

N-dimensional medians, and a hybrid between median and average - cool-RR
http://cool-rr.com/median

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seles
This seems like such a good generalization that I almost can't believe it
hasn't been discovered before. (Also nice to see an article where the author
wants the material to be understandable instead of trying to impress us with
unnecessary complexity)

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cool-RR
It was indeed discovered before. My goal was, exactly as you said it, to make
the material easily understandable.

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seles
I think this could also be used to calculate the mode?

lim n->0 argmin(x,sum(abs(x-s)^n))

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roundsquare
Very cool. That i variable becomes how much you want outliers to matter. i
could go higher than 2 and you'd really get skewed numbers.

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imurray
A relevant toy I threw together once to demonstrate finding a
median/mean/centroid by minimizing a cost defined by "springs":
<http://www.cs.toronto.edu/~murray/04medoid/>

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leif
So these are the means in the L^r norms, with r in the reals rather than the
integers?

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sesqu
That's what I got out of it too (well, substituting "natural centrality
measures" for "means"), except it bothers me that for n dimensions, it looks
like he uses L₂ for the vector norm.

I'd much prefer argmin 𝐱( sum 𝐬∈Sⁿ sum j≤n |𝐬ⱼ-𝐱ⱼ|^i )

