# Outlier Detection for Robust Multi-dimensional Scaling

arXiv: https://arxiv.org/abs/1802.02341 · HTML: https://mlsanity.com/paper/1802.02341/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2018.

## Built on by (most cited first, 3 of 3)

- [Supervised Anomaly Detection via Conditional Generative Adversarial Network and Ensemble Active Learning](https://mlsanity.com/paper/2104.11952/) (2021)
- [A Dual Basis Approach for Structured Robust Euclidean Distance Geometry](https://mlsanity.com/paper/2505.18414/) (2025)
- [Optimizing Multidimensional Scaling in Gini Metric Spaces](https://mlsanity.com/paper/2605.25124/) (2026)

## Abstract (arXiv)

Multi-dimensional scaling (MDS) plays a central role in data-exploration, dimensionality reduction and visualization. State-of-the-art MDS algorithms are not robust to outliers, yielding significant errors in the embedding even when only a handful of outliers are present. In this paper, we introduce a technique to detect and filter outliers based on geometric reasoning. We test the validity of triangles formed by three points, and mark a triangle as broken if its triangle inequality does not hold. The premise of our work is that unlike inliers, outlier distances tend to break many triangles. Our method is tested and its performance is evaluated on various datasets and distributions of outliers. We demonstrate that for a reasonable amount of outliers, e.g., under 20%, our method is effective, and leads to a high embedding quality.