I am trying to find an appropriate distance measure that reflects the differences of the vectors seen in the image below: The green vector is compared with the blue one and the orange one.
Most of the distance measures (like the Euclidean for example) would yield the same value despite the "phase shift". Therefore the straight line would look "the same" as the blue and the orange line!
The features are ordered but I am also interested in the case they were unordered.
I was also thinking to "split" the vectors in the middle and treat them as bags of two subvectors (like in a multi-instance setting) but then I would not know how to combine the two resulting distances in one.
So I guess my question is two-fold:
- Is there a distance measure that highlights these type of value symmetries in a single instance setting?
- Is there a way to combine multiple distances (in a multi-instance setting) in a way that symmetry (and therefore order) is highlighted in the final distance result?