Cosine similarity between two matrices

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Paola
Paola 2022-5-24
评论： Paola 2022-5-30
Dear all,
I have some vectors 32x1, representing force fields. I use the quiver function to plot and visualize the fields. (see pic attached) Obtaining a quiver showing 4x4 vectors, for a total of 16 vectors.
X = [1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4];
Y = [1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4];
U = W(1:2:31);
V = W(2:2:32);
figure, quiver(X,Y,U',V');
Even if visually they look very similar, I need to calculate a cosine similarity value, between the different vectors.
Checking online I found that this formula:
cosSim = dot(a,b)/(norm(a)*norm(b));
and also the function
D = pdist(X,'cosine').
I wonder if these two functions can be applied to my case and which one is better to obtain just a similarity value for each couple of vector compared.
Thank you!

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Matt J
Matt J 2022-5-24
I tend to prefer pdist2,
UV=[U(:),V(:)];
D=1-pdist2(UV,UV,'cosine')
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Matt J
Matt J 2022-5-25
编辑：Matt J 2022-5-25
There is no advantage to pdist2 if you are only comparing two vectors, a and b. You can just use your cosSim formula directly. However, it could hypothetically be done with,
1-pdist2(a(:).',b(:).','cosine')

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