Reason behind using Manhattan distance
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You can view and copy the source of this page.MN (talk)
my case is noise in another dimension ;)
however if noise is added to the main dimension,
it will be
sqrt((1 + x)^2 + 1)
|1 + x | + 1
and if we put two curves together (shifted so that tey intersects on x=0)
euclidean looks terrible with large noise in one dimension, and manhattan looks robust.