Summing rows by index using accumarray

Question

Can I sum rows or columns over several indices without using a for loop?

I have an n by n matrix, M, that represents the co-occurrence of vocabulary terms where n is the length of the vocabulary.

I also have a n by n logical mask, L, which represents the pairs of vocabulary where the pair has the form (singular, plural). For example, in pseudo-code, L('octopus', 'octopuses') = True

I want to add the entries in M for any pair which contains a plural to entry for the pair that contains the corresponding singular. For example, in pseudo-code, M_sum('octopus', 'swim') = M('octopus', 'swim') + M('octopuses', 'swim');

To illustrate what I've tried so far, let's use the following toy data.

vocabulary = {'octopus', 'octopuses', 'swim'};
% The co-occurrence matrix is symmetric
M = [0, 9, 3; 
     9, 0, 1;  
     3, 1, 0;];
% This example has only one plural singular pair
L = [0, 1, 0; 
     0, 0, 0; 
     0, 0, 0;];  

To find the singular to plural correspondence, I can use find

[singular, plural] = find(L == 1);

If there is only one plural for each singular, summing the rows or columns is simple

M_sum = M;
M_sum(singular, :) = M_sum(singular, :) + M(plural, :);
M_sum(:, singular) = M_sum(:, singular) + M(:, plural);
% Remove diagonal entries
M_sum(eye(size(M))==1) = 0; 

However, if there are several plurals that correspond to one singular, this approach cannot be used.

For example,

vocabulary = {'octopus', 'octopuses', 'octopi', 'swim'};
M = [0, 9, 5, 3; 
     9, 0, 7, 1; 
     5, 7, 0, 11; 
     3, 1, 11, 0;];
L = [0, 1, 1, 0; 
     0, 0, 0, 0; 
     0, 0, 0, 0; 
     0, 0, 0, 0;];  

The correct answer should be

M_sum = [0, 16, 12, 15;
         16, 0, 7, 1;
         12, 7, 0, 11;
         15, 1, 11, 0;];

But using the above method returns

M_sum = [0, 16, 5, 14;
         16, 0, 7, 1;
         5, 7, 0, 11;
         14, 1, 11, 0;];

Basically, M_sum(singular, :) = M_sum(singular, :) + M(plural, :); only uses the last plural index.

I think that I need to use accumarray here, but I'm having some trouble formulating the correct statement because I have two indices, plural and singular. If accumarray is not the correct approach, other solutions are also welcome.

Answer 1

Try this:

M_sum = (L + eye(size(L,1)))*M;
M_sum = triu(M_sum, 1);
M_sum = M_sum + M_sum.';

This works because you already have matrix L, so matrix multiplication can be used to select and sum the rows of M.

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Using accumarray here would have two drawbacks:

• You'd need to apply find to convert L into indices to be used as first input to accumarray. So one more step.
• accumarray can only sum numbers, not row vectors (its second input can only be a column vector, not a matrix). So you'd need to call accumarray once per column of M.