sparsePCAloc: Calculate Sparse Principle Components

In ssMRCD: Spatially Smoothed MRCD Estimator

Calculate Sparse Principle Components

Description

Calculate Sparse Principle Components

Usage

sparsePCAloc(
  eta,
  gamma,
  COVS,
  cor = FALSE,
  rho = NULL,
  k = NULL,
  eps_threshold = NULL,
  eps_ADMM = 1e-04,
  n_max = 200,
  eps_root = 0.1,
  maxiter_root = 50,
  increase_rho = list(TRUE, 100, 1),
  convergence_plot = TRUE,
  starting_value = NULL,
  adjust_eta = TRUE,
  trace = TRUE
)

Arguments

eta	numeric, degree of sparsity.
gamma	numeric, distribution of sparsity.
COVS	list of covariance or correlation matrices.
cor	logical, if starting value for correlation or covariance matrices should be used.
rho	numeric bigger than zero, penalty for ADMM.
k	number of components to calculate.
eps_threshold	tolerance for thresholding.
eps_ADMM	tolerance for ADMM convergence.
n_max	number of maximal iterations.
eps_root	tolerance for root finder.
maxiter_root	maximal number of iterations for root finder.
increase_rho	list with entries for stable convergence. See Details.
convergence_plot	logical, if convergence plot should be displayed.
starting_value	optional given starting value.
adjust_eta	logical, if eta should be adjusted by the variance.
trace	logical, if messages should be displayed.

Details

The input increase_rho consists of a logical indicating if rho should be adjusted if algorithm did not converged within the given maximal number of iterations. Two integers specify the maximal rho that is allowed and the step size.

Value

An object of class "PCAloc" containing the following elements:

PC	Matrix of dimension Np x k of stacked loading vectors.
p	Number of variables.
N	Number of neighborhoods.
k	Number of components.
COVS	List of covariance matrices sorted by neighborhood.
gamma	Sparsity distribution.
eta	Amount of sparsity.
converged	Logical, if ADMM converged with given specifications.
n_steps	Number of steps used.
summary	Description of result per component.
residuals	Primary and secondary residuals.

Examples

C1 = diag(c(1.1, 0.9, 0.6))
C2 = matrix(c(1.1, 0.1, -0.1,
              0.1, 1.0, -0.2,
             -0.1, -0.2, 0.7), ncol = 3)
C3 = (C1 + C2)/2

sparsePCAloc(eta = 1, gamma = 0.5, cor = FALSE, COVS = list(C1, C2, C3),
             n_max = 100, increase_rho = list(FALSE, 100, 1))

ssMRCD documentation built on Sept. 11, 2024, 5:14 p.m.