There are some doubts about using Jaccard formula, such as Wikipedia's explanation. The following should be
jaccard_score([0 1 1], [1 1 1])
0.6666666666666666
According to the Jaccard formula, the calculation method is
intersection / (size of A + size of B - intersection). So, it should be 2/(3+3-2) = 2/4 = 0.5.
But obviously this is not the case. Can anyone give a direct formula calculation method to get this 0.66666666?
You are interpreting the formula incorrectly; "size of A" refers to the cardinality of the set. The data [0, 1, 1] is a boolean representation of a set A in which the universe consists of three elements, and the value '1' indicates which element (from the universe) is in the set A. So the "size of A", where A is represented by [0, 1, 1], is 2.
The formula is such that: intersection/(sum/size of A + sum/size of B - intersection) Which in your case is:
2/(2 + 3 - 2) = 0.666
You are taking the size of A to be the length of the elements, whereas it is the sum. Similarly, for B just that your mistake got overlapped because the length and sum are same.