rpca_mfd function

Robust multivariate functional principal components analysis

It performs robust MFPCA as described in Capezza et al. (2024).

rpca_mfd(
  mfdobj,
  center = "fusem",
  scale = "funmad",
  nharm = 20,
  method = "ROBPCA",
  alpha = 0.8
)

Arguments

• mfdobj: A multivariate functional data object of class mfd.
• center: If TRUE, it centers the data before doing MFPCA with respect to the functional mean of the input data. If "fusem", it uses the functional M-estimator of location proposed by Centofanti et al. (2023) to center the data. Default is "fusem".
• scale: If "funmad", it scales the data before doing MFPCA using the functional normalized median absolute deviation estimator proposed by Centofanti et al. (2023). If TRUE, it scales data using scale_mfd. Default is "funmad".
• nharm: Number of multivariate functional principal components to be calculated. Default is 20.
• method: If "ROBPCA", MFPCA uses ROBPCA of Hubert et al. (2005), as described in Capezza et al. (2024). If "Locantore", MFPCA uses the Spherical Principal Components procedure proposed by Locantore et al. (1999). If "Proj", MFPCA uses the Robust Principal Components based on Projection Pursuit algorithm of Croux and Ruiz-Gazen (2005). method If "normal", it uses pca_mfd on mfdobj. Default is "ROBPCA".
• alpha: This parameter measures the fraction of outliers the algorithm should resist and is used only if method is "ROBPCA". Default is 0.8.

Returns

An object of pca_mfd class, as returned by the pca_mfd

function when performing non robust multivariate functional principal component analysis.

Examples

library(funcharts)
dat <- simulate_mfd(nobs = 20, p = 1, correlation_type_x = "Bessel")
mfdobj <- get_mfd_list(dat$X_list, n_basis = 5)

# contaminate first observation
mfdobj$coefs[, 1, ] <- mfdobj$coefs[, 1, ] + 0.05

# plot_mfd(mfdobj) # plot functions to see the outlier
# pca <- pca_mfd(mfdobj) # non robust MFPCA
rpca <- rpca_mfd(mfdobj) # robust MFPCA
# plot_pca_mfd(pca, harm = 1) # plot first eigenfunction, affected by outlier
# plot_pca_mfd(rpca, harm = 1) # plot first eigenfunction in robust case

References

Capezza, C., Centofanti, F., Lepore, A., Palumbo, B. (2024) Robust Multivariate Functional Control Chart. Technometrics, 66(4):531--547, doi:10.1080/00401706.2024.2327346.

Centofanti, F., Colosimo, B.M., Grasso, M.L., Menafoglio, A., Palumbo, B., Vantini, S. (2023) Robust functional ANOVA with application to additive manufacturing. Journal of the Royal Statistical Society Series C: Applied Statistics

72(5), 1210–1234 doi:10.1093/jrsssc/qlad074

Croux, C., Ruiz-Gazen, A. (2005). High breakdown estimators for principal components: The projection-pursuit approach revisited. Journal of Multivariate Analysis, 95, 206–226, doi:10.1016/j.jmva.2004.08.002.

Hubert, M., Rousseeuw, P.J., Branden, K.V. (2005) ROBPCA: A New Approach to Robust Principal Component Analysis, Technometrics 47(1), 64--79, doi:10.1198/004017004000000563

Locantore, N., Marron, J., Simpson, D., Tripoli, N., Zhang, J., Cohen K., K. (1999), Robust principal components for functional data. Test, 8, 1-28. doi:10.1007/BF02595862

Author(s)

C. Capezza, F. Centofanti