# Enhancing Multiview Synergy: Robust Learning by Exploiting the Wave Loss Function with Consensus and Complementarity Principles

arXiv: https://arxiv.org/abs/2408.06819 · HTML: https://mlsanity.com/paper/2408.06819/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 13 Aug 2024.

## Builds on (most cited first, 10 of 10)

- [Multiview Transformers for Video Recognition](https://mlsanity.com/paper/2201.04288/) (2022)
- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)
- [Feature Concatenation Multi-view Subspace Clustering](https://mlsanity.com/paper/1901.10657/) (2019)
- [Advancing Supervised Learning with the Wave Loss Function: A Robust and Smooth Approach](https://mlsanity.com/paper/2404.18101/) (2024)
- [Intuitionistic Fuzzy Generalized Eigenvalue Proximal Support Vector Machine](https://mlsanity.com/paper/2408.01713/) (2024)
- [Multi-view Laplacian Support Vector Machines](https://mlsanity.com/paper/1307.7024/) (2013)
- [Multiview learning with twin parametric margin SVM](https://mlsanity.com/paper/2408.01981/) (2024)
- [Stacked Penalized Logistic Regression for Selecting Views in Multi-View Learning](https://mlsanity.com/paper/1811.02316/) (2018)
- [Multi-View Graph Representation for Programming Language Processing: An Investigation into Algorithm Detection](https://mlsanity.com/paper/2202.12481/) (2022)
- [Support matrix machine: A review](https://mlsanity.com/paper/2310.19717/) (2023)

## Built on by (most cited first, 12 of 12)

- [TRKM: Twin Restricted Kernel Machines for Classification and Regression](https://mlsanity.com/paper/2502.15759/) (2025)
- [GRVFL-MV: Graph Random Vector Functional Link Based on Multi-View Learning](https://mlsanity.com/paper/2409.04743/) (2024)
- [Robust Universum Twin Support Vector Machine for Imbalanced Data](https://mlsanity.com/paper/2410.20335/) (2024)
- [Twin Restricted Kernel Machines for Multiview Classification](https://mlsanity.com/paper/2512.15757/) (2025)
- [Enhanced Feature Based Granular Ball Twin Support Vector Machine](https://mlsanity.com/paper/2410.05786/) (2024)
- [Randomized based restricted kernel machine for hyperspectral image classification](https://mlsanity.com/paper/2503.05837/) (2025)
- [GL-TSVM: A robust and smooth twin support vector machine with guardian loss function](https://mlsanity.com/paper/2408.16336/) (2024)
- [Enhancing Imbalance Learning: A Novel Slack-Factor Fuzzy SVM Approach](https://mlsanity.com/paper/2411.17128/) (2024)
- [Robust and sparse support vector machine via hybrid truncated loss for supervised classification](https://mlsanity.com/paper/2606.05814/) (2026)
- [XGRVFL-MV: Residual-Coupled Graph-Embedded Multi-View Random Vector Functional Link Network with FleXi Guardian Loss](https://mlsanity.com/paper/2607.23149/) (2026)
- [Robust Broad Learning System with Wave Loss for Classification under Data Uncertainty](https://mlsanity.com/paper/2608.29983/) (2026)
- [IFW-BLS: Dual-Robust Broad Learning System with Intuitionistic Fuzzy Wave Loss](https://mlsanity.com/paper/2609.02422/) (2026)

## Abstract (arXiv)

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 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. 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. The optimization problem is efficiently solved using a combination of GD and the ADMM, ensuring reliable convergence to optimal solutions. Theoretical analyses, grounded in Rademacher complexity, validate the generalization capabilities of the Wave-MvSVM model. Extensive empirical evaluations across diverse datasets demonstrate the superior performance of Wave-MvSVM in comparison to existing benchmark models.