# As2Vs: Convert low dimensional bootstrap components to high... In bootSVD: Fast, Exact Bootstrap Principal Component Analysis for High Dimensional Data

## 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

 `1` ```As2Vs(AsByB, V, pattern = NULL, ...) ```

## Arguments

 `AsByB` 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. `pattern` if `V` is a class `ff` object, the returned value will also be a class `ff` object. `pattern` is passed to `ff` in creation of the output. `...` 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```#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=50,n=dim(DUt)) bootSVD_LD_output<-bootSVD_LD(DUt=DUt,bInds=bInds,K=3,verbose=interactive()) 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 ```

bootSVD documentation built on Feb. 2, 2021, 5:06 p.m.