I would like to ask your opinion on how to choose a similarity measure. I have a set of vectors of length N, each element of which can contain either 0 or 1. The vectors are actually ordered sequences, so the position of each element is important. Suppose I have three vectors of length 10, x_1 x2, x3: x1 has three 1 at positions 6,7,8 (indexes start from 1. Both x2 and x3 have an additional 1, but x2 has it in position 9 while x3 has it in position 1. I am looking for a metric according to which x1 is more similar to x2 than to x3, in that the additional 1 is closer to the bulk of ones. I guess this is a relatively common problem, but I am confused on the best way to approach it.Many thanks in advance!
Similarity measure for ordered binary vectors
similarity