R/insert.mds.R

In dill/msg: Multidimensional Scaling for Generalized Additive Models

"insert.mds"<-function(new.points,old.points,cmd.object,bnd,faster=0,debug=0,oldD=NULL){
   # insert a new point into the MDS, see Gower (Biometrika, 1968.)
   # args
   #  new.points     points to insert into the MDS
   #  old.points     old points
   #  cmd.object     object returned from cmdscale, with eig=TRUE
   #  bnd            boundary
   #  faster         use grid speedups?
   #  oldD           if D has already been calculated, use that
   # ret
   # coordinates of new points in the mds?
   
   # want to calculate 1/2 * lambda^(-1) * X' * d

   # find lambda^(-1)
   #*NB*: versions of R before 2.12.1 returned
   #       only 'k' but were documented to return n-1.
   lambda.inverse<-diag(1/cmd.object$eig[1:dim(cmd.object$points)[2]])

   # take the original MDS coordinates
   # this is already double centred and dim(X)=nx2
   X<-cmd.object$points

   # finally d
   if(!is.null(oldD)){
      new.dist<-oldD
   }else{
      # new set of distances from the old points to new
      # should take the form of a n by m matrix, where there are
      # and n original points to measure to and m new points.
      new.dist<-woodpath(c(old.points$x,new.points$x),c(old.points$y,new.points$y),
                         bnd,start=length(old.points$x),faster=faster,debug=debug)

      # the ith element of d is -(d_{i,n+1}^2 - diag(S))
   }

   # cmd.object$x is the doubly centered symmetric distance matrix
   # from the original MDS configuration
   S<- -1/2*cmd.object$x
   #S<- -1/2*X%*%t(X)
   d<- -(new.dist^2-diag(S))
 
   # finally construct the product
   ret<-1/2*(lambda.inverse %*% t(X) %*% d)

   attr(ret,"D")<-new.dist

   return(t(ret))
}