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. :-)

Answer 2

[Lola Davidson]

For those stumbling on this more recently, MATLAB now has the grouptransform function introduced in R2018b. It can be used to make grouped calculations where the result is the same size as the input. It even has a built-in method for subtracting off group means:

x = [1,2,3,4,5,6,7,8,9,10]';
y = [1,1,1,2,2,1,2,1,1,5]'; 
grouptransform(x,y,"meancenter")

ans = 10x1

-3.8333 -2.8333 -1.8333 -1.3333 -0.3333 1.1667 1.6667 3.1667 4.1667 0

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