do.rpca: Robust Principal Component Analysis

Description

Robust PCA (RPCA) is not like other methods in this package as finding explicit low-dimensional embedding with reduced number of columns. Rather, it is more of a decomposition method of data matrix $X$ , possibly noisy, into low-rank and sparse matrices by solving the following, $minimize ‖ L ‖_{*} + λ ‖ S ‖_{1} s . t . L + S = X$ where $L$ is a low-rank matrix, $S$ is a sparse matrix and $‖ \cdot ‖_{*}$ denotes nuclear norm, i.e., sum of singular values. Therefore, it should be considered as preprocessing procedure of denoising. Note that after RPCA is applied, $L$ should be used as kind of a new data matrix for any manifold learning scheme to be applied.

Usage

do.rpca(
  X,
  mu = 1,
  lambda = sqrt(1/(max(dim(X)))),
  preprocess = c("null", "center", "scale", "cscale", "decorrelate", "whiten")
)

Arguments

an $(n \times p)$ matrix or whose rows are observations and columns represent independent variables.

an augmented Lagrangian parameter

lambda

parameter for the sparsity term $‖ S ‖_{1}$ . Default value is given accordingly to the referred paper.

preprocess

an additional option for preprocessing the data. Default is "null". See also aux.preprocess for more details.

Value

a named list containing

L: an $(n \times p)$ low-rank matrix.
S: an $(n \times p)$ sparse matrix.
trfinfo: a list containing information for out-of-sample prediction.

References

candes_robust_2011Rdimtools

Examples

Run this code

# NOT RUN {
## Load Iris data and put some noise
data(iris)
set.seed(100)
subid = sample(1:150,50)
noise = 0.2
X = as.matrix(iris[subid,1:4])
X = X + matrix(noise*rnorm(length(X)), nrow=nrow(X))
lab = as.factor(iris[subid,5])

## try different regularization parameters
rpca1 = do.rpca(X, lambda=0.1)
rpca2 = do.rpca(X, lambda=1)
rpca3 = do.rpca(X, lambda=10)

## apply identical PCA methods
Y1 = do.pca(rpca1$L, ndim=2)$Y
Y2 = do.pca(rpca2$L, ndim=2)$Y
Y3 = do.pca(rpca3$L, ndim=2)$Y

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(Y1, pch=19, col=lab, main="RPCA+PCA::lambda=0.1")
plot(Y2, pch=19, col=lab, main="RPCA+PCA::lambda=1")
plot(Y3, pch=19, col=lab, main="RPCA+PCA::lambda=10")
par(opar)

# }