# spca

From elasticnet v1.02
by Hui Zou

##### 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:
loadings The loadings of the sparse PCs pev Percentage of explained variance var.all Total variance of the predictors

##### References

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

##### See Also

princomp, arrayspc

##### 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)
## to get the loadings
out2$loadings
```

*Documentation reproduced from package elasticnet, version 1.02, License: GPL version 2 or newer*

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