On Fri, Aug 1, 2008 at 11:52 PM, Michael Rogers <[EMAIL PROTECTED]> wrote:
> Daniel Cheng wrote:
>> in a circular space, we can get infinite number of "average" by changing
>> point of reference. --- choose the point of reference with the smallest
>> standard deviation.
>
> From an infinite number of alternatives? Sounds like it might take a
> while. ;-) I think we can get away with just trying each location as the
> reference point, but that's still O(n^2) running time.

That's what I have in mind.
It is not as large as you think as we don't have to calculate every
single data point -- just take a good random sample of it should do.

> How about this: the average of two locations is the location midway
> along the shortest line between them. So to estimate the average of a
> set of locations, choose two locations at random from the set and
> replace them with their average, and repeat until there's only one
> location in the set.
>
> It's alchemy but at least it runs in linear time. :-)
>
> Cheers,
> Michael
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