MATLAB: Computing mean by group (need help with speed!)

accumarraydemean

Hi everyone,
I need to demean the columns of matrix Xw (200000 x 24) by group id. To do this, I need to compute means of the columns of Xw for each group identified by the vector id (200000 x 1). I have written the following code, which is the fastest I could do in light of this very similar post:
    %DEMEANING
    [cid,indx_i,indx_j]=unique(id);
    for i=1:size(Xw,2);
        bb = accumarray(indx_j, Xw(:,i), [], @mean);
        Xw(:,i) = Xw(:,i) - bb(indx_j);
    end
This is faster than the code suggested at the post linked above. Importantly, the matrix Xw is rather sparse, and only contains zeros and ones (it is a matrix of dummy variables).
My question: Is there any way to speed up this process further? It is quite time consuming as it stands, and given that this itself is inside of a loop, it is slowing everything else down. Please help!! Creative solutions welcome.
Thanks!

Best Answer

In the line of Andrei/Matt's answers and based on my comment (under Andrei's answer):
 [ii,jj] = ndgrid( id, 1:size( Xw, 2 )) ;
 iijj  = [ii(:), jj(:)] ;
 sums  = accumarray( iijj, Xw(:) ) ;
 cnts  = accumarray( iijj, ones( numel( Xw ), 1 )) ;
 means = sums ./ cnts ;
 Xw    = Xw - means(id, :) ;
Kelly's solution is still the most efficient on my (old) laptop for small numbers of groups (here 20):
 Time OP = 0.562232s
 Time KK = 0.239906s
 Time AB = 0.664438s
 Time ME = 0.602663s
 Time CW = 0.258647s
My variant of Andrei/Matt's solutions is slightly better with larger numbers of groups (here 1000):
 Time OP = 1.318130s
 Time KK = 0.342277s
 Time AB = 1.426827s
 Time ME = 1.355189s
 Time CW = 0.279261s
Actually, here is the profile as a function of the number of groups, still on my rather old laptop:
We see that my solution is pretty flat, and crosses Kelly's in the range 100 < n groups < 300.
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