# Principal Component Analysis for Multivariate Extremes

arXiv: https://arxiv.org/abs/2606.07213 · HTML: https://mlsanity.com/paper/2606.07213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 5 Jun 2026.

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

- [Decompositions of Dependence for High-Dimensional Extremes](https://mlsanity.com/paper/1612.07190/) (2016)
- [k-means clustering of extremes](https://mlsanity.com/paper/1904.02970/) (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)
- [Sparse Representation of Multivariate Extremes with Applications to Anomaly Ranking](https://mlsanity.com/paper/1603.09584/) (2016)
- [Identifying groups of variables with the potential of being large simultaneously](https://mlsanity.com/paper/1802.09977/) (2018)
- [Regular Variation in Hilbert Spaces and Principal Component Analysis for Functional Extremes](https://mlsanity.com/paper/2308.01023/) (2023)
- [Information criteria for the number of directions of extremes in high-dimensional data](https://mlsanity.com/paper/2409.10174/) (2024)
- [Transformed-Linear Models for Time Series Extremes](https://mlsanity.com/paper/2012.06705/) (2020)
- [Estimating probabilities of multivariate failure sets based on pairwise tail dependence coefficients](https://mlsanity.com/paper/2210.12618/) (2022)

## Abstract (arXiv)

This chapter explores ways to reduce the dimensionality of the data while preserving key information relevant to the analysis of multivariate extreme values.