An “asymmetric” pairwise distance matrix

Question

Suppose there are three sequences to be compared: a, b, and c. Traditionally, the resulting 3-by-3 pairwise distance matrix is symmetric , indicating that the distance from a to b is equal to the distance from b to a.

I am wondering if TraMineR provides some way to produce an asymmetric pairwise distance matrix.

Answer 1

No, TraMineR does not produce 'assymetric' dissimilaries precisely for the reasons stressed in Pat's comment.

The main interest of computing pairwise dissimilarities between sequences is that once we have such dissimilarities we can for instance

• measure the discrepancy among sequences, determine neighborhoods, find medoids, ...
• run cluster algorithms, self-organizing maps, MDS, ...
• make ANOVA-like analysis of the sequences
• grow regression trees for the sequences

Inputting a non symmetric dissimilarity matrix in those processes would most probably generate irrelevant outcomes.

It is because of this symmetry requirement that the substitution costs used for computing Optimal Matching distances MUST be symmetrical. It is important to not interpret substitution costs as the cost of switching from one state to the other, but to understand them for what they are, ie, edit costs. When comparing two sequences, for example aabcc and aadcc , we can make them equal either by replacing arbitrarily b with d in the first one or d with b in the second one. It would then not make sense not giving the same cost for the two substitutions.

Hope this helps.