cosine similarity built-in function in matlab
Short version by calculating the similarity with pdist
:
S2 = squareform(1-pdist(S1,'cosine')) + eye(size(S1,1));
Explanation:
pdist(S1,'cosine')
calculates the cosine distance between all combinations of rows in S1
. Therefore the similarity between all combinations is 1 - pdist(S1,'cosine')
.
We can turn that into a square matrix where element (i,j)
corresponds to the similarity between rows i
and j
with squareform(1-pdist(S1,'cosine'))
.
Finally we have to set the main diagonal to 1 because the similaritiy of a row with itself is obviously 1 but that is not explicitly calculated by pdist
.
Your code loops over all rows, and for each row loops over (about) half the rows, computing the dot product for each unique combination of rows:
n_row = size(S1,1);
norm_r = sqrt(sum(abs(S1).^2,2)); % same as norm(S1,2,'rows')
S2 = zeros(n_row,n_row);
for i = 1:n_row
for j = i:n_row
S2(i,j) = dot(S1(i,:), S1(j,:)) / (norm_r(i) * norm_r(j));
S2(j,i) = S2(i,j);
end
end
(I've taken the liberty to complete your code so it actually runs. Note the initialization of S2
before the loop, this saves a lot of time!)
If you note that the dot product is a matrix product of a row vector with a column vector, you can see that the above, without the normalization step, is identical to
S2 = S1 * S1.';
This runs much faster than the explicit loop, even if it is (maybe?) not able to use the symmetry. The normalization is simply dividing each row by norm_r
and each column by norm_r
. Here I multiply the two vectors to produce a square matrix to normalize with:
S2 = (S1 * S1.') ./ (norm_r * norm_r.');