# Kernel PCA for multivariate extremes

arXiv: https://arxiv.org/abs/2211.13172 · HTML: https://mlsanity.com/paper/2211.13172/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 23 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Causal discovery in heavy-tailed models](https://mlsanity.com/paper/1908.05097/) (2019)
- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [Sparse Structures for Multivariate Extremes](https://mlsanity.com/paper/2004.12182/) (2020)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (2019)
- [Principal Component Analysis for Multivariate Extremes](https://mlsanity.com/paper/1906.11043/) (2019)
- [Sparsity in Multivariate Extremes with Applications to Anomaly Detection](https://mlsanity.com/paper/1507.05899/) (2015)
- [Sparse regular variation](https://mlsanity.com/paper/1907.00686/) (2019)
- [Concentration bounds for the empirical angular measure with statistical learning applications](https://mlsanity.com/paper/2104.03966/) (2021)
- [Determining the Dependence Structure of Multivariate Extremes](https://mlsanity.com/paper/1809.01606/) (2018)
- [Estimation and Inference of Extremal Quantile Treatment Effects for Heavy-Tailed Distributions](https://mlsanity.com/paper/2110.06627/) (2021)
- [Spectral learning of multivariate extremes](https://mlsanity.com/paper/2111.07799/) (2021)

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

- [Estimation of Treatment Effects in Extreme and Unobserved Data](https://mlsanity.com/paper/2506.14051/) (2025)

## Abstract (arXiv)

We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the preimages obtained by kernel PCA, demonstrating that under certain conditions they can effectively identify clusters in the data. We build on these new insights to characterize rigorously the performance of kernel PCA based on an extremal sample, i.e., the angular part of random vectors for which the radius exceeds a large threshold. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure in extreme value theory and provide a careful analysis in the case where the extremes are generated from a linear factor model. We give theoretical guarantees on the performance of kernel PCA preimages of such extremes by leveraging their asymptotic distribution together with Davis-Kahan perturbation bounds. Our theoretical findings are complemented with numerical experiments illustrating the finite sample performance of our methods.