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amanpg

Description

Uses an alternating manifold proximal gradient (AManPG) method to find sparse principal components from the given data or covariance matrix.

Only base R is required to be installed.

Usage

spca.amanpg(z, lambda1, lambda2, f_palm = 1e5, x0 = NULL, y0 = NULL, k = 0, type = 0, gamma = 0.5,
                        maxiter = 1e4, tol = 1e-5, normalize = TRUE, verbose = FALSE)

Arguments

Name	Type	Description
`z`	matrix	Either the data matrix or sample covariance matrix
`lambda1`	matrix	List of parameters of length n for L1-norm penalty
`lambda2`	double	L2-norm penalty term
`f_palm`	double	Upper bound for the gradient value to reach convergence, default value is 1e5
`x0`	matrix	Initial x-values for the gradient method, default value is the first n right singular vectors
`y0`	matrix	Initial y-values for the gradient method, default value is the first n right singular vectors
`k`	integer	Number of principal components desired, default is 0 (returns min(n-1, p) principal components)
`type`	integer	If 0, b is expected to be a data matrix, and otherwise b is expected to be a covariance matrix; default is 0
`gamma`	double	Parameter to control how quickly the step size changes in each iteration, default is 0.5
`maxiter`	integer	Maximum number of iterations allowed in the gradient method, default is 1e4
`tol`	double	Tolerance value required to indicate convergence (calculated as difference between iteration f-values), default is 1e-5
`normalize`	logical	Center and normalize rows to Euclidean length 1 if True, default is True
`verbose`	logical	Function prints progress between iterations if True, default is False

Value

Returns a dictionary with the following key-value pairs:

Key	Value Type	Value
`iter`	integer	Total number of iterations executed
`f_manpg`	double	Final gradient value
`sparsity`	float	Number of sparse loadings (loadings == 0) divided by number of all loadings
`time`	double	Number of seconds for execution
`x`	matrix	Corresponding ndarray in subproblem to the loadings
`loadings`	matrix	Loadings of the sparse principal components

Authors

Shixiang Chen, Justin Huang, Benjamin Jochem, Shiqian Ma, Lingzhou Xue and Hui Zou

References

Chen, S., Ma, S., Xue, L., and Zou, H. (2020) “An Alternating Manifold Proximal Gradient Method for Sparse Principal Component Analysis and Sparse Canonical Correlation Analysis” INFORMS Journal on Optimization 2:3, 192-208

Zou, H., Hastie, T., & Tibshirani, R. (2006). Sparse principal component analysis. Journal of Computational and Graphical Statistics, 15(2), 265-286.

Zou, H., & Xue, L. (2018). A selective overview of sparse principal component analysis. Proceedings of the IEEE, 106(8), 1311-1320.

Example

See SPCA.R for a more in-depth example.

library('SPCA')

#see SPCA.R for a more in-depth example
      d <- 500  # dimension
      m <- 1000 # sample size
      set.seed(10)
      a <- normalize(matrix(rnorm(m * d), m, d))
      lambda1 <- 0.1 * matrix(data=1, nrow=4, ncol=1)
      x0 <- svd(a, nv=4)$v
      sprout <- spca.amanpg(a, lambda1, lambda2=Inf, f_palm=1e5, x0=x0, y0=x0, k=4, type=0, gamma=0.5,
                            maxiter=1e4, tol=1e-5, normalize = FALSE, verbose=FALSE)
      print(paste(sprout$iter, "iterations,", sprout$sparsity, "sparsity,", sprout$time))

      #extract loadings
      #print(sprout$loadings)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.