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I have some question concern similarity measure

Suppose that we have a matrix M where M(i,j) is the similarity measure between user i and user j .

Each user is characterised by : id-user | country | id-artist | id-track

For this I choose to use Jaccard similarity metric.

Jaccard is determined to compute similarity between users based on the tracks that they listened. My question is : is it possible to take account both id-track and id-artist to measure the similarity between users?

Thank you

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Yes, multiple different ways.

First, we could consider (id-artist,id-track) items as the elements of our set, and compute the Jaccard similarity by comparing those sets. Note that if the artist's id gives us no additional information beyond the track id, this will give the same result, whereas it will give different results if a particular track id could be associated with multiple artists.

Second, we could compute the Jaccard similarity on tracks, and then the Jaccard similarity on artists, and then add the two (probably with some constant coefficient scaling the two). This way two users who listen to the same artists, but none of the same songs by those artists, will be rated as more similar than users who listen to different songs by different artists.

What coefficient makes sense? Well, you could start with 0.5 for each (i.e. just .5*similarity_artist+.5*similarity_track), see if that's reasonable, and adjust if it's not.

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Yes, you can do it (indeed in many ways). I like to reduce the problem into a classification problem and derive the proper way to combine them. For details see: https://stats.stackexchange.com/questions/61351/how-to-combine-multiple-similarity-measures/166419#166419

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