The Jaccard coefficient measures similarity between finite sample sets, and is defined as the size of the intersection divided by the size of the union of the sample sets.
I had 100 sets all of same cardinality. By mistake I calculated the similarity measures as the ratio of intersection with total elements in a set (i.e 100).
This gives different similarity values than the original Jaccard formula.
I was wondering if the original formula has considered the union of two sets to handle cases where there might be sets with different cardinalities.
I think though numerically my values are different, they repersent the same idea.
If anybody could verify/disverify what I am trying to do ?