# Clustering by the Probability Distributions from Extreme Value Theory

arXiv: https://arxiv.org/abs/2202.09784 · HTML: https://mlsanity.com/paper/2202.09784/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 38 references that are in the map.
- First posted on arXiv 20 Feb 2022.

## Builds on (most cited first, 2 of 2)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [The Extreme Value Machine](https://mlsanity.com/paper/1506.06112/) (2015)

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

- [Graph Out-of-Distribution Generalization with Controllable Data Augmentation](https://mlsanity.com/paper/2308.08344/) (2023)

## Abstract (arXiv)

Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique cluster, while it does not utilize the information of sample distribution or density. Comparably, it would potentially be more beneficial to consider the probability of each sample in a possible cluster. To this end, this paper generalizes k-means to model the distribution of clusters. Our novel clustering algorithm thus models the distributions of distances to centroids over a threshold by Generalized Pareto Distribution (GPD) in Extreme Value Theory (EVT). Notably, we propose the concept of centroid margin distance, use GPD to establish a probability model for each cluster, and perform a clustering algorithm based on the covering probability function derived from GPD. Such a GPD k-means thus enables the clustering algorithm from the probabilistic perspective. Correspondingly, we also introduce a naive baseline, dubbed as Generalized Extreme Value (GEV) k-means. GEV fits the distribution of the block maxima. In contrast, the GPD fits the distribution of distance to the centroid exceeding a sufficiently large threshold, leading to a more stable performance of GPD k-means. Notably, GEV k-means can also estimate cluster structure and thus perform reasonably well over classical k-means. Thus, extensive experiments on synthetic datasets and real datasets demonstrate that GPD k-means outperforms competitors. The github codes are released in https://github.com/sixiaozheng/EVT-K-means.