Calculating a weighted average of multiple matrices
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Hello,
I was hoping that perhaps somebody could help me out with a problem that I have. It is a relatively simple operation (a weight average), just difficult to code.
Say I import 2 3x3 matrices into a cell array using the code below.
C = cell(2,1);
for ii = 1:2
C{ii} = importdata(['matrix' num2str(ii) '.txt']) ;
end
These matrices are transitional probability matrices.
I would like to calculate a weighted 'average' matrix of these 2 matrices. Unfortunately I cannot simply just calculate the average, its needs to be a weighted average.
Say for example the 2 matrices are:
0.0 0.5 0.5 2
A = 0 0 1 4
0 0.6 0.4 7
0.2 0.0 0.8 5
B = 0 0 0 0
0.3 0.0 0.7 3
The 4th column contains the number of counts for that particular row.
The weighted average formula would be
P(x) = P_A(x) x [1-B_N/(A_N+B_N)] + P_B(x) x [1-A_N/(A_N+B_N)]
Where,
P_A(x) represents the probability value in the same row at cell x for matrix A.
P_B(x) is the same thing for matrix B.
A_N is the total number of counts for the same row we are dealing with in matrix A
B_N is the total number of counts for the same row we are dealing with in matrix B
Using the numbers, the first cell would be:
= 0 x [1-5/(2+5)] + 0.2 x [1-2/(2+5)] = 0.14
So the full weighted average matrix would be
0.14 0.14 0.71
C= 0 0 1
0.1 0.4 0.5
I would really appreciate any help to code this as I'm fairly inexperienced with matlab. In practice I have about 100 matrices but I just presented 2 as an example.
Sincere Thanks
John
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Accepted Answer
Andrei Bobrov
on 24 Feb 2012
A =[ 0 0.5 0.5 2
0 0 1 4
0 0.6 0.4 7];
B =[ 0.2 0 0.8 5
0 0 0 0
0.3 0 0.7 3];
C1 = cat(3,A,B);
p1 = bsxfun(@rdivide,C1(:,end,:),sum(C1(:,end,:),3));
C = sum(bsxfun(@times,C1(:,1:end-1,:),p1),3)
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