Slice matrix upon "group ID" to get the mean

Hello,

I have a vector containing data, and a second one containing only group ids so I know which data point is member of which group. Now I want to compute the mean of each group and subtract that mean from each datapoint. That should be done group wise of course and that's the problem. I can only think of a very brutal loop solution that is awful slow (already tried it). I made a small example code to help you better understand my problem:

 x = [1,2,3,4,5,6,7,8,9,10]; % Data 
 y = [1,1,1,2,2,1,2,1,1,5]; % Vector containing the group id

 g1 = [1,2,3,6,8,9]; % Vector containing only data of group 1
 g2 = [4,5,7]; % Vector containing only data of group 2
 g3 = [10]; % Vector containing only data of group 3

So I don't know how to get g1:g3 or in other words, I don't know how to tell Matlab that it should create a vector m and store the mean of each group in that vector. Afterwards Matlab should subtract the mean from the data point.

The solution should look like this:

m = [(29/6),(16/3),10]; % Vector with the mean of each group 

x_demeaned = [1-m(1),2-m(1),3-m(1),4-m(2),5-m(2),6-m(1), . . .]; % demeaned data

Can you help me here? Thanks in advance!

[Walter Roberson]

There's probably a good use for accumarray here.

Answer 1

[Fangjun Jiang]

x = [1,2,3,4,5,6,7,8,9,10]; % Data 
y = [1,1,1,2,2,1,2,1,1,5]; % Vector containing the group id

[GroupId,indx_i,index_j]=unique(y);
GroupMean=arrayfun(@(k) mean(x(index_j==k)),1:length(GroupId))
New_x=x-GroupMean(index_j)

GroupMean =
    4.8333    5.3333   10.0000
New_x =
  Columns 1 through 7
   -3.8333   -2.8333   -1.8333   -1.3333   -0.3333    1.1667    1.6667
  Columns 8 through 10
    3.1667    4.1667         0

[Léon]

Thank you very much! I will learn that concept by heart. :-)