Question

I am using the sparcl package written by Witten and Tibshirani based on their paper:

Witten DM and R Tibshirani (2010) A framework for feature selection in clustering. Journal of the American Statistical Association 105(490): 713-726

I look into the example under the function HierarchicalSparseCluster:

# Generate 2-class data
set.seed(1)
x <- matrix(rnorm(100*50),ncol=50)
y <- c(rep(1,50),rep(2,50))
x[y==1,1:25] <- x[y==1,1:25]+2

# Do tuning parameter selection for sparse hierarchical clustering
perm.out <- HierarchicalSparseCluster.permute(x, wbounds=c(1.5,2:6),nperms=5)

# Perform sparse hierarchical clustering
sparsehc <- HierarchicalSparseCluster(dists=perm.out$dists, wbound=perm.out$bestw, method="complete")

Now I check dim(sparsehc$dists) and it returns 4950 and 50. From the simulation set-up, we know that n=100 and p=50. Also, according to the manual, the returned value dists is a (n*n)xp dissimilarity matrix for the data matrix x. Obviously the row dimension is not n*n as it should be 100*100=10000 instead of 4950. Did I misunderstand something? Thank you very much!

Answer 1

It seems to be the mistake in sparcl help page: dimensions of dissimilarity matrix dist are n2xp, where n2=n*(n-1)/2. Indeed, we don’t need nxn matrix of distances, but only part of this matrix over the main diagonal.

Sources of sparcl support what I said above:

distfun.R

distfun=function(x){
#if(!is.loaded("distfun")){
#  dyn.load("distfun.so")
#}
n<-nrow(x)
p <- ncol(x)
x[is.na(x)]=0
mode(x)="single"
n2=n*(n-1)/2
junk=.Fortran("distfun",
         x,
        as.integer(n),
       as.integer(p),
       as.integer(n2),
       d=single(n2*p), PACKAGE="sparcl"
)
return(junk$d)
}

Here we can see how n2 is calculated and passed to Fortran function.

distfun.f

C Output from Public domain Ratfor, version 1.0
      subroutine distfun(x,n,p,n2,d)
      implicit double precision (a-h,o-z)
      integer n,p,n2
      real x(n,p),d(n2,p)
      ii=0
      do23000 i=1,n-1
      do23002 ip=i+1,n
      ii=ii+1
      do23004 j=1,p
      d(ii,j)=abs(x(i,j)-x(ip,j))
23004 continue
23005 continue
23002 continue
23003 continue
23000 continue
23001 continue
      return
      end

Here for each feature in dist matrix there is a column of size n2 constructed, that holds a sequence of pairwise distances between objects. For example, for n=4, p=2 and n2=4*3/2=6 the final matrix will be 6x2 and designed like this:

    |    1     |     2    |
---------------------------
  1 | d(1,2)_1 | d(1,2)_2 |
  2 | d(1,3)_1 | d(1,3)_2 |
  3 | d(1,4)_1 | d(1,4)_2 |
  4 | d(2,3)_1 | d(2,3)_2 |
  5 | d(2,4)_1 | d(2,4)_2 |
  6 | d(3,4)_1 | d(3,4)_2 |

Where, say, d(2,4)_1 is a distance between 2nd and 4th object for 1st feature.