pcaRobSparse: Sparse Robust Principal Principal Components Analysis
In abnormally-distributed/cvreg: Cross Validation and Robust Estimation Utilities

Description Usage Arguments Value References Examples

This function is based on the original paper by Zou, Hastie, and Tibsharini (2006) where an elastic net formulation of principal components analysis was demonstrated. The algorithm can be initialized using one of two methods. The first option is the robust principal components method in the pcaRobust function which utilizes the method of Filzmoser, Maronna, and Werner (2008). The second option is spherical principal components analysis (Locantore et al., 1999) as suggested by Maronna (2005). After the initial principal components analysis, the elastic net penalization is applied to this initial fit. The elastic net objective function is modified such that the sum of squared errors is weighted utilizing a bisquare function, leading to the objective function 0.5 * ∑_i{ε_i * w_i} + ∑(|B|) * λ_1 + 0.5 * λ_2 * ∑(B^2).

pcaRobSparse(
  x,
  ncomp = min(nrow(x) - 1, ncol(x)),
  alpha = 0.75,
  lambda = 1e-04,
  delta = 0.5,
  init = c("robust", "sphere"),
  scale = T,
  max.iter = 200,
  tol = 1e-16
)

`x`	a data frame or matrix of numeric variables
`ncomp`	the number of components to extract.
`alpha`	the elastic net mixing parameter, which can take values of 0 ≤ α ≥ 1.
`lambda`	the shrinkage parameter. as in the elastic net, the L1 shrinkage penalty is λ_1 = α λ, and the L2 shrinkage penalty is λ_2 = (1-α) * λ*.
`delta`	the desired breakdown point. defaults to 0.50, which is the maximum.
`scale`	should the variables be scaled prior to analysis? Defaults to TRUE.
`max.iter`	maximum number of iterations
`tol`	tolerance for convergence

a PrincipalComp object

Hawkins, D.M., Liu, L., & Young, S.S. (2001) Robust Singular Value Decomposition, National Institute of Statistical Sciences, Technical Report Number

Locantore, N., Marron, J., Simpson, D, Tripoli, N., Zhang, J., & Cohen, K. Robust principal component analysis for functional data. (1999) Sociedad de Estadistica e Investigacion Operativa Test. 8: 1. https://doi.org/10.1007/BF02595862

Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics. 15 (2): 262–286. doi:10.1198/106186006x113430.

Maronna, R.A. (2005) Principal components and orthogonal regression based on robust scales, Technometrics, 47, 264–273

Filzmoser, P., Maronna, M., & Werner., M. (2008) Outlier identification in high dimensions, Computational Statistics and Data Analysis, 52, 1694-1711.