[R] Maximize volume of cloud

Stefaan Lhermitte stefaan.lhermitte at biw.kuleuven.be
Thu May 12 19:54:59 CEST 2005

Dear R-ians,

I have a datamatrix X of nrows (large) and 3 colums. The 3 columns 
represent the coordinates of a cloud in a 3 dimensional space.
Now I want to find the extremes of my cloud by using the N-FINDR 
algoritm. This algorithm consists of  maximizing the volume between tree 
points. Therefore I need an optimaztion script, but I don't have any 
idea how to program it.

According to literature the maximization of the volume can be replaced 
by  maximizinng the determinant of E,
E<-matrix(c(1,e1,1,e2,1,e3), ncol=3)
and e1 to e3 are initially column vectors of the coordinates of random 

The procedure works by replacing an existing e1, e2 or e2 with another 
trial point. If the replacement results in an increase of 
determinant(E), the newly chosen pixel will replace the previous pixel. 
The procedure has to be repeated till there are no possible replacements 
left. In this way I get the coordinates of my extremes by e1 to e3.

Anyone any idea how to program this?

Kind regards and thanx in advance!

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