maxstablePCA (version 0.1.2)

max_stable_prcomp: Calculate max-stable PCA with dimension p for given dataset

Description

Find an optimal encoding of data of extremes using max-linear combinations by a distance minimization approach. Can be used to check if the data follows approximately a generalized max-linear model. For details on the statistical procedure it is advised to consult the articles "F. Reinbott, A. Janßen, Principal component analysis for max-stable distributions (https://arxiv.org/abs/2408.10650)" and "M.Schlather F. Reinbott, A semi-group approach to Principal Component Analysis (https://arxiv.org/abs/2112.04026)".

Usage

max_stable_prcomp(
  data,
  p,
  s = 3,
  n_initial_guesses = 150,
  norm = "l1",
  optim_style = "full",
  ...
)

Value

object of class max_stable_prcomp with slots p, inserted value of dimension, decoder_matrix, an array of shape (d,p), where the columns represent the basis of the max-linear space for the reconstruction. encoder_matrix, an array of shape (p,d), where the rows represent the loadings as max-linear combinations for the compressed representation. reconstr_matrix, an array of shape (d,d), where the matrix is the mapping of the data to the reconstruction used for the distance minimization. loss_fctn_value, float representing the final loss function value of the fit. optim_conv_status, integer indicating the convergence of the optimizer if greater than 0.

Arguments

data,

array or data.frame of n observations of d variables with unit Frechet margins. The max-stable PCA is fitted to reconstruct this dataset with a rank p approximation.

p,

integer between 1 and ncol(data). Determines the dimension of the encoded state, i.e. the number of max-linear combinations in the compressed representation.

s

(default = 3), numeric greater than 0. Hyperparameter for the

n_initial_guesses

number of guesses to choose a valid initial value for optimization from. This procedure uses a pseudo random number generator so setting a seed is necessary for reproducibility. stable tail dependence estimator used in tn the calculation.

norm

(delfault "l1") which norm to use for the spectral measure estimator, currently only l1 and sup norm "linfty" are available.

optim_style

(delfault "full") choose between two different optimization strategies. The default being "full" that optimizes both matrices simultaneously. the other choice "alternating" fixes one matrix then optimizes the other matrix until converged, then optimizes the other matrix in the same style. This can lead to more accurate results in some cases.

...

additional parameters passed to link{nloptr::slsqp()}

Examples

# generate some data with the desired margins
dat <- matrix(evd::rfrechet(300), 100, 3)
maxPCA <- max_stable_prcomp(dat, 2)

# look at summary to obtain further information about 
# loadings the space spanned and loss function
summary(maxPCA)

# transfrom data to compressed representation
# for a representation that is p-dimensional,
# preserves the max-stable structure and is numeric solution to 
# optimal reconstruction.
compr <- compress(maxPCA, dat)

# For visual examination reconstruct original vector from compressed representation
rec <- reconstruct(maxPCA, dat)