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.

A "spca" object is returned. The below are some quantities which the user may be interested in:

The loadings of the sparse PCs

Percentage of explained variance

Total variance of the predictors

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().

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

princomp, arrayspc

# NOT RUN { 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 # }