The weight matrix is zeros along the diagonal. Thus you can use it as-is in the summation, since the terms where i==j (which correspond to the diagonal elements of W) will be 0.
To get the same effect in the denominator, you can set the diagonal elements of x.*x.' to zero and use that.
x = [1,2,3,4]; % feature vector
w = rand(4,2);
D = pdist(w);
W = squareform(D) % weight matrix
denom_matrix = x.*x.';
denom_matrix(1:numel(x)+1:end) = 0
G = sum(W.*x.*x.','all')/sum(denom_matrix,'all')
For reference, here is a way to do the same thing using for loops:
denominator = 0;
numerator = 0;
for ii = 1:numel(x)
for jj = 1:numel(x)
if ii == jj % skip the ii == jj terms
continue
end
denominator = denominator + x(ii)*x(jj);
numerator = numerator + W(ii,jj)*x(ii)*x(jj);
end
end
G_loop = numerator/denominator
Check that the results are identical:
isequal(G,G_loop)
