I am trying to find a distance formula or a method that can give the non-commutative distance between two points in a feature space.
Suppose there are two movies represented in an R^n feature space. Now I want that when I try to find the distance/similarity between these movies using the feature vectors, I get different values with respect to which movie is the reference point i.e.,
Dist(Mov1, Mov2) != Dist(Mov2, Mov1)
I know this is slightly vague, but I am trying to understand my thoughts and would like your help. I found that there is a field called non-commutative geometry, but that seems a little too much and the last resort to dive into. Kindly direct my thoughts.