition datasets demonstrate that V-CMMC consistently outperforms existing methods under noise and class imbalance.