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