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I have some question concern similarity measure and i need your help (Iam new in statistics)

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

Question : 1- what similarity measure choose and why?

2- What is the maximum size of the matrix? What are its properties? How would you choose the store?

Thank you very much for your help bests

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The matrix will be mxm (assuming you have m items) but you don't need to fill it entirely, since a similarity measure should ideally be symmetric (sim(a,b) = sim(b,a)).

As to choosing one, it depends entirely on what you store and what you plan to do with it. Assuming you are storing vectors of objects, some popular simple ones are Jaccard similarity and Cosine similarity. This page has a bit more information on them (along with some other similarity measures). I would encourage you to search for books and research papers in the area that you are exploring and see what common similarity metrics are used by the community.

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