SparsePCA {sharp}

Sparse Principal Component Analysis

Description

Runs a sparse Principal Component Analysis model using implementation from spca (if algo="sPCA") or spca (if algo="rSVD"). This function is not using stability.

Usage

SparsePCA(
  xdata,
  Lambda,
  ncomp = 1,
  scale = TRUE,
  keepX_previous = NULL,
  algorithm = "sPCA",
  ...
)

Arguments

xdata

data matrix with observations as rows and variables as columns.

Lambda

matrix of parameters controlling the number of selected variables at current component, as defined by ncomp.

ncomp

number of components.

scale

logical indicating if the data should be scaled (i.e. transformed so that all variables have a standard deviation of one).

keepX_previous

number of selected predictors in previous components. Only used if ncomp > 1.

algorithm

character string indicating the name of the algorithm to use for sparse PCA. Possible values are: "sPCA" (for the algorithm proposed by Zou, Hastie and Tibshirani and implemented in spca) or "rSVD" (for the regularised SVD approach proposed by Shen and Huang and implemented in spca).

...

additional arguments to be passed to spca (if algorithm="sPCA") or spca (if algorithm="rSVD").

Value

A list with:

selected

matrix of binary selection status. Rows correspond to different model parameters. Columns correspond to predictors.

beta_full

array of model coefficients. Rows correspond to different model parameters. Columns correspond to predictors (starting with "X") or outcomes (starting with "Y") variables for different components (denoted by "PC").

References

Zou H, Hastie T, Tibshirani R (2006). “Sparse Principal Component Analysis.” Journal of Computational and Graphical Statistics, 15(2), 265-286. doi:10.1198/106186006X113430.

Shen H, Huang JZ (2008). “Sparse principal component analysis via regularized low rank matrix approximation.” Journal of Multivariate Analysis, 99(6), 1015-1034. ISSN 0047-259X, doi:10.1016/j.jmva.2007.06.007.

See Also

VariableSelection, BiSelection

Other penalised dimensionality reduction functions: GroupPLS(), SparseGroupPLS(), SparsePLS()

Examples

# Data simulation
set.seed(1)
simul <- SimulateRegression(n = 100, pk = 50, family = "gaussian")
x <- simul$xdata

# Sparse PCA (by Zou, Hastie, Tibshirani)
if (requireNamespace("elasticnet", quietly = TRUE)) {
  mypca <- SparsePCA(
    xdata = x, ncomp = 2,
    Lambda = c(1, 2), keepX_previous = 10, algorithm = "sPCA"
  )
}

# Sparse PCA (by Shen and Huang)
if (requireNamespace("mixOmics", quietly = TRUE)) {
  mypca <- SparsePCA(
    xdata = x, ncomp = 2,
    Lambda = c(1, 2), keepX_previous = 10, algorithm = "rSVD"
  )
}