Calculating a weighted average of multiple matrices

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

Answer 1

[Andrei Bobrov]

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)

[John]

Hello Andrei,

Thank very much for your help.

Could I ask how to do one further application?

Say if I had 100 matrices instead of 2 and I imported them using this code

C = cell(100,1);

for ii = 1:100

C{ii} = importdata(['matrix' num2str(ii) '.txt']) ;

end

How would I get the weighted average of the 100 matrices?

Many thanks

John

[Andrei Bobrov]

try this is code

C1 = zeros(3,4,100); % in our case

for ii = 1:100

C1(:,:,ii) = importdata(['matrix' num2str(ii) '.txt']) ;

end

[Andrei Bobrov]

Or

C2 = cell(100,1);

for ii = 1:100

C2{ii} = importdata(['matrix' num2str(ii) '.txt']) ;

end

C1 = cat(3,C2{:});

[John]

Thank you very much, they both give the correct answer!

[John]

Hello Andrei,

Thank you for your help with my weighted average problem.

I'm just wondering if the code for pl and C needs to be changed if I change the size of the matrices say from 3x3 to 9x9?

It seems to be working fine, but I thought I should double check with you.

Many thanks

John

[Andrei Bobrov]

No, do not change

[John]

Thanks