# Fast and Exact Outlier Detection in Metric Spaces: A Proximity Graph-based Approach

arXiv: https://arxiv.org/abs/2110.08959 · HTML: https://mlsanity.com/paper/2110.08959/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [Estimating the Contamination Factor's Distribution in Unsupervised Anomaly Detection](https://mlsanity.com/paper/2210.10487/) (2022)
- [Learned k-NN Distance Estimation](https://mlsanity.com/paper/2208.14210/) (2022)
- [Rethinking Unsupervised Outlier Detection via Multiple Thresholding](https://mlsanity.com/paper/2407.05382/) (2024)
- [Streaming algorithms for robust max-min diversification](https://mlsanity.com/paper/2610.01456/) (2026)

## Abstract (arXiv)

Distance-based outlier detection is widely adopted in many fields, e.g., data mining and machine learning, because it is unsupervised, can be employed in a generic metric space, and does not have any assumptions of data distributions. Data mining and machine learning applications face a challenge of dealing with large datasets, which requires efficient distance-based outlier detection algorithms. Due to the popularization of computational environments with large memory, it is possible to build a main-memory index and detect outliers based on it, which is a promising solution for fast distance-based outlier detection. Motivated by this observation, we propose a novel approach that exploits a proximity graph. Our approach can employ an arbitrary proximity graph and obtains a significant speed-up against state-of-the-art. However, designing an effective proximity graph raises a challenge, because existing proximity graphs do not consider efficient traversal for distance-based outlier detection. To overcome this challenge, we propose a novel proximity graph, MRPG. Our empirical study using real datasets demonstrates that MRPG detects outliers significantly faster than the state-of-the-art algorithms.