# 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