I am learning about some techniques to find similarity between documents. One of the methods is Min Hashing. According to Min Hashing we can find a signature matrix given a random permutation, P. According to this technique in order to calculate signature matrix, we have to take the index of the first row in which document d has value 1.
Is it necessary to do that? If so, then can anyone please explain why? If not, can we take any nth row of boolean matrix permutation P?