# spca

by Hui Zou
0th

Percentile

##### Sparse Principal Components Analysis

Using an alternating minimization algorithm to minimize the SPCA criterion.

Keywords
multivariate
##### Usage
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)
##### Arguments
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.
##### Details

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().

##### Value

• A "spca" object is returned. The below are some quantities which the user may be interested in:
• pevPercentage of explained variance
• var.allTotal variance of the predictors

##### References

Zou, H., Hastie, T. and Tibshirani, R. (2004) "Sparse principal component analysis" Technical report, Statistics Dept. Stanford University.

princomp, arrayspc

• spca
##### Examples
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)
out2\$loadings