Sparse Principal Components Analysis
Using an alternating minimization algorithm to minimize the SPCA criterion.
spca(x, K, para, type=c("predictor","Gram"),
sparse=c("penalty","varnum"), use.corr=FALSE, lambda=1e-6,
max.iter=200, trace=FALSE, eps.conv=1e-3)x |
A matrix. It can be the predictor matrix or the sample covariance/correlation matrix. |
K |
Number of components |
para |
A vector of length K. All elements should be positive. If sparse="varnum", the elements integers. |
type |
If type="predictor", x is the predictor matrix. If type="Gram", the function asks the user to provide the sample covariance or correlation matrix. |
sparse |
If sparse="penalty", para is a vector of 1-norm penalty parameters. If sparse="varnum", para defines the number of sparse loadings to be obtained. This option is not discussed in the paper given below, but it is convenient in practice. |
lambda |
Quadratic penalty parameter. Default value is 1e-6. |
use.corr |
Perform PCA on the correlation matrix? This option is only effective when the argument type is set "data". |
max.iter |
Maximum number of iterations. |
trace |
If TRUE, prints out its progress. |
eps.conv |
Convergence criterion. |
PCA is shown to be equivalent to a regression-type optimization problem, then sparse loadings are obtained by imposing the 1-norm constraint on the regression coefficients. If x is a microarray matrix, use arrayspc().
A "spca" object is returned. The below are some quantities which the user may be interested in:
loadings |
The loadings of the sparse PCs |
pev |
Percentage of explained variance |
var.all |
Total variance of the predictors |
Hui Zou and Trevor Hastie
Zou, H., Hastie, T. and Tibshirani, R. (2006) "Sparse principal component analysis" Journal of Computational and Graphical Statistics, 15 (2), 265–286.
princomp, arrayspc
data(pitprops) out1<-spca(pitprops,K=6,type="Gram",sparse="penalty",trace=TRUE,para=c(0.06,0.16,0.1,0.5,0.5,0.5)) ## print the object out1 out1 out2<-spca(pitprops,K=6,type="Gram",sparse="varnum",trace=TRUE,para=c(7,4,4,1,1,1)) out2 ## to see the contents of out2 names(out2) ## to get the loadings out2$loadings
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