Cosine Similarity and distances between nodes

Question

Christian Basa 2021-4-16

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https://ww2.mathworks.cn/matlabcentral/answers/804411-cosine-similarity-and-distances-between-nodes

回答： Austin Thai 2021-4-17

Is it possible to use cosine similarity to find the distances on a graph between a node and other nodes surrounding it? For example, I have 80 nodes. I find the distance from node 1 to nodes 2:80 and then node 2 from node 1 and nodes 3:80 and repeat that process until i get all the distances?

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Answer 1

Austin Thai 2021-4-17

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https://ww2.mathworks.cn/matlabcentral/answers/804411-cosine-similarity-and-distances-between-nodes#answer_677561

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I assume you are trying to calculate the cosine distance using the cosine similarity.

You can use a for loop , e.g.

nodalCoordinates=rand(80,3); % Replace these with your coordinates
nodalNorms=vecnorm(nodalCoordinates,2,2);
cosineDistances=zeros(80,80); % Include the distance to itself (zero) for simplicity
for i=1:80
    cosineSimilarity=nodalCoordinates*nodalCoordinates(i,:)'./(nodalNorms(i)*nodalNorms);
    cosineDistances(i,:)=1-cosineSimilarity;
end

If you simply want the spatial distance,

spatialDistances=zeros(80,80); % Include the distance to itself (zero) for simplicity
for i=1:80
    spatialDistances(i,:)=vecnorm(nodalCoordinates-nodalCoordinates(i,:),2,2);
end