# Robustness of Generalized Median Computation for Consensus Learning in Arbitrary Spaces

arXiv: https://arxiv.org/abs/2503.05215 · HTML: https://mlsanity.com/paper/2503.05215/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 7 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Learning Representations by Predicting Bags of Visual Words](https://mlsanity.com/paper/2002.12247/) (2020)
- [A Survey on Ensemble Learning under the Era of Deep Learning](https://mlsanity.com/paper/2101.08387/) (2021)
- [Robust Fitting in Computer Vision: Easy or Hard?](https://mlsanity.com/paper/1802.06464/) (2018)
- [HARA: A Hierarchical Approach for Robust Rotation Averaging](https://mlsanity.com/paper/2111.08831/) (2021)
- [The Flag Median and FlagIRLS](https://mlsanity.com/paper/2203.04437/) (2022)
- [Chordal Averaging on Flag Manifolds and Its Applications](https://mlsanity.com/paper/2303.13501/) (2023)
- [Weighted Clustering Ensemble: A Review](https://mlsanity.com/paper/1910.02433/) (2019)
- [Ensembling Low Precision Models for Binary Biomedical Image Segmentation](https://mlsanity.com/paper/2010.08648/) (2020)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [Breakdown Point of Robust Support Vector Machine](https://mlsanity.com/paper/1409.0934/) (2014)
- [Kernel-Based Generalized Median Computation for Consensus Learning](https://mlsanity.com/paper/2209.10208/) (2022)
- [Single Image Estimation of Cell Migration Direction by Deep Circular Regression](https://mlsanity.com/paper/2406.19162/) (2024)

## Built on by (most cited first, 1 of 1)

- [SNAP: A Self-Consistent Agreement Principle with Application to Robust Computation](https://mlsanity.com/paper/2602.02013/) (2026)

## Abstract (arXiv)

Robustness in terms of outliers is an important topic and has been formally studied for a variety of problems in machine learning and computer vision. Generalized median computation is a special instance of consensus learning and a common approach to finding prototypes. Related research can be found in numerous problem domains with a broad range of applications. So far, however, robustness of generalized median has only been studied in a few specific spaces. To our knowledge, there is no robustness characterization in a general setting, i.e. for arbitrary spaces. We address this open issue in our work. The breakdown point >=0.5 is proved for generalized median with metric distance functions in general. We also study the detailed behavior in case of outliers from different perspectives. In addition, we present robustness results for weighted generalized median computation and non-metric distance functions. Given the importance of robustness, our work contributes to closing a gap in the literature. The presented results have general impact and applicability, e.g. providing deeper understanding of generalized median computation and practical guidance to avoid non-robust computation.