# Advancing Supervised Learning with the Wave Loss Function: A Robust and Smooth Approach

arXiv: https://arxiv.org/abs/2404.18101 · HTML: https://mlsanity.com/paper/2404.18101/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 46 references that are in the map.
- First posted on arXiv 28 Apr 2024.

## Builds on (most cited first, 6 of 6)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalization](https://mlsanity.com/paper/1906.02314/) (2019)
- [Comprehensive Review On Twin Support Vector Machines](https://mlsanity.com/paper/2105.00336/) (2021)
- [RoBoSS: A Robust, Bounded, Sparse, and Smooth Loss Function for Supervised Learning](https://mlsanity.com/paper/2309.02250/) (2023)
- [Incremental Learning from Low-labelled Stream Data in Open-Set Video Face Recognition](https://mlsanity.com/paper/2012.09571/) (2020)
- [HawkEye: Advancing Robust Regression with Bounded, Smooth, and Insensitive Loss Function](https://mlsanity.com/paper/2401.16785/) (2024)

## Built on by (most cited first, 11 of 11)

- [Enhancing Multiview Synergy: Robust Learning by Exploiting the Wave Loss Function with Consensus and Complementarity Principles](https://mlsanity.com/paper/2408.06819/) (2024)
- [Wave-RVFL: A Randomized Neural Network Based on Wave Loss Function](https://mlsanity.com/paper/2408.02824/) (2024)
- [Advancing RVFL networks: Robust classification with the HawkEye loss function](https://mlsanity.com/paper/2410.00510/) (2024)
- [Enhanced Feature Based Granular Ball Twin Support Vector Machine](https://mlsanity.com/paper/2410.05786/) (2024)
- [GL-TSVM: A robust and smooth twin support vector machine with guardian loss function](https://mlsanity.com/paper/2408.16336/) (2024)
- [Flexi-Fuzz least squares SVM for Alzheimer's diagnosis: Tackling noise, outliers, and class imbalance](https://mlsanity.com/paper/2410.14207/) (2024)
- [Enhancing Imbalance Learning: A Novel Slack-Factor Fuzzy SVM Approach](https://mlsanity.com/paper/2411.17128/) (2024)
- [CI-RKM: A Class-Informed Approach to Robust Restricted Kernel Machines](https://mlsanity.com/paper/2504.11476/) (2025)
- [Data-Driven Pinball-Loss Selection for Vertically Distributed Elastic-Net SVMs](https://mlsanity.com/paper/2608.00949/) (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)

Loss function plays a vital role in supervised learning frameworks. The selection of the appropriate loss function holds the potential to have a substantial impact on the proficiency attained by the acquired model. The training of supervised learning algorithms inherently adheres to predetermined loss functions during the optimization process. In this paper, we present a novel contribution to the realm of supervised machine learning: an asymmetric loss function named wave loss. It exhibits robustness against outliers, insensitivity to noise, boundedness, and a crucial smoothness property. Theoretically, we establish that the proposed wave loss function manifests the essential characteristic of being classification-calibrated. Leveraging this breakthrough, we incorporate the proposed wave loss function into the least squares setting of support vector machines (SVM) and twin support vector machines (TSVM), resulting in two robust and smooth models termed Wave-SVM and Wave-TSVM, respectively. To address the optimization problem inherent in Wave-SVM, we utilize the adaptive moment estimation (Adam) algorithm. It is noteworthy that this paper marks the first instance of the Adam algorithm application to solve an SVM model. Further, we devise an iterative algorithm to solve the optimization problems of Wave-TSVM. To empirically showcase the effectiveness of the proposed Wave-SVM and Wave-TSVM, we evaluate them on benchmark UCI and KEEL datasets (with and without feature noise) from diverse domains. Moreover, to exemplify the applicability of Wave-SVM in the biomedical domain, we evaluate it on the Alzheimer Disease Neuroimaging Initiative (ADNI) dataset. The experimental outcomes unequivocally reveal the prowess of Wave-SVM and Wave-TSVM in achieving superior prediction accuracy against the baseline models.