bpmat: Flury back-projection matrix

In bbolker/cpcbp: common principal components/back-projection analysis

Description

Constructs and applies the Flury back-projection matrix, which when multiplied by a data vector removes a particular directional component

Usage

bpmat(evec)
bpfun(x,f,evec,center=TRUE)

Arguments

x	(numeric) A data matrix (observations as rows, variables as columns) to back-project, or (if f is missing) a list of a data matrix and a grouping variable
f	(factor) A grouping factor to use to calculate CPC1 of x, if evec is not specified
evec	(numeric) A direction vector to remove from the data by back-projection (typically the first common principal component): it should be normalized (sum of squares equals 1)
center	mean-correct data before back-projecting?

Details

The back-projection matrix B is I - e*t(e); back-projecting a vector x is done by multiplying B * x.

Value

Either the back-projection matrix or the back-projected data matrix

Note

mean correction is done so that the grand mean of the entire data set is zero. It doesn't matter for balanced data sets, but for unbalanced data sets it should (?) probably be done so that the means of the group means are zero instead.

Author(s)

Ben Bolker

References

Flury etc.

Examples

  X = matrix(c(1,2,3,4,5,6),ncol=3,byrow=TRUE)
  dir = c(0,1,1)/sqrt(2)
  bpmat(dir)
  bpfun(X,evec=dir)

bbolker/cpcbp documentation built on May 11, 2019, 9:28 p.m.