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Calculating a weighted average of multiple matrices

Asked by John

John (view profile)

on 24 Feb 2012
Latest activity Edited by Mona MK

Mona MK (view profile)

on 24 Oct 2013

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

0 Comments

John

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1 Answer

Answer by Andrei Bobrov

Andrei Bobrov (view profile)

on 24 Feb 2012
Accepted answer
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)

7 Comments

John

John (view profile)

on 28 Feb 2012

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

Andrei Bobrov (view profile)

on 28 Feb 2012

No, do not change

John

John (view profile)

on 28 Feb 2012

Thanks

Andrei Bobrov

Andrei Bobrov (view profile)

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