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I have a scenario where I have a User which likes 10 different sports and there is another user which likes 20 different sports. I need to find the correlation between them. What kind of correlations can be used in such a scenario. Any kind of guide would be helpful. I tried with Pearson correlation but was not helpful. I would like to program using MATLAB. Thanks in advance.

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Exactly what do you plan to do with this correlation once you compute it? – whuber♦ Apr 26 '11 at 21:14
We would deduce whether the two users according to their sports interest are related or not. Something like If I like soccer and football, and some one likes just football, still we both are related by some percentage. So i want to calculate that percentage of similarity – user4341 Apr 26 '11 at 21:24
Do you have a large matrix where rows are users and sports are columns and values are measures how much someone likes a sport? – GaBorgulya Apr 26 '11 at 22:21
yes, i have a matrix for individual users where columns are different sports and the one they like have a value one. – user4341 Apr 26 '11 at 23:12

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This is like inter-rater reliability. The code here should do it.

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The OP said the number of liked objects is not the same for the two raters. How would you apply Cohen's $\kappa$ in this case? – chl♦ Apr 27 '11 at 9:33
@chi I was thinking of the users each rating each of a few dozen sports as one of two levels (like or not). Does that answer your question? If not, I should probably review how Cohen's $\kappa$ works. – Thomas Levine Apr 29 '11 at 20:21
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If your goal is to measure similarity between individual users or groups of users you may use similarity or distance measures used in cluster analysis, biclustering or multidimensional scaling. In situations where you need such a measure the above techniques themselves may be useful, too.

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