select_sparsity: Optimal Sparsity Parameter Selection for PCA

In ssMRCD: Spatially Smoothed MRCD Estimator

Optimal Sparsity Parameter Selection for PCA

Description

Optimal Sparsity Parameter Selection for PCA

Usage

select_sparsity(
  COVS,
  k = 1,
  rho = NULL,
  cor = FALSE,
  eta = seq(0, 5, by = 0.2),
  gamma = seq(0, 1, 0.05),
  eps_threshold = 0.001,
  eps_root = 0.1,
  eps_ADMM = 1e-04,
  n_max = 300,
  adjust_eta = FALSE,
  cores = 1,
  increase_rho = list(TRUE, 100, 1),
  convergence_plot = FALSE,
  trace = FALSE,
  stop.sparse = TRUE
)

Arguments

COVS	list of covariance or correlation matrices.
k	number of components to be returned.
rho	penalty parameter for ADMM.
cor	logical, if starting values for covariances or correlation matrices should be used.
eta	vector of possible values for degree of sparsity.
gamma	vector of possible values for distribution of sparsity. If only one value is provided, the optimal eta is calculated.
eps_threshold	tolerance for thresholding.
eps_root	tolerance for root finder.
eps_ADMM	tolerance for ADMM iterations.
n_max	maximal number of ADMM iterations.
adjust_eta	if eta should be adjusted for further components.
cores	number of cores for parallel computing.
increase_rho	list of settings for improved automated calculation and convergence. See Details.
convergence_plot	logical, if convergence plot should be plotted. Not applicable for cores > 1.
trace	logical, if messages should be displayed. Not applicable for cores > 1.
stop.sparse	calculate if AUC should be calculated for PCAs until full sparsity is reached (TRUE) or over the whole eta range (FALSE). Set to TRUE.

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

Returns list with

PCA	object of type PCAloc.
PC	local loadings of PCA
gamma	optimal value for gamma.
eta	optimal value for eta.
eta_tpo	values of Trade-Off-Product for eta from optimization process.
auc	area under the curve for varying gamma values.
pars	parameters and respective sparsity entrywise and mixed and explained variance.
plot	ggplot object for optimal parameter selection.
plot_info	additional data for plotting functions.

Examples

C1 = matrix(c(1,0,0,0.9), ncol = 2)
C2 = matrix(c(1.1, 0.1, 0.1, 1), ncol = 2)
C3 = matrix(c(1.2, 0.2, 0.2, 1), ncol = 2)

select_sparsity(COVS = list(C1, C2, C3),
                k = 1,
                rho = 5,
                eta = c(0, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5 ,0.75,  1),
                gamma =c(0, 0.25, 0.5, 0.75, 1),
                eps_threshold = 0.005,
                increase_rho = list(FALSE, 20, 5))

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