I am trying to wrap my head around exactly what the Canberra distance captures and how/when it would be better or worse than standard distances like the Eulidean distance or the Minkowski distance of order 1. Just for clarity, I'm referring to the standard Canberra distance:
$d(\mathbf{p}, \mathbf{q}) = \sum_{i=1}^n \frac{|p_i-q_i|}{|p_i|+|q_i|}$
For two vectors $\mathbf{p}$ and $\mathbf{q}$.
It's a somewhat rare and esoteric distance metric, so I can't find any good explanation of why one would select this.
EDIT: From looking at some of the papers on this, it seems to apply most commonly to situations where differences close to zero are seen as more important than differences far from zero, e.g., for ranked lists (https://academic.oup.com/bioinformatics/article/24/2/258/226884) where differences at one end of the ranking matter less than at the other end.
