R/projectDataInto1d.R

In tsieger/tsiMisc: Miscelaneous utility functions, mostly related to exploratory statistical analysis

projectDataInto1d<-structure(
function # Project multidimensional data onto a line.
##description<<
## Project multidimensional dataset onto a line described by two points (centers).
##
(x, ##<< multidimensional data (\code{n} x \code{k} matrix)
c0, ##<< first center (vector in \code{k}-dimensional space)
c1 ##<< second center (vector in \code{k}-dimensional space)
) {
  x<-as.matrix(x)
  if (length(c0)!=ncol(x)) stop('invalid c0, expected a vector of',ncol(x),'numbers')
  if (length(c1)!=ncol(x)) stop('invalid c1, expected a vector of',ncol(x),'numbers')

  # projection vector
  v<-c1-c0

  # shift data to c0
  x<-x-matrix(c0,nrow(x),ncol(x),byrow=T)

  # project
  p<-(x%*%cbind(v))/sum(v^2)
  return(p)
  ### A vector of length \code{n} holding the projection of data onto
  ### the line aligned along centers \code{c0} and \code{c1}.
  ### Points in the hyperplane perpendicular to the line and
  ### intersecting center \code{c0} get mapped to \code{0}, points in
  ### the hyperplane perpendicular to the line and intersecting center
  ### \code{c1} get mapped to \code{1}, etc.
},ex=function() {
  set.seed(1)
  x1<-cbind(rnorm(100,-2),rnorm(100))
  x2<-cbind(rnorm(100,2),rnorm(100))
  p<-projectDataInto1d(rbind(x1,x2),c0=c(-2,0),c1=c(2,0))

  layout(rbind(1,2))
  plot(rbind(x1,x2),frame=FALSE,main='2D data')
  hist(p,breaks=50,main='1D projection')
  layout(1)
})