Enhancing multiview synergy: Robust learning by exploiting the wave loss function with consensus and complementarity principles

Abstract

Multiview learning (MvL) is an advancing domain in machine learning, leveraging multiple data perspectives to enhance model performance through view-consistency and view-discrepancy. Despite numerous successful multiview-based support vector machine (SVM) models, existing frameworks predominantly focus on the consensus principle, often overlooking the complementarity principle. Furthermore, they exhibit limited robustness against noisy, error-prone, and view-inconsistent samples, prevalent in multiview datasets. To tackle the aforementioned limitations, this paper introduces Wave-MvSVM, a novel multiview support vector machine framework leveraging the wave loss (W-loss) function, specifically designed to harness both consensus and complementarity principles. Unlike traditional approaches that often overlook the complementary information among different views, the proposed Wave-MvSVM ensures a more comprehensive and resilient learning process by integrating both principles effectively. The W-loss function, characterized by its smoothness, asymmetry, and bounded nature, is particularly effective in mitigating the adverse effects of noisy and outlier data, thereby enhancing model stability. Theoretically, the W-loss function also exhibits a crucial classification-calibrated property, further boosting its effectiveness. The proposed Wave-MvSVM employs a between-view co-regularization term to enforce view consistency and utilizes an adaptive combination weight strategy to maximize the discriminative power of each view, thus fully exploiting both consensus and complementarity principles. The optimization problem is efficiently solved using a combination of gradient descent (GD) and the alternating direction method of multipliers (ADMM), ensuring reliable convergence to optimal solutions. The generalization abilities of the proposed Wave-MvSVM model is theoretically supported through analyses based on Rademacher complexity. Extensive empirical evaluations across diverse datasets demonstrate the superior performance of Wave-MvSVM in comparison to existing benchmark models, highlighting its potential as a robust and efficient solution for MvL challenges. Furthermore, we implemented the proposed Wave-MvSVM model on Schizophrenia dataset, showcasing the model's efficacy in real-world applications. The source code of the proposed Wave-MvSVM model is available at https://github.com/mtanveer1/Wave-MvSVM. © 2025