Generalized robust loss function driven learning framework for pattern recognition

This study introduces a novel semi-algebraic generalized robust loss function, R(x), integrated with the Kurdyka-Łojasiewicz (KL) property, designed for robust pattern classification. The proposed loss function uniquely combines hybrid loss mechanisms to achieve an optimal trade-off between sensitivity to minor errors and robustness against outliers while preserving computational efficiency. Within the M-estimation framework, its robustness is rigorously proven through boundedness analysis of the influence function. Extending R(x) to the twin support vector machine (TWSVM) framework, we develop a generalized robust TWSVM (GR-TSVM) for classification tasks. To solve the resultant non-convex, non-smooth optimization problem, an alternating direction method of multipliers (ADMM) is employed, decomposing the problem into closed-form hyperplane updates and proximal gradient steps for slack variables. Theoretically, we establish convergence guarantees and demonstrate that the objective function satisfies the KL property, ensuring stable and reliable optimization. Bridging robust statistical learning with efficient optimization, GR-TSVM addresses the limitations of quadratic loss functions and advances pattern classification by harmonizing theoretical rigor with computational tractability. Extensive comparative experiments on benchmark datasets validate the proposed method, which shows statistically significant improvements in both classification accuracy and robustness metrics compared to traditional robust learning paradigms. The code needed to reproduce all our experiments is publicly available at https://github.com/junma1990-max/GR-TSVM-MATLAB-Demo.git.