Merge confusion matrices in nice, vectorized way.

Hello everyone,

I have several confusion matrices, which are a 2D cell array. The first row and the first columns are strings. The rest are numbers. Something like this:

MATRIX 1

      A    B    C
  A 100   10   15
  B  20  150   25
  C  10   10  200

MATRIX 2

      A    B    D
  A 150    5   10
  B  10  100   15
  D  15   15  100

MATRIX 3

      B    E
  B 100   15
  E   5  150

How can I merge the matrices in a vectorized way so the output is something like this?

DESIRED OUTPUT

      A    B    C    D    E 
  A 250   15   15   10    0
  B  30  350   25   15   15
  C  10   10  200    0    0
  D  15   15    0  100    0
  E   0    5    0    0  150

Which means merge all the matrices into one, including the labels in the first row and the first column label. Where the rows and columns overlap, add them. I could do this with some loops, but I am interested in the nice, vectorized way :) .

Answer 1

[Oleg Komarov]

m1 = {''   'A'  'B'  'C'
      'A'  100   10   15
      'B'   20  150   25
      'C'   10   10  200};

m2 = {''  'A'  'B'  'D'
      'A' 150    5   10
      'B'  10  100   15
      'D'  15   15  100};

m3 =  {''  'B'  'E'
       'B' 100   15
       'E'   5  150};

m = [unPivot(m1); unPivot(m2); unPivot(m3)];
Pivot(m,@sum,[],0) 

ans = 
    [NaN]    'A'      'B'      'C'      'D'      'E'  
    'A'      [250]    [ 15]    [ 15]    [ 10]    [  0]
    'B'      [ 30]    [350]    [ 25]    [ 15]    [ 15]
    'C'      [ 10]    [ 10]    [200]    [  0]    [  0]
    'D'      [ 15]    [ 15]    [  0]    [100]    [  0]
    'E'      [  0]    [  5]    [  0]    [  0]    [150]

Lin to Pivot/unPivot

One suggestion, using text labels is highly inefficient because the resulting cell array will be very memory demanding. Convert the labels to numbers 1 2 3 ... and you'll see the difference.

Answer 2

[Kelly Kearney]

You might want to add a loop over the columns if your matrices will be varying sizes, but otherwise...

Your data:

    m{1} = {...
    'rowA.' 1  2  3
    'rowB.' 1  2  3
    'rowC.' 1  2  3};

    m{2} = {...
    'rowA.' 2  3  4
    'rowD.' 2  3  4
    'rowE.' 2  3  4};

    m{3} = {...
    'rowD.' 3  4  5
    'rowF.' 3  4  5};

Combine matrices into one...

    mall = cat(1, m{:});
    lbl = mall(:,1);
    data = cell2mat(mall(:,2:end));

... and sum by label:

    [lbl, blah, idx] = unique(lbl);
    data = [accumarray(idx, data(:,1)) ...
            accumarray(idx, data(:,2)) ...
            accumarray(idx, data(:,3))];

[Kelly Kearney]

Hey, you changed your question and example completely while I was typing my answer!

[Adriano]

Sorry, my mistake, I hadn't realized the real problem :-(