Does anyone use the $L_1$ or $L_.5$ metrics for clustering, rather than $L_2$ ?
Aggarwal et al., On the surprising behavior of distance metrics in high dimensional space said (in 2001) that
$L_1$ is consistently more preferable then the Euclidean distance metric $L_2$ for high dimensional data mining applications
and claimed that $L_.5$ or $L_.1$ can be better yet.
Reasons for using $L_1$ or $L_.5$ could be theoretical or experimental, e.g. sensitivity to outliers / Kabán's papers, or programs run on real or synthetic data (reproducible please). An example or a picture would help my layman's intuition.
This question is a follow-up to Bob Durrant's answer to When-is-nearest-neighbor-meaningful-today. As he says, the choice of $p$ will be both data and application dependent; nonetheless, reports of real experience would be useful.
Notes added Tuesday 7 June:
I stumbled across "Statistical data analysis based on the L1-norm and related methods", Dodge ed., 2002, 454p, isbn 3764369205 — dozens of conference papers.
Can anyone analyze distance concentration for i.i.d. exponential features ? One reason for exponentials is that $|exp - exp| \sim exp$; another (non-expert) is that it's the max-entropy distribution $\ge$ 0; a third is that some real data sets, in particular SIFTs, look roughly exponential.