Description
Apply a PCA Like Procedure Suited for Multivariate Extreme Value Distributions.
Description
Dimension reduction for multivariate data of extreme events with a PCA like procedure as described in Reinbott, Janßen, (2024), <doi:10.48550/arXiv.2408.10650>. Tools for necessary transformations of the data are provided.
README.md
maxstablePCA
A package for dimensionality reduction of multivariate extremes using the idea of PCA to obtain a resonable compact description of the data.
Main functionalities
- Transform a dataset to standard margins to use well known ideas from extreme value theory
- Perform a dimensionality reduction of a dataset to a fixed number of encoding variables. For further information about the theory of this consider looking at the references.
- Evaluate the quality of this reconstruction.
- Transform the data back to the distribution of the original dataset.
Examples on simulated and real world data
For a better feeling of what this algorithm does, please consider looking at the following repo, providing example data analyses and simulation studies https://github.com/FelixRb96/maxstablePCA_examples.
References
- Principal component analysis for max-stable distributions, Reinbott F., Janßen A. , arxiv preprint, https://arxiv.org/abs/2408.10650
- A semi-group approach to Principal Component Analysis, Schlather M., Reinbott F., arxiv preprint, https://arxiv.org/pdf/2112.04026.pdf, 2021