bootSVD (version 0.1)

As2Vs: Convert low dimensional bootstrap components to high dimensional bootstrap components

Description

Let $B$ be the number of bootstrap samples, indexed by $b=1,2,...B$. As2Vs is a simple function converts the list of principal component (PC) matrices for the bootstrap scores to a list of principal component matrices on the original high dimensional space. Both of these lists, the input and the output of As2Vs, are indexed by $b$.

Usage

As2Vs(As, V, mc.cores = 1, ...)

Arguments

As

a list of the PCs matrices for each bootstrap sample, indexed by $b$. Each element of this list should be a ($n$ by $K$) matrix, where $K$ is the number of PCs of interest, and $n$ is the sample size.

V

a tall ($p$ by $n$) matrix containing the PCs of the original sample, where $n$ is sample size, and $p$ is sample dimension.

mc.cores

passed to mclapply, for parallelizing the computation procedure.

...

(optional) passed to mclapply.

Value

• a B-length list of (p by K) PC matrices on the original sample coordinate space (denoted here as $V^b$). This is achieved by the matrix multiplication $V^b=VA^b$. Note that here, $V^b$ denotes the $b^{th}$ bootstrap PC matrix, not $V$ raised to the power $b$. This notation is the same as the notation used in (Fisher et al., 2014).

References

Aaron Fisher, Brian Caffo, and Vadim Zipunnikov. Fast, Exact Bootstrap Principal Component Analysis for p>1 million. 2014. http://arxiv.org/abs/1405.0922

Examples

#use small n, small B for a quick illustration
set.seed(0)
Y<-simEEG(n=100, centered=TRUE, wide=TRUE)
svdY<-fastSVD(Y)
DUt<- tcrossprod(diag(svdY$d),svdY$u)
bInds<-genBootIndeces(B=200,n=dim(DUt)[2])
bootSVD_LD_output<-bootSVD_LD(DUt=DUt,bInds=bInds,K=3,talk=TRUE)

Vs<-As2Vs(As=bootSVD_LD_output$As,V=svdY$v)
# Yields the high dimensional bootstrap PCs (left singular
# vectors of the bootstrap sample Y),
# indexed by b = 1,2...B, where B is the number of bootstrap samples.