| Type: | Package |
| Title: | Sparse Principal Component Analysis with Multiple Principal Components |
| Version: | 0.1.0 |
| Date: | 2025-12-02 |
| Description: | Implements an algorithm for computing multiple sparse principal components of a dataset. The method is based on Cory-Wright and Pauphilet "Sparse PCA with Multiple Principal Components" (2022) <doi:10.48550/arXiv.2209.14790>. The algorithm uses an iterative deflation heuristic with a truncated power method applied at each iteration to compute sparse principal components with controlled sparsity. |
| License: | MIT + file LICENSE |
| Imports: | Rcpp (≥ 1.0.11) |
| LinkingTo: | Rcpp, RcppEigen |
| RoxygenNote: | 7.3.3 |
| Encoding: | UTF-8 |
| NeedsCompilation: | yes |
| Packaged: | 2025-12-02 21:29:55 UTC; jeanpauphilet |
| Author: | Ryan Cory-Wright 
[aut, cph],
Jean Pauphilet
[aut, cre, cph] |
| Maintainer: | Jean Pauphilet <jpauphilet@london.edu> |
| Repository: | CRAN |
| Date/Publication: | 2025-12-09 08:50:02 UTC |
Fraction of variance explained
Description
Computes the fraction of variance explained (variance explained normalized by the trace of the covariance/correlation matrix) by a set of PCs.
Usage
fraction_variance_explained(C, U)
Arguments
C |
A matrix. The correlation or covariance matrix (p x p). |
U |
A matrix. The matrix containing the r PCs (p x r). |
Value
A float.
Examples
library(datasets)
TestMat <- cor(datasets::mtcars)
mspcares <- mspca(TestMat, 2, c(4,4))
fraction_variance_explained(TestMat, mspcares$x_best)
Fraction of variance explained per PC
Description
Computes the fraction of variance explained (variance explained normalized by the trace of the covariance/correlation matrix) by each PC.
Usage
fraction_variance_explained_perPC(C, U)
Arguments
C |
A matrix. The correlation or covariance matrix (p x p). |
U |
A matrix. The matrix containing the r PCs (p x r). |
Value
An array.
Multiple Sparse PCA
Description
Returns multiple sparse principal component of a matrix using an iterative deflation heuristic.
Usage
mspca(
Sigma,
r,
ks,
maxIter = 200L,
verbose = TRUE,
violationTolerance = 1e-04,
stallingTolerance = 1e-08,
maxIterTPW = 200L,
timeLimitTPW = 20L
)
Arguments
Sigma |
A matrix. The correlation or covariance matrix, whose sparse PCs will be computed. |
r |
An integer. Number of principal components (PCs) to be computed. |
ks |
A list of integers. Target sparsity of each PC. |
maxIter |
(optional) An integer. Maximum number of iterations of the algorithm. Default 200. |
verbose |
(optional) A Boolean. Controls console output. Default TRUE. |
violationTolerance |
(optional) A float. Tolerance for the violation of the orthogonality constraints. Default 1e-4 |
stallingTolerance |
(optional) A float. Controls the objective improvement below which the algorithm is considered to have stalled. Default 1e-8 |
maxIterTPW |
(optional) An integer. Maximum number of iterations of the truncated power method (inner iteration). Default 200. |
timeLimitTPW |
(optional) An integer. Maximum time in seconds for the truncated power method (inner iteration). Default 20. |
Value
An object with 4 fields: 'x_best' (p x r array containing the sparse PCs), 'objective_value', 'orthogonality_violation', 'runtime'.
Examples
library(datasets)
TestMat <- cor(datasets::mtcars)
mspca(TestMat, 2, c(4,4))
Orthogonality constraint violation
Description
Computes the orthogonality constraint violation defined as the distance (infinity norm) between U^\top U and the identity matrix.
Usage
orthogonality_violation(U)
Arguments
U |
A matrix. Each column correspond to an p-dimensional PC. |
Value
A float.
Examples
library(datasets)
TestMat <- cor(datasets::mtcars)
mspcares <- mspca(TestMat, 2, c(4,4))
orthogonality_violation(mspcares$x_best)
Print mspca output
Description
Displays the output of the msPCA algorithm.
Usage
print_mspca(sol_object, C)
Arguments
sol_object |
A list. The output of the mspca or twp function. |
C |
A matrix. The correlation or covariance matrix (p x p). |
Value
None. Prints output to console.
Examples
library(datasets)
TestMat <- cor(datasets::mtcars)
mspcares <- mspca(TestMat, 2, c(4,4))
print_mspca(mspcares, TestMat)
Truncated Power Method
Description
Returns the leading sparse principal component of a matrix using the truncated power method.
Usage
tpw(Sigma, k, maxIter = 200L, verbose = TRUE, timeLimit = 10L)
Arguments
Sigma |
A matrix. The correlation or covariance matrix, whose sparse PCs will be computed. |
k |
An integer. Target sparsity of the PC. |
maxIter |
(optional) An integer. Maximum number of iterations of the algorithm. Default 200. |
verbose |
(optional) A Boolean. Controls console output. Default TRUE. |
timeLimit |
(optional) An integer. Maximum time in seconds. Default 10. |
Value
An object with 3 fields: 'x_best' (p x 1 array containing the sparse PC), 'objective_value', 'runtime'.
References
Yuan, X. T., & Zhang, T. (2013). Truncated power method for sparse eigenvalue problems. The Journal of Machine Learning Research, 14(1), 899-925.
Examples
library(datasets)
TestMat <- cor(datasets::mtcars)
tpw(TestMat, 4)
Variance explained per PC
Description
Computes the variance explained by each PC.
Usage
variance_explained_perPC(C, U)
Arguments
C |
A matrix. The correlation or covariance matrix (p x p). |
U |
A matrix. The matrix containing the r PCs (p x r). |
Value
An array.