frobenius_norm_funct_robust {adamethods}

Functional robust Frobenius norm

Description

Computes the functional robust Frobenius norm.

Usage

frobenius_norm_funct_robust(m, PM, prob)

Arguments

m

Data matrix with the residuals. This matrix has the same dimensions as the original data matrix.

PM

Penalty matrix obtained with eval.penalty.

prob

Probability with values in [0,1].

Details

Residuals are vectors. If there are p variables (columns), for every observation there is a residual that there is a p-dimensional vector. If there are n observations, the residuals are an n times p matrix.

Value

Real number.

Author(s)

Irene Epifanio

References

Moliner, J. and Epifanio, I., Robust multivariate and functional archetypal analysis with application to financial time series analysis, 2019. Physica A: Statistical Mechanics and its Applications 519, 195-208. https://doi.org/10.1016/j.physa.2018.12.036

Examples

library(fda)
mat <- matrix(1:9, nrow = 3)
fbasis <- create.fourier.basis(rangeval = c(1, 32), nbasis = 3)
PM <- eval.penalty(fbasis)
frobenius_norm_funct_robust(mat, PM, 0.8)