This code is intended for the PCA for multivariate extremes.
The input data should be a numeric matrix.
The procedure contains 4 steps:
1: Data preprocessing. This step is used to transform the margins of the
random vector which rarely have the same marginal distribution in practice
to have the same marginal distribution.
2: Estimation of the Tail Pairwise Dependence Matrix (TPDM). Each
element of this matrix describes the pairwise tail dependence of two
components of the random vector, e.g., the dependence between
precipitation over a high threshold at a pair of locations.
3: PCA of the TPDM. This step outputs the eigenvectors in the positive
orthant for the TPDM, and the corresponding principle components (PCs).
4: Reconstruct observation using the basis vectors.