do.rpcag {Rdimtools}

Robust Principal Component Analysis via Geometric Median

Description

This function robustifies the traditional PCA via an idea of geometric median. To describe, the given data is first split into k subsets for each sample covariance is attained. According to the paper, the median covariance is computed under Frobenius norm and projection is extracted from the largest eigenvectors.

Usage

do.rpcag(
  X,
  ndim = 2,
  k = 5,
  preprocess = c("center", "scale", "cscale", "whiten", "decorrelate")
)

Arguments

X

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

ndim

an integer-valued target dimension.

k

the number of subsets for X to be divided.

preprocess

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

Value

a named list containing

Y

an (n\times ndim) matrix whose rows are embedded observations.

trfinfo

a list containing information for out-of-sample prediction.

projection

a (p\times ndim) whose columns are basis for projection.

Author(s)

Kisung You

References

Minsker S (2015). “Geometric Median and Robust Estimation in Banach Spaces.” Bernoulli, 21(4), 2308–2335.

Examples

## use iris data
data(iris)
X     = as.matrix(iris[,1:4])
label = as.integer(iris$Species)

## try different numbers for subsets
out1 = do.rpcag(X, ndim=2, k=2)
out2 = do.rpcag(X, ndim=2, k=5)
out3 = do.rpcag(X, ndim=2, k=10)

## visualize
opar <- par(no.readonly=TRUE)
par(mfrow=c(1,3))
plot(out1$Y, col=label, main="RPCAG::k=2")
plot(out2$Y, col=label, main="RPCAG::k=5")
plot(out3$Y, col=label, main="RPCAG::k=10")
par(opar)