ltsspca {ltsspca}

Sparse Principal Component Analysis Based on Least Trimmed Squaers (LTS-SPCA)

Description

the function that computes the initial LTS-SPCA

Usage

ltsspca(x, kmax, alpha = 0.5, mu.choice = NULL, l.search = NULL,
  ls.min = 1, tol = 1e-06, N1 = 3, N2 = 2, N2bis = 10,
  Npc = 10)

Arguments

x

the input data matrix

kmax

the maximal number of PCs searched by the intial LTS-SPCA

alpha

the robust parameter which takes value between 0 to 0.5, default is 0.5

mu.choice

the center estimate fixed by the user; by default, the center will be estimated automatically by the algorithm

l.search

a list of length kmax which contains the search grids chosen by the user; default is NULL

ls.min

the smallest grid step when searching for the sparsity of each PC; default is 1

tol

convergence criterion

N1

the number controls the updates for a without updating b in the concentration step for LTS-PCA

N2

the number controls outer loop in the concentration step for LTS-PCA

N2bis

the number controls the outer loop for the selected b for both LTS-PCA and LTS-SPCA

Npc

the number controls the inner loop for both LTS-PCA and LTS-SPCA

Value

the object of class "ltsspca" is returned

loadings

the initially estimated loading matrix by LTS-SPCA

mu

the center estimates associated with each PC

spca.it

the list that contains the results of LTS-SPCA when searching for the individual PCs

ls

the list that contains the final search grid for each PC direction

Author(s)

Yixin Wang

References

Wang, Y., Van Aelst, S. (2019), “ Sparse Principal Component Based On Least Trimmed Squares”, Technometrics, accepted.

Examples

library(mvtnorm)
dataM <- dataSim(n = 200, p = 20, bLength = 4, a = c(0.9, 0.5, 0),
                SD = c(10, 5, 2), eps = 0, seed = 123)
x <- dataM$data
ltsspcaMI <- ltsspca(x = x, kmax = 5, alpha = 0.5)
ltsspcaMR <- ltsspcaRw(x = x, obj = ltsspcaMI, k = 2, alpha = 0.5)
matplot(ltsspcaMR$loadings,type="b",ylab="Loadings")