I know we can quantify the similarity between two sequences with the same length and same elements by rank order correlation. But how to measure similarity between two sequences of different length, and only having some elements in common?
For example, if I have three rank ordered numeric sequences like this:
sequence A: 1,2,3,4,5,6,7,8,9;
sequence B: 2,3,4,5,6,7,8,9,10,11,12,13
sequence C: 4,2,9,7,11,13,14,16,18
Intuitively, I guess sequence A and B are more similar, since they have more numbers in common and the common numbers have same order in both sequences. Sequence A and C are less similar since they have less number in common and the common numbers have difference orders in each sequence. Is there any quantitative measurement to capture both the order similarity in common elements and the percentage of common elements in two sequences?