Why does the similarity function used in the label space adopt negative absolute distance?

[bicheng1225]

Why is the similarity function (sigma^y) used to calculate the similarity matrix (S^y) in the label-space negative absolute distance instead of absolute distance?

As far as I know, the similarity function used in feature space is cosine similarity, which has a range of -1 to 1, where -1 indicates that the two quantities are opposite, 0 indicates that they are orthogonal, and 1 indicates that they are in the same direction.

What problems would it cause if the absolute distance was directly used to calculate the similarity function?
Or, what are the considerations for using the negative absolute distance in the paper?

Thanks :))